Now Casts of Separations and Divorces an Application of the

Now-Casts of Separations and Divorces: an Application of the Holt-Winters Method Stime anticipate di separazioni e divorzi: un’applicazione del metodo di Holt-Winters Adriano Pareto, Annamaria Urbano Istituto Nazionale di Statistica, Roma e-mail: pareto@istat.it Keywords: now-casts, time series, Holt-Winters method 1. Introduction The aim of this paper is to provide a tool for making now-casts in the Judicial Statistics produced by the Italian National Statistical Institute (Istat). Now-casts are short-run forecasts that provide preliminary estimates of variables of interest for the current year. Used variables are: number of separations and divorces, number of children in separations and divorces and number of minor children under custody. Data consists of quarterly figures - from 1995 to 2005 – and now-casts are based on the forecasts for the fourth quarter. Therefore, when figures on the variable of interest in the first three quarters of the year are available, the year total can be estimated by adding the estimated quarterly number for the last quarter of the current year to the observed figures for the first three quarters. 2. Methods and results Methods that can be used for making now-casts on the basis of quarterly figures range from very simple extrapolation procedures to sophisticated stochastic time-series models. Obviously the main criterion for the selection of an optimal method for making now-casts is forecast accuracy. However, other criteria are to be taken into account also. For example, data requirements should be as limited as possible and the selected method should be easy to use (Pareto and Sorvillo, 2003). The proposed tool in this study is based on the Holt-Winters method. It is among the most widely known and used forecasting techniques in industry and business for seasonal time series and it has had some success in forecasting competitions (Makridakis and Hibon, 2000). Its popularity is due to its simple model formulation and good forecasting results. Four models were tested (additive/multiplicative Holt-Winters model with constant/ linear trend) for searching for the most reliable method and a zero correlation was found between rankings of the forecasting models by goodness of fit and rankings by now-cast accuracy (Average Spearman ρ = -0.06). An alternative method for correlated data, called ratio method, was introduced to improve the forecast accuracy. Finally, a mixed version of Holt-Winters model with constant trend (additive for separations and multiplicative for divorces) has been proposed. Ratio method is used for forecasting the total number of children/minor children under custody in separations/divorces and it consists in getting a forecast of the average number of children/minor children under custody for separations/divorces and then multiplying this value by the forecast of the total number of separations/divorces. The results for 2003-2005 are shown in Table 1. Table 1: Percentage Error (PE) of the now-casts by geographical area Separations Geographical Area Total Children Total Awarded Total 2003 North-west North-east Centre South North-west North-east Centre South North-west North-east Centre South Average APE -0.13 0.47 -1.68 -0.75 -1.06 -0.76 0.96 0.59 0.98 -0.06 -1.48 1.94 0.91 0.02 -0.24 -1.64 -0.61 -0.98 -0.91 1.11 0.09 -0.20 0.06 -1.63 1.86 0.78 -0.46 -1.38 -2.06 -0.69 -1.05 -1.11 1.22 0.12 -0.32 0.49 -1.38 2.66 1.08 -0.52 0.48 1.91 -2.00 2004 -0.35 -0.23 2.10 -1.22 2005 -0.17 -1.91 -3.66 1.43 1.33 -0.11 -2.06 -2.20 0.54 1.25 0.47 -3.49 -3.89 1.19 1.62 0.37 1.34 2.37 1.60 1.16 0.27 -1.04 1.17 -2.63 -0.04 0.67 2.16 -1.65 0.63 0.79 1.45 1.05 -1.62 0.10 0.74 -2.48 -1.65 -1.06 1.10 -2.10 0.73 0.62 1.52 1.44 Divorces Children Total Awarded Average APE Ratio method performs better, on average, than classic method. The average absolute percentage error (APE) of now-cast is equal to 1.16% and varies from 0.78%, for the number of children in separations, to 1.62% for the number of minor children under custody in divorces. In addition, forecast errors for Centre and South are in general larger than those for the other areas, because of some anomalies in time series connected to the different working context and organization of judicial offices. 3. Conclusions This methodology allows to improve data coverage and reduce enough time dissemination of data. Consequently data quality of the statistical surveys analyzed increases. The good results obtained are pushing to apply the method to other statistical surveys on justice, after changes necessary to forecast the new variables’ figures. References Makridakis S., Hibon M. (2000) The M3-competition: results, conclusions and implications, Journal of Forecasting, 16, 451-476. Pareto A., Sorvillo M.P. (2003) Methods for demographic now-casts, Giornate di Studio sulla Popolazione, V edizione, Bari.