Model Selection, Seasonal Adjustment, Analyzing Results Necmettin Alpay KOÇAK UNECE Workshop on Short-Term Statistics (STS) and Seasonal Adjustment 14 – 17 March 2011 Astana, Kazakhstan 1 27.07.2019

Model Selection Pre-treatment is the most important stage of the seasonal adjustment X-12-ARIMA and TRAMO&SEATS methods use very similar (nearly same) approaches to obtain the linearized (pre-treated) series. Both method use ARIMA model for pre-treatment. The most appropriate ARIMA model → Linearized series of top quality 27.07.2019 2

ARIMA Model selection zt = ytβ+xt Φ(B)δ(B)xt=θ(B)at (p,d,q)(P,D,Q)s → Structure of ARIMA (0,1,1)(0,1,1)4,12 For the model Parsimonious Significance of parameters Smallest BIC or AIC For the residuals Normality Lack of auto-correlation Linearity Randomness 27.07.2019 3

Diagnostics Are there really any seasonal fluctations in the series ? Seasonality test If, yes Diagnostics based on residuals are the core of the analysis. If, no No need to seasonal adjustment.

Diagnostics Seasonality test Residual diagnostics Friedman test Kruskall-wallis test Residual diagnostics Normality Skewness Kurtosis Auto-correlation First and seasonal frequencies (4 or 12) Linearity Auto-correlation in squared residuals Randomness Number of sign (+) should be equal the number of sign (-) in residuals. Final Comment... We select the appropriate model according to the state of the diagnostics.i

Seasonal Adjustment 2.1 Choice of SA approach 2.2 Consistency between raw and SA data 2.3 Geographical aggregation: direct versus indirect approach 2.4 Sectoral aggregation: direct versus indirect approach (Source : ESS Guidelines)

Choice of seasonal adjustment method Most commonly used seasonal adjustment methods Tramo-Seats X12ARIMA Tramo-Seats: model-based approach based on Arima decomposition techniques X-12-ARIMA: non parametric approach based on a set of linear filters (moving averages) Univariate or multivariate structural time series models (Source : ESS Guidelines)

Filtering data : Difference in methods X-12-ARIMA use fixed filters to obtain seasonal component in the series. A 5-term weighted moving average (3x3 ma) is calculated for each month of the seasonal-irregular ratios (SI) to obtain preliminary estimates of the seasonal factors Why is this 5-term moving average called a 3x3 moving average?

Filtering data : Difference in methods TRAMO&SEATS use a varying filter to obtain seasonal component in the series. This variation depends on the estimated ARIMA model of the time series. For example, if series follows an ARIMA model like (0,1,1)(0,1,1), it has specific filter or it follows (1,1,1)(1,1,1), it has also specific filter. Then, estimated parameters affect the filters. Wiener-Kolmogorov filters are used in Tramo&Seats. It fed with auto-covariance generating functions of the series. (more complicated than X-12-ARIMA) But, it is easily interpreted since it has statistical properties.

Consistency between raw and SA data We do not expect that the annual totals of raw and SA data are not equal. Since calendar effect exists (working days in a year) It is possible to force the sum (or average) of seasonally adjusted data over each year to equal the sum (or average) of the raw data, but from a theoretical point of view, there is no justification for this. Do not impose the equality over the year to the raw and the seasonally adjusted or the calendar adjusted data (ESS Guidelines)

Direct and indirect adjustment Direct seasonal adjustment is performed if all time series, including aggregates, are seasonally adjusted on an individual basis. Indirect seasonal adjustment is performed if the seasonally adjusted estimate for a time series is derived by combining the estimates for two or more directly adjusted series. The direct and indirect issue is relevant in different cases, e.g. within a system of time series estimates at a sector level, or aggregation of similar time series estimates from different geographical entities. Mining and Quarrying EU-27 Aggregate Industrial Production Index Manufacturing Germany France Electricity, Water, Natural Gas and etc. Spain ... Romania

Analyzing result Use a detailed set of graphical, descriptive, non-parametric and parametric criteria to validate the seasonal adjustment. Particular attention must be paid to the following suitable characteristics of seasonal adjustment series: existence of seasonality absence of residual seasonality absence of residual calendar effects absence of an over-adjustment of seasonal and calendar effects absence of significant and positive autocorrelation for seasonal lags in the irregular component stability of the seasonal component In addition, the appropriateness of the identified model used in the complete adjustment procedure should be checked using standard diagnostics and some additional considerations. An important consideration is that the number of outliers should be relatively small, and not unduly concentrated around the same period of the year.

Analyzing results Seasonally Adjusted Series

Revisions to seasonal adjustment Forward factors / current adjustment: annual analysis to determine seasonal and trading day factors Preferable for time series with constant seasonal factor or large irregular factor causing revision Concurrent adjustment: uses the data available at each reference period to re-estimate seasonal and trading day factors

Revisions to seasonal adjustment Forecast seasonal factors for the next year (current adjustment) Forecast seasonal factors for the next year, but update the forecast with new observations while the model and parameters stay the same Forecast seasonal factors for the next year, but re-estimate parameters of the model with new observations while the model stays the same (partial concurrent adjustment) Compute the optimal forecast at every period and revise the model and parameters (concurrent adjustment) Sources: Eurostat working paper on Seasonal Adjustment Policy, ESS Guidelines on Seasonal Adjustment

Evaluation of revision alternatives The use of fixed seasonal factors can lead to biased results when unexpected events occur Re-estimation in every calculation increases accuracy but also revision Re-estimation once a year decreases accuracy but also revision Re-identification usually once a year However, time series revise in every release