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Volatility in the Natural Gas Market: GARCH, Asymmetry, Seasonality and Announcement Effects* Duong T. Le* Division of Finance Michael F. Price College of Business University of Oklahoma Norman, OK 73019-0450 Abstract This paper examines the cause and behavior of natural gas volatility. Although natural gas prices are among the most volatile, they have received very little academic scrutiny heretofore. I theorize and find that (1) the natural gas market is characterized by volatility persistence (2) a negative shock to the natural gas market has a smaller impact on predicted volatility than a positive shock of the same magnitude (3) there are day-of-the- week effects in the natural gas market, (4) natural gas volatility is higher in the winter months, (5) the weekly storage report release causes increased volatility on announcement days and (6) the announcement has no further impact on volatility on the subsequent days. * This research is conducted under the guidance of Dr. Louis H. Ederington, who is also the PhD coordinator for the Division of Finance. 1 1. Introduction In this paper, I examine the cause and behavior of volatility in the US natural gas market from January 1997 to December 2005. Natural gas is an essential energy source in the US accounting for about one quarter of the nation’s energy consumption and a higher percentage of energy production.1 Trading activity in the natural gas market has also increased significantly in recent years. For example, the notional value of natural gas futures contracts traded daily in 2005 ranged from $0.63 billion to $2.75 billion with an average of approximately $1.0 billion. Particularly since its evolution from a highly regulated market to a largely deregulated market in which prices are driven by supply and demand, natural gas is one of the most volatile markets. The average natural gas price in 2005 was four times the average price in 1997 and double the average price in 2000. In 2005, the annualized standard deviation of the daily percentage change in natural gas prices was 56.81%. By comparison that number was 8.84% for the US dollar-Euro exchange rate, 12.36% for the S&P 500 and 16.61% for the 10-year T-bond interest rates2. This high volatility in natural gas prices is likely due to the short-term inelasticity of supply and demand. Natural gas supplies are often constrained by storage levels so natural gas suppliers are unable to increase production levels in a short time period. Similarly, when a sharp increase in natural gas prices occurs, it is difficult for consumers to quickly reduce their consumption, especially during winter. Since natural gas supplies cannot rapidly adjust to match demand changes, supply and demand imbalances may result in sharp price changes. This high variability in natural gas prices makes it extremely difficult for natural gas consumers to forecast their costs and for natural gas producers to forecast their profits. The desire to protect market participants against such price fluctuations has led to the creation of and active trading in natural gas futures, options and swaps where the market value of the latter two is determined mostly by the natural gas volatility. 1 Natural gas has various applications, including heating more than 59 million homes and 5 million businesses, powering industrial and agricultural production and generating a substantial amount of peak electricity needs. Source: Natural Gas Analysis of Changes in Market Price, Report to Congressional Committees and Members of Congress. 2 The data for the US dollar-Euro exchange rate, S&P 500 and the 10-year T-bond interest rates were collected from http://www.oanda.com, CRSP and the Department of the Treasury website (http://www.treasury.gov), respectively. 2 Volatility in other markets has been a subject of intense research activity in recent decades. While it is difficult to forecast the direction of future price changes from past price behavior, the absolute magnitude of price changes, i.e. volatility, has proven much more predictable. It is generally found that highly volatile markets tend to be followed by volatile markets and stable markets by stable markets. Whether this is also the case for natural gas is unknown at present. The vast majority of the research on market volatility has focused on the volatility of financial markets such as stock, bond, interest rates and foreign exchange futures markets, etc. Despite the fact that natural gas prices tend to be more volatile than most other prices, research into the cause and behavior of natural gas volatility is very limited. For instance in a well-known and comprehensive study of the volatility literature, Poon and Granger (2003) surveyed 93 articles examining volatility in all sorts of markets but, to the best of my knowledge, not one of these examined volatility in natural gas prices. I intend to fill this gap in our understanding. An understanding of the cause and behavior of volatility in the natural gas market is essential to market participants since the market value of risk management products such as options and swaps depends mostly on volatility. In this paper, I examine volatility in the natural gas market and attempt to answer the following questions: (1) Does volatility in the natural gas market follow a GARCH type process in which future volatility is partially predictable from past volatility? (2) Does an unexpected drop in the natural gas price one day increase predicted volatility for the following day more or less than an unexpected increase in price of similar magnitude? (3) Is there a day-of-the-week pattern in the natural gas market? (4) Does natural gas volatility increase in winter months? (5) Does the release of the Weekly American Gas Storage Report (hereafter called the weekly storage report) increase natural gas volatility on the announcement days? (6) Does the report release have any further impact on volatility on the days following the announcement? A few of these questions have been discussed in earlier studies but there are important difference between their studies and mine. Using monthly data and an ARCH type model, Susmel and Thompson (1997) found no evidence of seasonality in the natural gas market. Moreover, they found asymmetric volatility in the natural gas market but in a direction opposite to my findings. They estimated that a negative shock has a larger 3 impact on volatility than a positive shock of equal size whereas I find that a negative shock has a smaller impact on volatility than a positive shock of equal size. Utilizing intraday data and a GMM regression model, Linn and Zhu (2004) studied the impact of the storage report announcement on the intraday natural gas volatility within the day of the announcement and found that volatility remains higher than normal for up to 30 minutes after the announcement. In contrast, I analyze the response of volatility to the report release not only on the days when the announcements occur but also on the days after and in a GARCH framework. Also neither of these previous studies considered the possibility that natural gas volatility may be higher in the winter months. My paper has a major methodological improvement over a number of studies on volatility in other markets (See, for example, Berument and Kiymaz (2001)). I use a variant of a regime-switching GARCH type model outlined in Jones et al. (1998) which allows conditional volatility to differ on each day of the week, in the winter months, on announcement days and non-announcement days. The separation of volatility into a persistent part and a non-persistent part allows me to implement a nice clean study of the determinants of natural gas volatility. To the best of my knowledge, my paper will be the first full study of persistence, asymmetry, seasonality and announcement effects within a GARCH framework for this market. The paper is organized as follows. In Section 2, I propose hypotheses of the study. The data is presented in Section 3. In Section 4, I employ several GARCH type models for natural gas volatility. I find evidence of volatility persistence, asymmetric volatility, days-of-the-week and winter effects in the natural gas market. Furthermore, storage report announcements cause increased volatility but this increase does not persist to the following day. Section 5 concludes the paper. 