Testing seasonal adjustment with Demetra+ Dovnar Olga Alexandrovna The National Statistical Committee, Republic of Belarus

Check the original time series This report presents the results of the seasonal adjustment of time series of the index of industrial production of the Republic of Belarus Conclusions about the quality of source data  Original time series is a monthly index of industrial production with base year 2005  Length of time series is 72 observations ( )  In 2011, the statistical classification NACE/ISIC rev.3 was introduced into the practice of the Republic of Belarus. In this regard, this time series of indices of industrial production by NACE was obtained not by processing raw data, but by recalculating the structure of previously existing series of monthly indices based on the previous classification.  The quality of the series received in that way Belstat considers not sufficiently precise, but quite satisfactory for statistical analysis, as the proportion of data relating to the industry by NCES is 98% of the total industrial output by NACE.  In process of receipt of the new observations based on NACE, the quality of the time series will be improved.

The presence of seasonality in the original series Fig. 1 In the original time series a seasonal factor is present, what is indicated by the presence of spectral peaks at seasonal frequencies, and calendar effects.

Approach and predictors The approach TRAMO/SEATS was used User-defined specification TramoSeatsSpec-1 was used: OptionsValues Transformation – Function Auto Calendar holidays of Belarus, td2 The Easter No Automatic modelling ARIMA True Deviating values True

Pre-treatment  The estimated period: [ : ]  Logarithmically transformed series was chosen.  Calendar effects (2 variables: the working days, a leap year). No effects of Easter.  Type of used model is ARIMA model [(0,1,1)(0,1,1)]..  Deviating values: ​​ identified one deviating value in November.

Graph of results Fig. 2 Seasonal component in the irregular component is not lost

Decomposition The basic model ARIMA of the time series of industrial production indices of the Republic of Belarus : (1-0,34В)(1 - 0,25 B 12 )a t, σ 2 = 1, decomposed into three sub-models: Trend model: (1 + 0,1B - 0,9B 2 )a p,t., σ 2 = 0,0334 Seasonal model: (1 + 1,43B + 1,51B 2 + 1,45 B 3 + 1,25B 4 + 1,01B 5 + 0,74B ,47B 7 + 0,24B 8 + 0,03B 9 + 0,11B ,40B 11 )a s,t, σ 2 = 0,1476 Irregular model: white noise (0; 0,1954). Dispersion of seasonal and trend components are lower than the irregular component. This means that stable trend and seasonal components were obtained.

The main diagnostic of quality Diagnosis and resultExplanation Summary Good In general, good quality seasonal adjustment means that an adequate model of decomposition is chosen basic checks: definition: Good (0,000) annual totals: Good (0,003) Match the annual totals of the original series and the seasonally adjusted series. visual spectral analysis spectral seas peaks: Good spectral td peaks: Good In the original series seasonal peaks and peaks of days are visually present Friedman statistic = 8,7207, P-value= Kruskall-Wallis st. = 47,1172, P-value=0.000 In the original series are present stable seasonal variations in the level of significance of 1%. regarima residuals normality: Good (0,461 ) independence: Good (0,873 ) spectral td peaks: Uncertain (0,088) spectral seas peaks: Uncertain (0,024) Residuals distributed normally, randomly and independently. The uncertainty of the visual assessment of spectral seasonal peaks and peaks of operating days in residuals (perhaps there are seasonal and calendar effects in residuals) residual seasonality on sa: Good (0,978) on sa (last 3 years): Good (0,994) on irregular: Good (1,000) There are no seasonal effects in the seasonally adjusted series, during the last 3 years, as well in the irregular components series. Residual seasonality test No evidence of residual seasonality in the entire series at the 10 per cent level: F=0,3231 No evidence of residual seasonality in the last 3 years at the 10 per cent level: F=0,2228 There are no indications of residual seasonal fluctuations in the entire series at 10% significance level. outliers number of outliers: Good (0,014) There are diverging values, but their number is not critical seats seas variance: Good (0,374) irregular variance: Good (0,323) seas/irr cross-correlation: Good (0, 113) Trend, seasonal and irregular component are independent (uncorrelated).

Check on a sliding seasonal factor Fig. 3

Stability of the model The graphs of seasonally adjusted series (SA, Fig. 4) and trend (Fig. 5) shows that the updates are insignificant. The model can be considered as stable, because the difference between the first and the last estimates does not exceed 3%. There is one value on the graph of the Trend, exceeding the critical limit (March 2010 = 1.976). January July February1.211 August March1.259 September April October May0.113 November June0.794 December Fig. 4 Fig. 5 Mean=0,3792 rmse= January0.222 July February1.167 August March1.976 September April October May November June1.042 December Seasonally adjusted series (SA) Trend

Analysis of the residuals Fig. 6 The test results shows that residuals are independent, random and normal. Tests for nonlinearity did not show non-linearity in the form of trends. P-value Ljung-Box on squared residuals(24)0,8708 Box-Pierce on squared residuals(24)0,9670

Residual seasonal factor Fig. 7 We can assume that there are no indicators of residual seasonal fluctuations in the residues. But there is one peak at the small spectral seasonal frequency and one at the frequency of operating days, which may mean that the used filters are not the best to remove them.

Some problematic results 1. How to connect the national calendar of holidays when applying built-in specs? 2. The curve of the seasonality graph has not a visually clear structure (Fig. 8). How to interpret this? 3. When using the model ARIMA model (0, 1, 0)(1, 0, 0) a purple line appeared on the chart (Fig. 9). What does it mean? 4. What does the lack of graphs in the autoregressive spectrum of the spectral analysis of residuals mean? Is it a problem if there are small spectral peaks in the periodogram? (Fig. 7, slide 12). Fig. 9Fig. 8

Some problematic results (continued) 5. How to correctly interpret a situation where innovation variance of the irregular component is lower than the trend and seasonality when using the ARIMA (0,1,0)(1, 0, 0) model? trend. Innovation variance = 0,0821 seasonal. Innovation variance = 0,1989 irregular. Innovation variance = 0, Is it a problem if there is hypothetical autocorrelation in the seasonally adjusted series of lag 6, with using the ARIMA (0,1,1)(0, 1, 1) model? Autocorrelation function seasonal : LagComponentEstimatorEstimatePValue 60,1167-0,6202-0,28980, Can they be considered as acceptable results of the Ljung-Box and Box-Pierce tests for the presence of seasonality in residuals at lags 24 and 36 when using ARIMA (0,1,0) (1, 0, 0), or does it mean not using a suitable model? LagAutocorrelationStandard deviationLjung-Box testP-Value 240,19180,11874,94820, ,11030,11876,75100,0342