# ch4

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```					Financial Econometrics I

Part II
Hans Dewachter
Vector Autoregression (VAR)
   Why use only one variable?
   Financial variables depend on past
values of other variables
   VAR
   Linear model
   Used for forecasting and impulse
responses and variance decomposition
VAR: A simple example
2-variable VAR(1): output gap (y), interest rate (r)
VAR: A simple example
VAR: A simple example
Results
Impulse Response Function (IRF)
   Innovations are correlated

   Choleski decomposition

   Uncorrelated innovations
Impulse Response Function (IRF)
Impulse Response Function (IRF)
   So, to estimate a VAR you need to
decide on:
   Variables to be included
   Ordering of the variables
   Number of lags
Variance decomposition
Forecasting
Forecasting
Model selection
   Variables:
   Important economic effects on each other
   Lags
Monetary policy rules
   3-variable VAR(p): output (y), inflation (pi),
interest rate (r)
VAR(1)
Impulse response funcion
Variance decomposition
Forecasting
Forecasting
Forecasting
VAR: the general case
   N-variable VAR(p)

   Y is a n x 1 vector of variables
   B1…Bp are n x n matrices of coefficients
VAR: the general case

   And you have again a VAR(1):
Impulse response function
   Applying Choleski decomposition

   Response function will follow easily as:
Forecasting
   Forecast conditional on time t

   Can also be computed recursively:
Conclusion
   VAR does not impose rigid a priori restrictions
on the data generation process
   Estimation is easy (OLS equation by
equation)
   IRFs allow us to analyze dynamic behavior
   Variance decompositions show us the relative
importance of each shock
   Forecasting can be done in a simple way

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 views: 2 posted: 2/9/2012 language: pages: 26
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