2. Hypotheses In this study, I attempt to answer the following questions: 1. Are natural gas prices characterized by volatility persistence as has been documented in other markets? It has been observed in other markets that volatile markets tend to follow volatile markets and stable markets tend to follow stable markets. Among 4 the many studies documenting volatility persistence are: Adrian, Pagan and Schwert (1990), Andersen, Bollerslev, Diebold and Ebens (2001), Wu (2001) and Flannery and Protopapadakis (2002) for the stock market, Ederington and Lee (1993, 1995 and 2001) for interest rates, Harvey and Huang (1991), Ederington and Lee (1993, 1995 and 2001), Andersen and Bollerslev (1998) and Low and Zhang (2005) for foreign exchange markets and Jones, Lamont and Lumsdaine (1998) for bond markets. I hypothesize that similar volatility persistence exists in the natural gas market. 2. Is there volatility asymmetry in the natural gas market? That is do equal positive and negative shocks have different impacts on future volatility? This hypothesis is inspired by the generally documented evidence of an asymmetric volatility in the stock market and, to a lesser extent, in some other markets such as Treasury bonds and Treasury bond futures markets. French and Roll (1986), French, Schwert and Stambaugh (1987), Campbell and Hentschel (1992), Veronesi (1999), Bekaert and Wu (2000) and Wu (2001) found that in the stock market, an unexpected decrease in price has a bigger impact on predicted volatility than an unexpected increase in price of equal magnitude. The asymmetric volatility in the stock market is generally attributed to either a leverage effect and/or a volatility feedback effect (a survey on the determinants of asymmetric volatility in the stock market can be found in Wu (2001)). The same asymmetric volatility was documented for the Treasury bond futures options by Simon (1997) and for the long end of the treasury market by Brunner and Simon (1996). Hsieh (1989), Kim (1999), McKenzie (2002) and Kwek and Koay (2006) studied volatility in the foreign exchange market and found that although volatility in this market is not symmetric, it is difficult to conclude on the direction of that asymmetry since a depreciation in one currency is an appreciation of the matching currency. Given the previous studies on asymmetric volatility, I attempt to examine whether asymmetric volatility exists in the natural gas market and, if yes, the direction of that asymmetry. Using monthly data, Susmel and Thompson (1997) found that in the natural gas market, as in other markets, a negative shock has more impact on predicted volatility than a positive shock of the same size. Contrary to the evidence from the stock and several other markets and that presented by Susmel and Thompson (1997), I think there are good reasons to expect a negative shock in the natural gas market to have a smaller 5 impact on the predicted volatility tomorrow than a positive shock of equal magnitude. My reasoning for this hypothesis is based on the likely shape of the supply and the demand curves. Consider the depictions of the supply and demand curves for natural gas in Figure 1 by Energy and Environmental Analysis Inc. Production and Storage Gas Price Gas Price Inelastic Demand P2 Distillate Switching P1 Residual Oil Switching P0 Deliverability Production Quantity Consumed Gas Supply Gas Demand Figure 1 Supply and Demand in the Natural Gas market Courtesy: Energy and Environmental Analysis, Inc. According to these industry observers, at low volume and prices, supply is highly elastic but once storage limits are reached, supply becomes quite inelastic as natural gas producers, due to infrastructure constraints, can not increase their production levels within a short time period. Also according to these industry observers, the demand curve for natural gas also contains an elastic portion and an inelastic portion. When the natural gas price is low (below P0), natural gas users utilize natural gas entirely to meet their demand. When the natural gas price fluctuates in the range from P0 to P2, some industrial and power generation facilities have the capacity to switch from natural gas to residual fuel oil and distillate fuel oil to maintain operations. However, natural gas users can only switch to fuel oil for short periods of time due to the limited storage capacity. Given the 6 hypothesized shape of the natural gas supply and demand curves, the same fluctuation in demand when prices are low (at the lower parts of the supply and demand curves) should cause a smaller change in natural gas prices than when prices are high (at the higher parts of the supply and demand curves). Thus a positive price shock which moves the market up the supply and demand curves is likely to presage higher future volatility than a negative shock moving down the curves. Evidence that a negative shock has less impact on predicted volatility than a positive shock would be interesting since to our knowledge all studies for other markets have found that when asymmetry exists, negative shocks have a greater impact on future volatility than positive shocks. 3. Does volatility differ by day of the week? Some academic studies found that volatility of financial assets returns varies across days of the week. The literature on day- of-the-week effect on volatility includes French and Roll (1986), Berument and Kiymaz (2001) for stock market, Harvey and Huang (1991), Ederington and Lee (1993) for interest rates and foreign exchange futures market and Jones et al. (1998) for bond markets. I expect that consistent with the evidence in other markets, natural gas volatility also differs across days of the week. Also, in some financial markets, the three day volatility from Friday close to Monday close is higher than that of a normal one day period but not as high as that for a three weekday period because there is not much information coming out during the weekend. I hypothesize that natural gas volatility is also higher over the weekend. 4. Is volatility higher in the winter months? A winter effect is likely unique in the natural gas market due to the dependence of natural gas price on weather conditions. In winter, especially when the weather is severe, the demand for natural gas may rise dramatically. In such a situation, natural gas supplies can not increase accordingly since suppliers can not increase production within a short time period and furthermore, the natural gas supply is constrained by storage capacity. This observation motivates my hypothesis that natural gas volatility is higher during winter months. To my knowledge, this hypothesis has not been tested heretofore. 5. Does the weekly storage report release cause increased natural gas volatility on announcement days? The Weekly American Gas Storage Survey report was compiled 7 and issued by the American Gas Association through March, 2002 and by the U.S Energy Information Administration from April, 2002. This report is ”designed to provide a weekly estimate of the change in inventory level for working gas in storage facilities across the United States, using a representative sample of domestic underground storage operators.”3 Given that natural gas supply is constrained by the storage level, the weekly storage announcement is reportedly one of the most important news influencing the natural gas market. Susmel and Thompson (1997) found that there is a positive relationship between changes in predicted volatility and changes in storage capacity. It has been documented that in other markets, prices are generally more volatile when lots of new information is coming to the market. Ederington and Lee (1993, 1995) found that following the releases of scheduled macroeconomic news such as the employment report, the consumer price index (CPI) and the producer price index (CPI), interest rate and exchange rate volatility is considerably higher than normal. Jones et al. (1998) found that the releases of employment and producer price index data are responsible for an increase in volatility in T-bond markets on announcement days. Flannery et al. (2002) found that 3 macroeconomic announcements significantly increase volatility in the stock market when they are released. Linn and Zhu (2004) documented that natural gas volatility increases within 30 minutes after the storage report release. I expect that consistent with the evidence in other markets, natural gas volatility is higher on storage report announcement days. 6. If there is evidence that natural gas volatility increases on announcement days, does the high volatility persist on the days following the announcement? In other words, is public information about natural gas storage immediately incorporated in natural gas prices or does the announcement impact persist over several days? If market participants in the natural gas market finish adjusting prices according to the new information within the day of the report release, volatility should fall all the way back to normal level on the following day. Studies in other markets have generally found that public information about the macroeconomy is fully incorporated in prices within the announcement day. Ederington and Lee (1993, 1995) documented that market prices in interest rates and foreign 3 Issue Brief 2001-03, Policy Analysis Group, American Gas Association. 