How to select regressors and specifications in Demetra+? N. Alpay KOÇAK Turkish Statistical Institute

An observation mechanism on Tramo&Seats in Demetra+ The main issue is whether the series has a significant seasonal and/or calendar affect component? To check seasonality, seasonal chart, seasonal periodogram or AR spectrum seasonality tests part of Demetra+! To check calendar effects, look at spectrum graphics of original series and residuals!

Checking Seasonality and Calendar Effects

Checking Seasonality and Calendar Effects

An observation mechanism on Tramo&Seats in Demetra+ SEATS may change the ARIMA model identifed by TRAMO. This is because TRAMO aims to fit better to series for forecasting, but SEATS aims to decompose the series underlying components using by proper ARIMA model. Since our aims to find best seasonally adjusted series, this change has no negative effect on seasonal adjustment process.

An observation mechanism on Tramo&Seats For example, let’s assume that TRAMO selected an ARIMA model (0,1,1)(1,0,0)12 for a monthly time series. This model may be evaoluated as a good model to forecast the series. But, SEATS can not design a decomposition scheme using this ARIMA model. Then, SEATS changes this model to (0,1,1)(0,1,1). Not only this situation, but also there are several case that SEATS changes the model.

SEATS may change the model!

An observation mechanism on Tramo&Seats Significancy of calendar effects is very important. It may affect directly the specification of the model, outliers and estimated parameters. Default calendar variables (TD1, TD2, TD6, TD7), Easter, National holidays or user-created calendar regressors will be tested, and if it is not significant then removed.

An observation mechanism on Tramo&Seats For example, let’s assume that TRAMO selected an ARIMA model (3,1,0)(0,1,1)12 for a monthly time series without TD6 calendar effect. When TD6 is added to the model (assume that it issignificant), the model is changed to (0,1,1)(0,1,1)12 with TD6 calendar effect.

An observation mechanism on Tramo&Seats TRAMO can be evaluated with some statistical diagnostics since it is a model-based approach. Significancy of ARIMA parameters estimated Independence of the residuals Normality of the residuals Randomness of the residuals Linearity of the residuals (Less importance)

An observation mechanism on Tramo&Seats Problems and possible solutions of those are given below Insignificant parameters → Change ARIMA model specification Independence of the residuals (significant autocorrelations at first, second and seasonal lag) → Check the number outliers, if it does no work, increase MA order Normality of the residuals (excessive kurtosis or skewness) → Check the number outliers or check data span consistency Randomness of the residuals (too much positive or negative residuals) It is a sign of nonlinearity → Check the number outliers or check data span consistency Linearity of the residuals (Less importance) If the only problem is this, leave it ! It does not effect the value of estimated parameters to be used in filter design of SEATS

An observation mechanism on Tramo&Seats SEATS can also be evaluated with some statistical diagnostics since it is a model-based approach. Variance and autocorrelation fuctions of the components Under or over adjustment judgement from variances Significant autocorrelations in seasonal lags Cross-correlations of components There is not any exact solution of those problem. It can depends on time span, models, calendar etc. But, If any of them has problem, try Airline model (0,1,1)(0,1,1) which is most useful model for a number of series.

An observation mechanism on Tramo&Seats Since the aim of the process is to extract all seasonal variations, it has to be checked that remaining components has no seasonality, anymore. Residual seasonality test results Spectral analysis

An observation mechanism on Tramo&Seats Revision policy has to be determined to publish the data officially. Revision history Sliding spans