Performance of Seasonal Adjustment Procedures

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.
• Three methods of seasonal adjustment, that is,
  Census X12-ARIMA, TRAMO/SEATS and Dainties, are
  evaluated.
• We use simulated data and actual BCS data.

3
BCS data

• Business and consumer survey data are qualitative
  data.
• They are also bounded between 100 and -100
• 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.
• On the other hand, a unit root model can capture
  level shifts at unknown moments.

5
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.
• 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.
• 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.

7
Main idea of our study

• 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.
• 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.
• We use simulated and actual data for this
  purpose.

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Diagnostics

• 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?
• 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 consider cases with and without outliers

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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

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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.
• Finally, the BCS data come close to
  deterministic seasonality case, and this
  implies that the Dainties method is very useful.