8 exchange futures markets quickly incorporate the information in macroeconomic announcements and that volatility quickly returns to preannouncement levels within one day. Jones et al. (1998) confirmed this result by finding that the increase in predicted volatility in T-bond market on announcement days does not persist to the following day. Linn and Zhu (2004) found that the release of the storage report causes increased volatility but only for 30 minutes after the report announcement. I attempt to examine Linn and Zhu (2004)’s findings from a different perspective. By using daily natural gas prices in a GARCH (1,1) type model, I test whether the announcement continues to cause increased volatility or whether conditional volatility falls all the way back to normal level on the following day. 3. Data and preliminary analysis This study examines the natural gas volatility using daily closing prices for the nearby and next maturity natural gas futures contracts traded on the New York Mercantile Exchange (NYMEX)4. Natural gas futures contracts, which began trading on the NYMEX on April 3, 1990, trade in units of 10,000 million British thermal units (BTUs) (see Appendix for details). My sample period is January 1, 1997 to December 16, 2005 totaling 2,241 daily observations. Daily data for the nearby and next futures prices are from Norman's Historical Data. Futures prices are used in place of spot prices for the following reasons. First, futures prices are the major prices in the natural gas market. When newspapers report natural gas prices, they are actually reporting futures prices. Second, the futures market for natural gas is big and centralized since most natural gas futures contracts are traded on the NYMEX. On the contrary, the daily spot markets for gas are small and largely decentralized. Third, futures prices are the prices normally used in most risk management contracts such as swaps and options. Fourth, as documented in Ates and Wang (2005), futures markets play the dominant role in the price discovery process in the natural gas markets. Spot prices are also not readily available. 4 The nearby futures contract is the contract with the closest expiration date and the next futures contract is the one that matures just after the nearby futures contract. 9 To examine natural gas volatility, I examine daily log returns5 where return is defined as Rt=ln(Pt/Pt-1) with Pt is the price of the nearby (next) futures contract on day t and Pt-1 is the price of the same nearby (next) futures contract the previous day. Data on the release dates of Weekly Report of American Gas Storage were collected from the Energy Information Administration (EIA) website6. Of the 2,241 observations, 448 are announcement days. From January 01, 1997 to April 01, 2002, 235 announcements were made on Monday and 31 on Tuesday. From April 02, 2002 to December 16, 2005, 179 announcements were made on Thursday and 1 announcement was made on Monday, 1 on Wednesday and 1 on Friday. I choose to start my sample in January, 1997 since information on storage announcement dates is available from January, 1997. Table 1 provides summary statistics for daily natural gas returns. As can be seen from Table 1, the annualized standard deviation of the daily percentage change in natural gas prices is 58.51% for the nearby futures contracts and 50.63% for the next shortest contracts. As reported earlier, the volatilities over the same period are 16.61% for the 10- year T-bond rates, 12.36% for the S&P 500 and 8.84% for the US dollar-Euro exchange rate. So the natural gas market is characterized by very high volatility. There is also evidence of autocorrelation in natural gas returns; the first-order correlation coefficient for the nearby and next futures returns are -0.046 and -0.045, respectively which are both significant at the 0.05 level7. Table 1 also provides preliminary evidence of volatility persistence in this market in that the first order autocorrelation coefficient for absolute daily returns for the nearby and the next futures contracts are 0.097 and 0.072, respectively which are both significant at the 0.01 level. For squared daily returns (not reported in Table 1), the autocorrelation coefficients are 0.064 and 0.148 which are significant at the 0.01 level. Clearly, this market like many others is characterized by volatility persistence. 4. Model Specification and Analysis 5 The daily natural gas “returns” are used to measure price changes only. These “returns” are not investment returns since no money is actually invested. 6 http://www.eia.doe.gov/oil_gas/natural_gas/data_publications/natural_gas_weekly_market_update/ngwmu.html 7 These could be due to bid-ask “bounce”. 10 4.1 Volatility Persistence Perhaps the most popular model of financial asset return volatility is the GARCH (1,1) model proposed by Bollerslev (1986) and numerous studies have found that GARCH (1,1) fits many financial assets returns volatility very well (See, for instance, Engle (2001)). Comprehensive surveys of this literature can be found in Bollerslev et al. (1992) and Poon and Granger (2003). Surveying studies that compare the volatility forecasting ability of various time-series models, Poon and Granger (2003) reported that a majority found that GARCH (1,1) forecasts best. Therefore I first use a basic GARCH (1,1) specification to model volatility persistence in this market. Since there is also evidence of first-order autocorrelation in ordinary daily returns, I add the lagged natural gas return as an independent variable to the standard GARCH (1,1) mean equation. So the estimated mean and variance equations are: Rt = μ + Φ1Rt-1+ εt, (1)8 ht = ω + αεt-12 + βht-1, (2) Rt=ln(Pt/Pt-1) where Pt is the price of the nearby (next) futures contract on day t and Pt-1 is the price of the nearby (next) futures contract on the previous day. εt is presumed to be an independent random variable with conditional mean zero and conditional variance ht. If volatility persistence is an attribute of the natural gas market, α and β should be significantly positive implying that predicted volatility depends on (1) unexpected price changes and (2) forecast volatility on the previous days. The results for equations (1)-(2) are reported in Table 2a. As expected, the estimates of α for both nearby and next futures daily returns are positive and significant at the 0.001 level, implying that conditional volatility depends on the shocks in the previous day. The estimates of β for both nearby and next futures daily returns are also positive and significant at 0.001 level, implying that conditional volatility also depends on the forecast volatility the previous day. Thus, highly volatile periods in the natural gas market tend to be followed by volatile periods in the future. 8 Although Equation (1) is always estimated simultaneously with my models of the conditional variance h , I do not report its t parameter estimates in the tables to conserve space and focus on the main issue. 11 For comparison, I summarize the estimates of α and β in some other markets in Table 2b. The estimates of α and β for the natural gas market are reasonable and consistent with what have been found in other markets. 