1. Performance of Seasonal Adjustment Procedures Philip Hans Franses, Richard Paap, and Dennis Fok Econometric Institute Erasmus University Rotterdam

2. Outline This study concerns the seasonal adjustment of business and consumer survey [BCS] data. This study concerns the seasonal adjustment of business and consumer survey [BCS] data. Three methods of seasonal adjustment, that is, Census X12-ARIMA, TRAMO/SEATS and Dainties, are evaluated. Three methods of seasonal adjustment, that is, Census X12-ARIMA, TRAMO/SEATS and Dainties, are evaluated. We use simulated data and actual BCS data. We use simulated data and actual BCS data.

3. BCS data Business and consumer survey data are qualitative data. Business and consumer survey data are qualitative data. They are also bounded between 100 and -100 They are also bounded between 100 and -100 What are the time series properties? What are the time series properties?

4. Trend For the trend, a deterministic trend model is implausible. Similarly, a trend model of the unit root type is more plausible. For the trend, a deterministic trend model is implausible. Similarly, a trend model of the unit root type is more plausible. On the other hand, a unit root model can capture level shifts at unknown moments. On the other hand, a unit root model can capture level shifts at unknown moments.

5. Seasonality Strictly speaking, there should be no seasonality! Strictly speaking, there should be no seasonality! The surveys involve questions where respondents should compare the past months to future months. For the consumer surveys the comparison period is 12 months, whereas for the business surveys it is mostly 3 months. In all cases respondents are explicitly asked to disregard seasonal influences. The surveys involve questions where respondents should compare the past months to future months. For the consumer surveys the comparison period is 12 months, whereas for the business surveys it is mostly 3 months. In all cases respondents are explicitly asked to disregard seasonal influences. If there is seasonality, it is either due to the respondents’ inability to disregard seasonality or to features from the outside, like the weather or festivals. In sum, seasonal variation in BCS data is probably not strong, and also, it is unlikely to change much over time. If there is seasonality, it is either due to the respondents’ inability to disregard seasonality or to features from the outside, like the weather or festivals. In sum, seasonal variation in BCS data is probably not strong, and also, it is unlikely to change much over time.

6. Outliers BCS data may have outliers, either additive outliers or innovation outliers. BCS data may have outliers, either additive outliers or innovation outliers. When a unit-root trend model is imposed, all outlier observations will be of the additive type. When a unit-root trend model is imposed, all outlier observations will be of the additive type. Seasonal adjustment should be robust to an unknown but not too large amount of additive outliers at unknown locations. Seasonal adjustment should be robust to an unknown but not too large amount of additive outliers at unknown locations.

7. Main idea of our study We examine the link between models for seasonal data and the assumptions underlying the three seasonal adjustment methods. We examine the link between models for seasonal data and the assumptions underlying the three seasonal adjustment methods. The methods do not specifically assume a certain model, but it can be envisaged that some methods would work best for data which could be described by a certain model. The methods do not specifically assume a certain model, but it can be envisaged that some methods would work best for data which could be described by a certain model. For example, if the seasonal adjustment method would simply be that one subtracts seasonal means from the data, then data according to a model with constant deterministic seasonality would be best adjusted using that particular method. For example, if the seasonal adjustment method would simply be that one subtracts seasonal means from the data, then data according to a model with constant deterministic seasonality would be best adjusted using that particular method. In sum, we aim to see which type of data would be “best adjusted” by which method. In sum, we aim to see which type of data would be “best adjusted” by which method. We use simulated and actual data for this purpose. We use simulated and actual data for this purpose.

8. Diagnostics We use tests, which are based on the statistical relevance of parameters in certain regression models. We use tests, which are based on the statistical relevance of parameters in certain regression models. These diagnostics either focus on (i) does the seasonal adjustment method effectively remove seasonality?, (ii) does the seasonal adjustment method change features of the time series other than seasonality? These diagnostics either focus on (i) does the seasonal adjustment method effectively remove seasonality?, (ii) does the seasonal adjustment method change features of the time series other than seasonality? They concern seasonal unit roots, seasonality in variance, seasonality in means, and periodicity in AR parameters. They concern seasonal unit roots, seasonality in variance, seasonality in means, and periodicity in AR parameters.

9. Data generating processes We use six data generating processes in the simulations. These concern stable seasonality, unit root-type seasonality, time-varying parameter seasonality, and no seasonality. All have parameters that are commonly found in practice. We use six data generating processes in the simulations. These concern stable seasonality, unit root-type seasonality, time-varying parameter seasonality, and no seasonality. All have parameters that are commonly found in practice. We consider cases with and without outliers We consider cases with and without outliers

10. Findings (1) Census X12-ARIMA and TRAMO/SEATS methods are most robust to variations in the data generating process. This implies that in case one would not have any strong indications as to which model could best describe the raw (unadjusted) data, then these two methods are to be preferred. (2) Dainties method performs relatively well when the data show patterns that are close to deterministic seasonality.

11. Findings-2 (3) The effect of additive outliers on the performance of the adjustment methods is relatively small. Especially, the Census X-12 method seems to handle these outliers quite well. (4) All three adjustment methods are very sensitive to innovation outliers. It seems that none of the methods is capable of removing these types of outliers adequately from the series before seasonal adjustment. This is especially true if the series contains seasonal unit roots. (5) No differences between “first aggregation and then adjustment” and “first adjustment and then aggregation”

12. Findings BCS data When we compare the performance of the three seasonal adjustment methods on 300 series from the business and consumer surveys, we find that there are no marked differences in the performance of the three seasonal adjustment methods. When we compare the performance of the three seasonal adjustment methods on 300 series from the business and consumer surveys, we find that there are no marked differences in the performance of the three seasonal adjustment methods. Finally, the BCS data come close to “deterministic seasonality case”, and this implies that the Dainties method is very useful. Finally, the BCS data come close to “deterministic seasonality case”, and this implies that the Dainties method is very useful.