Model Selection, Seasonal Adjustment, Analyzing Results

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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

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04.04.2016
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Model Selection

• Pre-treatment is the most important stage of the
  seasonal adjustment
• X-12-ARIMA and TRAMOSEATS 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

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04.04.2016
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ARIMA Model selection

• zt ytßxt
• F(B)d(B)xt?(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

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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.

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Diagnostics

• Seasonality test
• 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

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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)

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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)

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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?

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Filtering data Difference in methods

• TRAMOSEATS 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
  TramoSeats. 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.

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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)

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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
Germany
Manufacturing
France
Electricity, Water, Natural Gas and etc.
Spain
...
Romania
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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.

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Analyzing results
Seasonally Adjusted Series
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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

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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
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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