4.2 Asymmetric Volatility While the GARCH (1,1) model in equation 2 assumes that positive and negative shocks affect future volatility equally, previous academic studies have found evidence of asymmetric volatility in a number of financial markets. The literature on asymmetric volatility includes French and Roll (1986), French et al. (1987), Campbell and Hentschel (1992), Glosten et al. (1993), Veronesi (1999), Bekaert and Wu(2000) and Wu(2001) for the stock market, Hsieh (1989), Kim (1999), Mc Kenzie (2002) and Kwek and Koay (2006) for the foreign exchange market, Simon (1997) for the Treasury bond futures options and Brunner and Simon (1996) for the long end of the treasury market. Except for the studies on asymmetric volatility in the foreign exchange market, all other studies found evidence that a negative unexpected price change has a larger impact on volatility than an equal positive unexpected price change.9 Consequently, I examine the question of asymmetric volatility in the natural gas market. There are two questions to be answered in this regard. (1) In the natural gas market, does a negative shock have a different impact on predicted future volatility than a positive shock of the same magnitude? (2) If volatility asymmetry exists in the natural gas market, what is the direction of that asymmetry? More specifically, I attempt to test my hypothesis that a negative shock on the previous day has a smaller impact on predicted volatility than a positive shock of the same magnitude. As pointed out earlier, all other studies on asymmetric volatility found that a negative shock has a larger impact on predicted volatility than a positive shock. Susmel and Thompson (1997) also found that in the natural gas market, a negative shock has larger impact on volatility than a positive shock but they used monthly data and did not provide any economic explanation for this phenomenon. I use the GJR (Glosten, Jagannathan, and Runkle(1993)) model 9 Although asymmetric volatility exists in the foreign exchange market, the direction of asymmetry does not matter since a depreciation in one currency is an appreciation in the matching currency. 12 estimation to answer these questions.10 Specifically, the estimated mean and variance equations are: Rt = μ + Φ1Rt-1+ εt, (1) ht = ω + αεt-12 + βht-1+ γ εt-12It-1, (3) where εt is a random variable with conditional mean zero and conditional variance ht; It- 1=1 if εt-1<0 and 0 otherwise. Asymmetric volatility implies γ ≠ 0 in equation (3). γ >0 implies that a negative shock increases conditional volatility more than a positive shock of the same magnitude. The results for equations (1) and (3) are reported in Table 3. As expected, γ is significantly different from zero implying asymmetric volatility in the natural gas market. This concurs with earlier findings for the stock market, Treasury bond futures options and the long end of the Treasury bond markets. However while previous studies (including the study by Susmel and Thompson (1997) for the natural gas volatility) obtained positive estimates of γ, in my estimation the estimated γ is significantly negative implying that a negative shock on the previous day has less impact on the predicted volatility than a positive shock of the same magnitude.11 This behavior of natural gas volatility can be explained by the likely shape of the supply and demand curves as depicted in Figure 1. The same fluctuation in demand when prices are low (at the lower part of the supply and demand curves) should cause a smaller change in natural gas prices than when prices are high (at the higher part of the supply and demand curves). Thus a positive price shock which moves the market up the supply and demand curves is likely to presage higher future volatility than a negative shock moving down the curves. 10 GJR model and EGARCH model (by Nelson (1992)) are the two most popular models of asymmetric volatility. Engle and Ng (1993) compared different ARCH specifications using the Japanese daily stock return data from 1980-1988 and showed that the GJR and EGARCH models are the best models to describe the asymmetric effect of negative shocks. 11 The results do not change if I use the EGARCH (Nelson(1991)) specification instead. In the EGARCH specification, the conditional variance is: Log(h ) = ω + βlog(h )+α│ε /h │+ γ(ε /h ) where the asymmetric effect is captured by γ. If γ<0, a t t-1 t-1 t-1 t-1 t-1 negative shock has a bigger impact on the conditional volatility than a positive shock of the same magnitude. When I estimated the natural gas nearby and next futures returns using the EGARCH specification, the estimates of γ are 0.0405 and 0.0505, respectively and both are significant at the 0.001 level, implying that in the natural gas market, a positive shock has a bigger impact than a negative shock of the same magnitude which is consistent with the results from GJR model. 13 The different impact of positive and negative shocks on predicted volatility according to the estimates in Table 3 is depicted in Figure 2. As shown there a positive shock to natural gas prices has a more persistent impact than an equivalent negative shock of the same magnitude. ht (12%)2 (10%)2 (8%)2 (6%)2 -40% -30% -20% -10% 0% 10% 20% 30% 40% εt-1 Figure 2 The asymmetric impact of the return shocks on conditional volatility in the natural gas futures market This news impact curve depicts how positive and negative return shocks at time t-1 impact conditional volatility in the natural gas market according to the estimates of the GJR model. This curve measures how the return shock this period is incorporated into volatility estimates next period. The equation for the GJR news impact curve is: ht = ω + αεt-12 + βht-1+ γεt-12It-1 (3) where It-1=1 if εt-1<0 and 0 otherwise, ω, α, β and γ are estimates from the GJR variance equation (Equation 3). 14 4.3 Day-of-the-week effects Several studies have examined whether volatility differs by day of the week in various financial markets. (See French and Roll (1986), Berument and Kiymaz (2001) for stock market, Harvey and Huang (1991), Ederington and Lee (1993) for interest rates and foreign exchange futures market and Jones et al. (1998) for bond markets, Hsieh (1989) for foreign exchange market and Linn and Zhu (2004) for natural gas market). In this study, I employ a new procedure to examine whether volatility in the natural gas market varies by day-of-the-week. I estimate a model in which the conditional variance follows a regime-switching GJR type process using a variant of the model outlined in Jones et al. (1998). Specifically, the new mean and variance equations are: Rt = μ + Φ1Rt-1 + st1/2εt, (4) st = (1+ δM DMONt)(1+δTDTUEt)(1+δRDTHURt)(1+δFDFRIt), (5a) ht = ω+ αεt-12+βht-1+ γεt-12It-1, (6) where st is the volatility seasonal for time t, δM, δT, δR, and δF measures the day-of-the- week effects on the conditional volatility. εt is a random variable with conditional mean zero and conditional variance ht independent of st. DMONt, DTUEt, DTHURt and DFRIt are zero-one dummy variables for each of the four weekdays. I choose to leave out the dummy variable for Wednesday because of the 2,241 observations, only one announcement was made on Wednesday. The specification (4)-(6) allow the estimated volatility to differ by day of the week. On Wednesday, the estimated variance of natural gas returns is ht. On Monday, the estimated variance is ht (1+δM). On Tuesday, the estimated variance is ht (1+δT) and so on for other days. Thus δX estimates the percentage difference between volatility on day X (as measured by the variance) and volatility on Wednesday. I expect that some weekday dummy estimates will differ from zero. More specifically, I expect higher volatility on Friday-close-to-Monday-close return since this is a three day return including the weekend. I also anticipate that volatility could be higher on Monday and Thursday since most storage reports were released on those two dates. Linn and Zhu (2004) also documented seasonality in the natural gas market but this was done in an Ordinary Least Square (OLS) and Generalized Method of Moments (GMM) framework. Hsieh (1989), Berument and Kiymaz (2001) and Ederington and Lee 15 (2001) used GARCH type models to examine day-of-the-week effects. In the three studies mentioned above, the authors placed weekday dummies in the ht equation (equation 6) to estimate how conditional volatility changes across weekdays. Thus using their approach, equation (6) becomes: ht = ω+ αεt-12+βht-1+ γεt-12It-1+ δM DMONt + δTDTUEt + δRDTHURt + δFDFRIt, (6’) and there is no s equation (equation 5a). In contrast, I employ a separate volatility seasonal specification (equation 5a) to measure day-of-the-week effects. This provides a much clearer estimation of day-of-the-week effects than if the weekday dummies are placed directly in the ht equation as in equation (6’). When day-of-the-week dummies are in the ht equation (as in equation 6’), the dummy for any day of the week impacts volatilities on all days of the week through the ht-1 term on the right-hand side of the equation. Suppose for instance that day t is Monday. ∂ht/∂DMONt = δM. Now consider the impact of the Monday dummy on the Tuesday (day t+1) volatility. Since ht+1 = ω + αεt2 + βht + γεt2It+ δMDMONt+1 + δTDTUEt+1 + δRDTHURt+1 + δFDFRIt+1 and ∂ht/∂DMONt = δM, ∂ht+1/∂DMONt = βδM. Likewise the Monday dummy impact on Wednesday’s