Testing seasonal Testing seasonal adjustment adjustment

with Demetra+with Demetra+

Dovnar Olga AlexandrovnaThe 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 (1.2005-12.2010) 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. 1In 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 usedUser-defined specification TramoSeatsSpec-1 was

used:

Options Values

Transformation – Function

Auto

Calendar holidays of Belarus, td2

The Easter No

Automatic modelling ARIMA

True

Deviating values True

Pre-treatment

The estimated period: [1-2005 : 12-2010]

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. 2Seasonal 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 B12)at , σ2 = 1,

decomposed into three sub-models: Trend model: (1 + 0,1B - 0,9B2)ap,t., σ2 = 0,0334

Seasonal model: (1 + 1,43B + 1,51B2 + 1,45 B3 + 1,25B4 + 1,01B5 + 0,74B6 + +0,47B7 + 0,24B8 + 0,03B9 + 0,11B10 - 0,40B11)as,t, σ2 = 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 qualityDiagnosis and result Explanation

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=0.000. 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 testNo evidence of residual seasonality in the entire series at the 10 per cent level: F=0,3231No 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 -0.009 July 0.380

February 1.211 August 0.831

March 1.259 September 0.509

April -0.249 October -0.363

May 0.113 November -0.385

June 0.794 December

Fig. 4 Fig. 5

Mean=0,3792 rmse=0.6888 Mean=0,3792 rmse=0.6888January 0.222 July 0.369

February 1.167 August 1.128

March 1.976 September 1.138

April -0.196 October -0.517

May -0.077 November -0.697

June 1.042 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.

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 results1. 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 = 0,0821seasonal. Innovation variance = 0,1989irregular. Innovation variance = 0,0971

6. 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 :

Lag Component Estimator Estimate PValue

6 0,1167 -0,6202 -0,2898 0,0490

7. 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?

Lag Autocorrelation Standard deviation Ljung-Box test P-Value

24 0,1918 0,1187 4,9482 0,0261

36 -0,1103 0,1187 6,7510 0,0342