volatility is ∂ht+2/∂DMONt = β2 δM. Thus when the day-of-the-week dummies are in the ht equation, as in equation 6’, δM does not measure how much higher volatility is on Monday than on the left out day. Indeed depending on the coefficient pattern, the day of the week with the highest δ coefficient may not be the day with the highest volatility. Separating the variance of returns into a persistent part, equation 6, and non- persistent part, equation 5, allows me to estimate a model in which DMONt impacts only Monday volatility. As explained above, δM measures how much higher or lower in percentage terms the volatility is on Monday than on the left out day (Wednesday) and δ T measures how much higher or lower volatility is on Tuesday. Thus, the introduction of a volatility seasonal s into the specification allows me to implement a nice clean study on how much the estimated variance differs by day of the week. 16 The results for equations (4), 5(a) and (6) are represented in Table 4. As indicated by the likelihood ratios statistics in the last row of Table 4, volatility differs significantly by day of the week. 12 As expected, conditional volatility over the three day period from the close on Friday to the close on Monday is higher than that on Wednesday or any other weekday. Specifically, the standard deviation of natural gas nearby futures returns and next futures returns from Friday-close-to-Monday-close are 30.86% and 28.46% higher than that on Wednesday, respectively. The difference between Friday-close-to-Monday-close volatility and Wednesday volatility is significantly different from zero at the 0.001 level. I see two possible explanations for the higher Friday-close-to-Monday-close volatility. First, the Friday-close-to-Monday-close volatility is not just one-day volatility but it also incorporates volatility over the weekend. Second, the higher Monday volatility may be due to the fact that many storage announcements were released on Monday (From January 1997 through March 2002, 235 out of 266 announcements were released on Monday). However, even when I estimate the specification (4), 5(a) and (6) with the sub- period from 2002 through 2005 (only one announcement was released on Monday during this period), the Friday-close-to-Monday-close volatility is still highest and the difference between the Friday-close-to-Monday-close volatility and Wednesday volatility is still significantly different from zero at 0.001 level. (The interaction between Monday/weekend effect and announcement effect will be discussed further in Section 4.6.) These results suggest that there is a Monday/weekend effect on volatility in the natural gas market and that at least part of the high Friday-close-to-Monday-close volatility is due to the accumulation of the new information during the weekend. As indicated in Table 4, volatility is higher on Thursday and the difference between volatility on Thursday and on Wednesday is significantly different from zero at the 0.05 level. However, as noted above many of the storage announcements occur on Thursday and when I estimate the specification (4)-(6) with the sub-period from January 1997 through March 2002 (no storage announcement was made on Thursday during this 12 The likelihood ratio is based on the log likelihood for estimation 4, 5(a) and 6 and estimation 1 and 3 where all weekday dummies coefficients are forced to be zero, i.e., there are no weekday effects in the natural gas market. For instance, for the natural gas nearby futures returns, the likelihood ratio is: 2(5974.469-5914.264) = 121.041. This statistic is distributed as a chi-square with 4 degrees of freedom. 17 period), the volatility on Thursday is not significantly different from the volatility on Wednesday. This suggests that volatility is higher on Thursday because for the later period (from April 2002 to December 2005), most announcements were made on Thursday, i.e., that the high Thursday volatility is due to an announcement effect. Volatility is lower on Friday than on Wednesday and all other days of the week except Tuesday and this difference is significantly different from zero at the 0.001 level. The standard deviation of natural gas prices on Friday is 21.49% lower than that on Wednesday. This is opposite to the findings for other markets. For example, Harvey and Huang (1991) reported higher volatility in interest rate and foreign exchange futures market on Friday. Ederington and Lee (1993) further support these results. Jones et al. (1998) and Berument and Kiymaz (2001) found similar evidence in the bond and stock markets. This contradiction may be due to the fact that many economic news releases which impact volatility in other markets are often announced on Friday whereas this is not the case in the natural gas market. 4.4 Winter effect It has been documented that returns in some markets differ by month-of-the-year. (see, for instance, Keim (1983), Lakonishok and Smidt(1984) for stock markets and Jordan and Jordan (1991) for corporate bond market). However, little attention has been given to whether volatility differs by month-of-the-year. I expect to find that natural gas volatility is higher in the winter months due to the fact that natural gas demand often increases during the winter months and if the weather becomes severe, this increase may be dramatic. If the supply is constrained by storage and natural gas suppliers can not increase production within a short time period, when this happens sharp price swings could result (this can be seen as the intersection of the inelastic portions of both the supply and demand curves in Figure 1). In order to test the hypothesis of winter effects, I employ a regime-switching model similar to that in section 4.3. First, I include a zero-one dummy variable, WIN, for the winter months (which include the time period from November through February) in the volatility seasonal equation. The specification is: Rt = μ + Φ1Rt-1 + st1/2εt, (4) st = (1+ δW WINt), (5b) 18 ht = ω+ αεt-12+βht-1+ γεt-12It-1, (6) Specification (4), (5b) and (6) allows conditional volatility to differ by month of the year. Specifically, natural gas conditional volatility is ht(1+ δW ) in the winter months and ht in other months of the year. A significantly positive parameter estimate of δW implies that volatility is higher in the winter months than in other months. The results from specification (4), (5b) and (6) are represented in Table 5. As expected, I find that volatility is higher in the winter months than in other months of the year. Specifically, the estimate in Table 5 indicates that the standard deviations of natural gas futures returns in the winter months is 12.09% higher than in other months for the nearby contracts and 11.83% higher for the next contracts and this difference is significant at the 0.001 level. To provide a more detailed estimation of how natural gas volatility differs by time of year, I expand equation (5b) to include the dummies for each month of the year. The revised specification is: Rt = μ + Φ1Rt-1 + st1/2εt, (4) st = (1+ δJJANt)(1+ δFFEBt)(1+ δMarMARt)(1+δAAPRt)(1+ δMayMAYt)(1+ δJuly JULYt)(1+ δAugAUGt)(1+ δSSEPt)(1+ δOOCTt)(1+ δNNOVt)(1+ δDDECt), (5c) ht = ω+ αεt-12+βht-1+ γεt-12It-1, (6) In this specification (4), (5c) and (6), conditional volatility differs in each month of the year. In June, the conditional volatility is simply ht and the volatility switches to ht(1+ δX) in month X. Consistent with the results from specification (4), (5b) and (6) above, the results from (4), (5c) and (6) confirm that natural gas volatility is higher in winter months. Natural gas volatility is higher in the winter months from November through February than in June and the differences are significant at the 0.05 level. A somewhat surprising time-of-the-year effect is that September has significantly higher conditional volatility than other months of the year.13 13 When I estimate the specification 4, 5(c) and 6 without the 2005 data, the estimate of September dummy is still high and significantly positive, implying that the high September natural gas volatility can not be explained only by the hurricane Katrina impact. 19 4.5 Impact of the Storage Report It has been documented that volatility in some financial markets is higher on days when important reports are released, i.e., announcement days (See, for instance, Ederington and Lee (1993, 1995), Jones et al. (1998), Linn and Zhu (2004)). On announcement days, new information comes to the market and thus, market participants adjust prices according to the new information. I expect that consistent with the findings in earlier studies, natural gas volatility is higher on days the storage report is released. To examine whether the storage report release increases natural gas volatility, I introduce a zero-one announcement dummy, DAt, into the volatility seasonal equation. The specification is: Rt = μ + Φ1Rt-1 + st1/2εt, (4) st = (1+ δ0DAt), (5d) ht = ω+ αεt-12+βht-1+ γεt-12It-1, (6) Again, the above specification allows conditional volatility to differ on announcement days and on non-announcement days. On non-announcement days, the conditional volatility is simply ht and on announcement days, conditional volatility switches to ht(1+δ0). I hypothesize that the storage report release increases the conditional volatility and thus, the estimate of δ0 should be significantly positive. As explained later in Section 4.7, the introduction of an announcement dummy in a volatility seasonal equation allows me to implement a clear examination of announcement impact on volatility. The results of specification (4), (5d) and (6) are represented in Table 7. As predicted, conditional volatility is higher on announcement days and this is significant at the 0.001 level. This result is consistent with what has been documented by Ederington and Lee (1993, 1995), Jones et al. (1998) and Flannery et al. (2001) for other markets and by Linn and Zhu (2004) for natural gas. As indicated in Table 7, the standard deviation of natural gas returns increases 18.02% for nearby contracts and 19.57% for next contracts on announcement days. 20 4.6 The interaction of day-of-the-week effects and announcement effects As discussed in section 4.3, volatility in the natural gas market is significantly higher on Monday and Thursday and significantly lower on Friday. As seen in section 4.5, natural gas volatility is significantly higher on announcement days. Since most of the storage announcements occur on Monday and Thursday, a question arises whether volatility is higher on Monday and Thursday due to the announcement effect or due to a day of the week effect. To answer this question, I estimate the specification 4, 5(a) and 6 for two sub-samples. The first sub-sample ranges from January, 1997 through March, 2002 (during this period, 235 out of 266 storage announcements were released on Monday) and the second sub-sample ranges from April, 2002 through December, 2005 (during this period, 179 out of 182 storage announcements were released on Thursday). The results are presented in Table 8. As indicated in the second and third columns of Table 8, in the period from January 1997 through March 2002 (no storage announcement was released on Thursday during this period), natural gas volatility on Thursday was not significantly different from the volatility on Wednesday. I conclude that higher Thursday volatility is due to announcement effect because for the later period (from April 2002 to December 2005), most announcements were made on Thursday. Also in the fourth and fifth columns of Table 8, in the period from April, 2002 through December, 2005 (only one announcement was made on Monday during this period), the Friday-close-to-Monday-close natural gas volatility is still highest and the difference between the Friday-close-to-Monday-close natural gas volatility and Wednesday volatility is still significantly different from zero at the 0.001 level. These results lead me to the conclusion that there is a weekend effect on natural gas volatility as the Friday-close-to-Monday-close natural gas volatility also incorporates volatility over the weekend. 4.7 Impact of the Storage Report on subsequent days The results from section 4.5 imply that the storage announcement report does increase conditional volatility on announcement days. The remaining question is whether this increased volatility is persistent or just transitory. Ederington and Lee (1993, 1995) 21 suggested that announcement shocks do not have impact on the volatility on the subsequent days for the interest rate and foreign exchange futures markets. Jones et al. (1998) further supported these results for the bond markets. Linn and Zhu (2004) documented that natural gas volatility increases within only 30 minutes after the report announcement. To examine the impact of the report release on natural gas volatility on the days following the announcement, I expand specification (4), (5c) and (6) to accommodate the possible impact of the report release on natural gas volatility on subsequent days after the announcements. The specification is: Rt = μ + Φ1Rt-1 + st1/2εt, (4) st = (1+ δ0DAt), (5d) ht = ω+ αεt-12+βht-1+ γεt-12It-1+ δ1DAt, (7) When announcement dummy is in the ht equation (equation 7), the announcement dummy impacts volatilities on the day after the announcement and all subsequent days through the ht-1 term on the right-hand side of the equation. Suppose for instance that day t is the announcement day. From equation 5(d) and equation 7, ∂st/∂DAt = δ0 and ∂ht/∂DAt = δ1. Now consider the impact of the announcement dummy on the following day (day t+1) volatility. ∂st+1/∂DAt = 0 and ∂ht+1/∂DAt = βδ1. Likewise the announcement dummy impact on day t+2 volatility are: ∂st+2/∂DAt = 0 and ∂ht+2/∂DAt = β2δ1. Thus, specification 4, 5(d) and 7 allows storage announcement to affect volatility in two parts: a persistent part (through δ1 in equation 7) and a non-persistent part (through δ0 in equation 5d). A number of previous studies which just placed announcement dummy into the ht equation (without the s equation) are inadequate to model the impact of announcement shocks on volatility since the announcement impact is forced to persist on the subsequent days. (∂ht/∂DAt = δ1, ∂ht+1/∂DAt = βδ1, ∂ht+2/∂DAt = β2δ1 and so on). On the contrary, separating the announcement impact into a persistent part, equation 5(d), and a non- persistent part, equation 7 allows me to estimate a model in which the announcement dummy has a separate impact on announcement days and on subsequent days. Given that the estimate of δ0 in equation (5d) is significantly positive (volatility increases on announcement days), a significantly positive estimate of δ1 in equation (7) implies that 22 announcement impact is accumulated in the estimated volatility on subsequent days after the announcement. On the contrary, if the estimate of δ1 is not significantly positive, we fail to reject the hypothesis that announcement shocks do not have impact on subsequent days following the announcement. The results of specification (4), (5d) and (7) are reported in the second and third columns of Table 9. Although both δ0 and δ1 are positive, I fail to reject the hypothesis that the report release has no impact on the conditional volatility on the days after the announcement. Even though volatility increases on announcement days, the market participants apparently complete most of the adjustment of natural gas prices within the announcement days and volatility falls most of the way back to normal level on the following day. It is likely that since the weekly storage report release is a scheduled event (most of the announcements occur on Mondays from 1997-March 2002 and on Thursdays from April 2002-2005), natural gas market participants are well prepared to receive and analyze the new information in the report and thus, the market will incorporate the information into prices quickly. When I estimate volatility using the specification which does not include the s equation and in which the announcement dummy is in the ht equation only, the estimate of δ1 is significantly positive, implying that conditional volatility increases on announcement days and this increase will persist on the subsequent days. The results are presented in the fourth and fifth columns of Table 9. These results demonstrate that the latter specification is inadequate to model the impact of announcement shocks on volatility since the announcement impact is forced to persist on the subsequent days whereas the former specification provides a much clearer approach to estimate the announcement impact on volatility since volatility is separated into a persistent part and a non-persistent part. The results from specification 4, 5(d) and 7 concur with the findings in Ederington and Lee (1993, 1995), Jones et al. (1998) and Linn and Zhu (2004) that market prices quickly incorporate the information contained in the relevant announcements and that volatility quickly returns to preannouncement levels. 23 5. Summary and Conclusions The contribution this paper makes is to provide an empirical examination of the causes and behavior of volatility in natural gas market. Daily returns data from January 1997 to December 2005 are used to estimate different variants of GARCH type model. In summary, I find that volatility persistence and volatility asymmetry are the attributes of volatility in the natural gas market. Also, there is evidence of day-of-the-week and winter effects on natural gas volatility. Consistent with the findings in other markets, natural gas volatility is higher on days storage report announcements are released but announcement shocks do not continue to impact natural gas volatility on subsequent days. The natural gas futures market is characterized by volatility persistence where highly volatile periods are followed by highly volatile periods and stable periods are followed by stable ones. Also, positive and negative returns shocks have different impact on future volatility. Contrary to previous studies of volatility in other financial markets, I find that in the natural gas market, a positive shock has a bigger impact on predicted volatility than a negative shock of the same magnitude. This is one of the main contributions of this paper since this is the first time volatility asymmetry is found in this direction. This can be explained by the hypothesized shape of the natural gas supply and demand curves. Since the natural gas supply and demand curves are both inelastic when prices are high, a fluctuation in natural gas demand when prices are high causes a larger change in volatility than the same fluctuation when prices are low. Consistent with the findings in other financial markets including that of Linn and Zhu (2004), there are day-of-the-week effects in the natural gas market where natural gas volatility is highest on Monday and lowest on Friday. The high Monday volatility is mainly due to the accumulation of information over the weekend. In contrast to the evidence in the stock, bond, interest rate and foreign exchange futures markets, natural gas volatility is lower on Friday. Natural gas volatility is also higher on Thursday but this is mainly because Thursday is the announcement days in almost half of all observations. A finding which has not appeared in previous literature on the natural gas market is that the natural gas volatility is significantly higher in the winter months than in other months of the year. Given that natural gas supply is constrained by storage limit, a large 24 increase in demand due to severe weather may cause a dramatic swing in natural gas volatility. Consistent with the findings in Linn and Zhu (2004), natural gas volatility is higher on report announcement days. However, the increase in natural gas volatility is only transitory since volatility falls most of the way back to normal level on the following days. A major methodological contribution of this paper is the separation of natural gas volatility into a persistent part and a non-persistent part using the regime-switching GJR model with a seasonal volatility equation. This model allows me to implement a clean study of the determinants of natural gas volatility since volatility is allowed to differ by day of the week, month of the year and on announcement days. 25 Appendix Contract Specification Natural Gas Trading Unit 10,000 million British thermal units (mmBtu). Trading Hours (All times are Open outcry trading is conducted from 10:00 AM until New York Time) 2:30 PM. Electronic trading is conducted from 6:00 PM until 5:15 PM via the CME Globex® trading platform, Sunday through Friday. There is a 45-minute break each day between 5:15PM (current trade date) and 6:00 PM (next trade date). Trading Months 72 consecutive months commencing with the next calendar month (for example, on January 6, 2004, trading occurs in all months from February 2004 through January 2010). Minimum Price Fluctuation $0.001 (0.1¢) per mmBtu ($10.00 per contract). Maximum Daily Price $3.00 per mmBtu ($30,000 per contract) for all Fluctuation months. If any contract is traded, bid, or offered at the limit for five minutes, trading is halted for five minutes. When trading resumes, the limit is expanded by $3.00 per mmBtu in either direction. If another halt were triggered, the market would continue to be expanded by $3.00 per mmBtu in either direction after each successive five-minute trading halt. There will be no maximum price fluctuation limits during any one trading session. Last Trading Day Trading terminates three business days prior to the first calendar day of the delivery month. Settlement Type Physical Delivery The Sabine Pipe Line Co. Henry Hub in Louisiana. Grade and Quality Pipeline specifications in effect at time of delivery. Specifications Position Accountability Levels Any one month/all months: 12,000 net futures, but not and Limits to exceed 1,000 in the last three days of trading in the spot month. Note: Contract Specifications are obtained from NYMEX webpage: http://www.nymex.com 26 Table 1 Summary Statistics: Natural gas daily returns The second (fourth) columns present the summary statistics for natural gas returns: Rt=ln(Pt/Pt-1) where Pt is the price of the nearby (next) futures contract on day t and Pt-1 is the price of the nearby (next) futures contract on the previous day. The third (fifth) columns present the summary statistics for absolute values of daily returns. (***), (**), (*) designate estimates significantly different from zero at the 0.001, 0.01 and 0.05 levels, respectively. The sample extends from January 01, 1997 through December 31, 2005. Nearby futures contracts Next futures contracts Returns Absolute Returns Returns Absolute Returns Mean 0.001 0.027 0.001 0.024 Maximum 0.324 0.324 0.188 0.188 Minimum -0.199 0.000 -0.155 0.000 Std Dev 0.037 0.026 0.032 0.021 Annualized Std Dev 0.585 0.406 0.506 0.332 Skewness 0.344 2.547 0.077 1.836 Kurtosis 7.91 16.65 5.043 8.345 Rho (First order autocorrelation coefficient) -0.046* 0.097*** -0.045* 0.072** 27 Table 2a The GARCH (1,1) model of natural gas volatility Estimates of the model: Rt = μ + Φ1Rt-1+ εt, (1)14 2 ht = ω + αεt-1 + βht-1, are presented where Rt is the natural gas daily returns, εt is an independent random variable with conditional mean zero and conditional variance ht. Returns are expressed in percent. Standard errors are shown in parentheses. (***), (**), (*) designate estimates significantly different from zero at the 0.001, 0.01 and 0.05 levels, respectively. The sample extends from January 01, 1997 through December 31, 2005. Nearby futures Next futures ω 0.3941*** 0.3054*** (0.0733) (0.0744) α 0.0943*** 0.0656*** (0.0082) (0.0098) β 0.8809*** 0.9040*** (0.0109) (0.0142) Log likelihood -5979.147 -5675.611 14 Although Equation (1) is always estimated simultaneously with my models of the conditional variance h , I do not report its t parameter estimates in the tables to conserve space and focus on the main issue. 28 Table 2b GARCH (1,1) estimates in representative previous studies Coefficient estimates Type of asset Period Source Omega Alpha Beta 0.00084** 0.07906** 0.90501** Stock 1963-1986 Akgiray (1989) Berument and Kiymaz 0.0009** 0.0369** 0.9567** Stock 1973-1997 (2001) 0.1907** 0.8056** BP 1974-1983 Hsieh (1989) 0.1263* 0.8511* CD 1974-1983 Hsieh (1989) 0.2296* 0.7329* DM 1974-1983 Hsieh (1989) 0.3708** 0.7138** JY 1974-1983 Hsieh (1989) 0.1723* 0.8229* SF 1974-1983 Hsieh (1989) 0.0008* 0.050* 0.938* 5-yr T-bond 1979-1995 Jones et al. (1998) 0.0021** 0.051** 0.937** 10-yr T-bond 1979-1995 Jones et al. (1998) 0.0031** 0.037** 0.955** 30-yr T-bond 1979-1995 Jones et al. (1998) Ederington and Lee 0.1809** 0.2925** 0.5939** Eurodollar 1989-1993 (2001) Ederington and Lee 0.1325** 0.2058** 0.6938** T-bond futures 1989-1993 (2001) Ederington and Lee 0.0667** 0.1768** 0.7522** Deutschmark 1989-1993 (2001) 29 Table 3 GJR model of asymmetric volatility Estimates of the model: Rt = μ + Φ1Rt-1+ εt, ht = ω + αεt-12 + βht-1+ γ εt-12It-1, are presented where Rt is the natural gas daily returns, εt is an independent random variable with conditional mean zero and conditional variance ht. It-1=1 if εt-1<0 and 0 otherwise. Standard errors are shown in parentheses. (***), (**), (*) designate estimates significantly different from zero at the 0.001, 0.01 and 0.05 levels, respectively. The sample extends from January 01, 1997 through December 31, 2005. Nearby futures Next futures ω 0.3280*** 0.2833*** (0.0673) (0.0665) α 0.1117*** 0.0954*** (0.0091) (0.0127) β 0.8947*** 0.9097*** (0.0107) (0.0129) γ -0.0539*** -0.0657*** (0.0098) (0.0122) Log Likelihood -5974.469 -5666.718 30 Table 4 GJR model with Day-of-the-week effects Estimates of the model: Rt = μ + Φ1Rt-1 + st1/2εt, st = (1+ δM DMONt)(1+δTDTUEt)(1+δRDTHURt)(1+δFDFRIt), ht = ω+ αεt-12+βht-1+ γεt-12It-1, are presented where Rt is the natural gas daily return. It-1=1 if εt-1<0 and 0 otherwise, st is the volatility seasonal for time t, δM, δT, δR, and δF measure the day-of-the-week effects on the conditional volatility. εt is a random variable with conditional mean zero and conditional variance ht independent of st. DMONt, DTUEt, DTHURt and DFRIt are zero- one dummy variables for each of the four weekdays. Standard errors are shown in parentheses. (***), (**), (*) designate estimates significantly different from zero at the 0.001, 0.01 and 0.05 levels, respectively. Asterisks on the likelihood ratios indicate rejection at the 0.01 level of the null hypothesis that volatility does not vary by day of the week. The sample extends from January 01, 1997 through December 31, 2005. Nearby futures Next futures ω 0.324095*** 0.1998*** (0.0773) (0.0591) α 0.1108*** 0.0745*** (0.0126) (0.0122) β 0.8821*** 0.9135*** (0.0133) (0.0129) γ -0.0425** -0.0290* (0.0142) (0.0130) δM 0.7125*** 0.6503*** (0.1114) (0.1245) δT -0.0912 -0.0647 (0.0677) (0.0712) δR 0.2331* 0.3010** (0.0929) (0.1032) δF -0.3829*** -0.3234*** (0.0470) (0.0530) Log likelihood -5914.264 -5621.373 Likelihood ratio 120.410* 90.690* 31 Table 5 GJR model with a Winter effect Estimates of the model: Rt = μ + Φ1Rt-1 + st1/2εt, st = (1+ δW WINt), ht = ω+ αεt-12+βht-1+ γεt-12It-1, are presented where Rt is the natural gas daily return. It-1=1 if εt-1<0 and 0 otherwise, st is the volatility seasonal for time t, δW measures the winter effect on the conditional volatility. εt is a random variable with conditional mean zero and conditional variance ht independent of st. DWINt is a dummy variable which equals to 1 if the observation is in November, December, January and February. Standard errors are shown in parentheses. (***), (**), (*) designate estimates significantly different from zero at the 0.001, 0.01 and 0.05 levels, respectively. The sample extends from January 01, 1997 through December 31, 2005. Nearby futures Next futures ω 0.3835*** 0.2647*** (0.0848) (0.0745) α 0.1166*** 0.0734*** (0.0121) (0.0127) β 0.8837*** 0.9142*** (0.0137) (0.0144) γ -0.0669*** -0.0394*** (0.0122) (0.0118) δW 0.2564*** 0.2505*** (0.0591) (0.0684) Log likelihood -5967.707 -5666.000 32 Table 6 GJR model with Month-of-the-year effects Estimates of the model: Rt = μ + Φ1Rt-1 + st1/2εt, st = (1+δJJANt)(1+δFFEBt)(1+ δMarMARt)(1+δAAPRt)(1+ δMayMAYt)(1+ δJuly JULYt)(1+ δAugAUGt)(1+ δSSEPt)(1+ δOOCTt)(1+ δNNOVt)(1+ δDDECt), ht = ω+ αεt-12+βht-1+ γεt-12It-1, are presented where Rt is the natural gas daily returns. It-1=1 if εt-1<0 and 0 otherwise, st is the volatility seasonal for time t, δJ….δD measures the monthly effect on the conditional volatility. εt is a random variable with conditional mean zero and conditional variance ht independent of st. JANt…. DECt are zero-one dummies for each month of the year. Standard errors are shown in parentheses. (***), (**), (*) designate estimates significantly different from zero at the 0.001, 0.01 and 0.05 levels, respectively. Asterisks on the likelihood ratios indicate rejection at the 0.01 level of the null hypothesis that volatility does not vary by month. The sample extends from January 01, 1997 through December 31, 2005. Nearby futures Next futures ω 0.3872*** 0.1479** (0.0925) (0.0476) α 0.0691*** 0.0542*** (0.0129) (0.0098) β 0.9108*** 0.9503*** (0.0140) (0.0090) γ -0.0439*** -0.0457*** (0.0129) (0.0103) δJ 0.3743* 0.3223* (0.1600) (0.1508) δF 0.3922** -0.0538 (0.1264) (0.0924) δMar -0.2274* -0.2545** (0.0920) (0.0913) δA -0.3328*** -0.2959*** (0.0775) (0.0805) δMay -0.1131 -0.1132 (0.1102) (0.1086) 33 δJuly -0.2173* -0.1636 (0.0914) (0.0975) δAug 0.2282 0.2434 (0.1491) (0.1420) δS 0.8150*** 0.2273 (0.2059) (0.1407) δO 0.2298 0.1680 (0.1447) (0.1405) δN 0.3733* 0.3687* (0.1700) (0.1700) δD 0.5124* 0.6410** (0.2072) (0.2267) Log likelihood -5938.173 -5645.123 Likelihood ratio 72.592* 43.190* 34 Table 7 GJR model with Announcement effect Estimates of the model: Rt = μ + Φ1Rt-1 + st1/2εt, st = (1+ δ0DAt), ht = ω+ αεt-12+βht-1+ γεt-12It-1, are presented where Rt is the natural gas daily returns. It-1=1 if εt-1<0 and 0 otherwise, st is the volatility seasonal for time t, δ0 measures the announcement effect on the conditional volatility. εt is a random variable with conditional mean zero and conditional variance ht independent of st. DAt is announcement dummy. Standard errors are shown in parentheses. (***), (**), (*) designate estimates significantly different from zero at the 0.001, 0.01 and 0.05 levels, respectively. The sample extends from January 01, 1997 through December 31, 2005. Nearby futures Next futures ω 0.2860*** 0.1981*** (0.0696) (0.0573) α 0.1228*** 0.0784*** (0.0097) (0.0112) β 0.8879*** 0.9166*** (0.0122) (0.0126) γ -0.0687*** -0.0390*** (0.0105) (0.0109) δ0 0.3928*** 0.4298*** (0.0960) (0.0983) Log likelihood -5963.098 -5657.818 35 Table 8 GJR model with Day-of-the-week effects for two sub- periods (January 1997 to March 2002 and April 2002 to December 2005) Estimates of the model: Rt = μ + Φ1Rt-1 + st1/2εt, st = (1+ δM DMONt)(1+δTDTUEt)(1+δRDTHURt)(1+δFDFRIt), ht = ω+ αεt-12+βht-1+ γεt-12It-1, are presented where Rt is the natural gas daily return. It-1=1 if εt-1<0 and 0 otherwise, st is the volatility seasonal for time t, δM, δT, δR, and δF measure the day-of-the-week effects on the conditional volatility. εt is a random variable with conditional mean zero and conditional variance ht independent of st. DMONt, DTUEt, DTHURt and DFRIt are zero- one dummy variables for each of the four weekdays. Standard errors are shown in parentheses. (***), (**), (*) designate estimates significantly different from zero at the 0.001, 0.01 and 0.05 levels, respectively. January 1997 to March 2002 April 2002 to December 2005 Nearby futures Nearby futures Next futures Next futures ω 0.2426** 0.2426** 0.7445*** 0.3781* (0.0875) (0.0875) (0.2142) (0.1704) α 0.0952*** 0.0952*** 0.1547*** 0.0723*** (0.0209) (0.0209) (0.0244) (0.0185) β 0.8937*** 0.8937*** 0.8188*** 0.8844*** (0.0173) (0.0173) (0.0321) (0.0334) γ -0.0375** -0.0375** -0.1138*** -0.0375** (0.0131) (0.0131) (0.0256) (0.0131) δM 0.4468** 0.4468** 1.0928*** 1.0386*** (0.1593) (0.1593) (0.2071) (0.2280) δT -0.0592 -0.0592 -0.1224 0.0050 (0.0950) (0.0950) (0.1025) (0.1169) δR 0.1650 0.1650 0.3787* 0.5625** (0.1168) (0.1168) (0.1719) (0.1917) δF -0.4032*** -0.4032*** -0.3395*** -0.3240*** (0.0647) (0.0647) (0.0716) (0.0780) Log likelihood -3480.403 -3480.403 -2424.402 -2325.587 36 Table 9 GJR model with announcement effects on announcement days and on subsequent days Estimates of the model: Rt = μ + Φ1Rt-1 + st1/2εt, (4) st = (1+ δ0DAt), (5d) ht = ω+ αεt-12+βht-1+ γεt-12It-1+ δ1DAt, (7) and the model: Rt = μ + Φ1Rt-1 + εt, (4’) ht = ω+ αεt-12+βht-1+ γεt-12It-1+ δ1DAt, (7) are presented where Rt is the natural gas daily return. It-1=1 if εt-1<0 and 0 otherwise, st is the volatility seasonal for time t, δ0 measures the announcement effect on the conditional volatility on announcement days, δ1 measures the announcement effect on the conditional volatility on subsequent days. εt is a random variable with conditional mean zero and conditional variance ht independent of st. DA is announcement dummy. Standard errors are shown in parentheses. (***), (**), (*) designate estimates significantly different from zero at the 0.001, 0.01 and 0.05 levels, respectively. The sample extends from January 01, 1997 through December 31, 2005. Estimates of specification 4, 5(d) and 7 Estimates of specification 4’ and 7 Nearby futures Next futures Nearby futures Next futures ω 0.1743 0.4193** 0.1932 0.0012 (0.1971) (0.1554) (0.1452) (0.1213) α 0.1215*** 0.0754*** 0.1136*** 0.0989*** (0.0095) (0.0110) (0.0095) (0.0132) β 0.8838*** 0.9148*** 0.8940*** 0.9065*** (0.0123) (0.0127) (0.0110) (0.0133) γ -0.0612*** -0.0337** -0.0584*** -0.0703*** (0.0113) (0.0104) (0.0099) (0.0126) δ0 0.3214** 0.5562*** - - (0.1107) (0.1399) - - δ1 0.6916 1.0752 2.6420*** 1.5161** (0.9201) (0.7405) (0.6596) (0.5320) logL -5964.902 -5657.807 -5969.276 -5663.831 37 38

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electricity prices, futures prices, futures markets, electricity markets, time series, the futures, conditional variance, price volatility, natural gas, impulse response function, impulse response, futures contracts, journal of futures markets, crude oil, crude oil futures

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posted: | 11/10/2009 |

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