= graphical analysis, calendar adjustment, model selection, filters, outliers and parameters
Frequency of updating parameters varies
Some do not regularly update the parameters
Some update them, when new data appends
One country updates also in case of atypical weather conditions
The choice of regressor differs
The most commonly used regressor in seasonal adjustment is either working days or working days and specific holidays
Outliers are detected in most cases by tests
Outliers are validated by experts in Armenia, Bosnia and Herzegovina and Kazakhstan
It is recommended to document events causing outliers!
Validation of Seasonal Adjustment
Mostly by using graphical inspection, autocorrelation function and measures of stability over time
Graphical inspection:
Deviation between the raw and SA series
Standard deviation relative to trend
Intuitive assessment
Two countries mentioned analysing significant peaks of the autocorrelogram of the raw series
One uses the Box-Pierce statistics and three use F-tests
Use of validation measures depends on the SA software used
Validation of Seasonal Adjustment
Residuals and fit statistics were less used
Four countries mentioned using M-Statistics as a quality measure of the results
A set of common quality measures are being constructed
US Census Bureau, Eurostat and the Bank of Spain
For all seasonally adjusted series to be assessed by the same criteria
> Demetra+ includes some quality measures both from X-12-ARIMA and TRAMO/SEATS
Validation of Seasonal Adjustment
Plans for Future Development
Future Measures
All reported some need for assistance
UNECE will organize training workshops in 2010 – 2012
Methodological material and practical guidelines will be produced and published also in Russian
What are your plans now?
Will be discussed next
Pre-treatment practices for Seasonal Adjustment Including Calendar Adjustment
Necmettin Alpay KOÇAK
UNECE Workshop on Short-Term Statistics (STS) and Seasonal Adjustment
14 – 17 March 2011
Astana, Kazakhstan
Introduction
Seasonal adjustment is a statistical procedure with the target of removing the seasonal (and calendar) component from a time series.
The idea behind is that a series is composed by unobserved components such as trend, cycle, seasonality, irregular
The seasonal component disturbs short-term analysis, so it is removed from the original series to facilitate the monitoring and interpretation of the economy by analysts
First step: the graph of the series
First step: the graph of the series
The unobserved components
Decomposition scheme
The REG-ARIMA model
The REG-ARIMA model is a convenient way to represent a time series with deterministic and stochastic effects. Given the observed time series zt , it is expressed as,
zt = ytβ+xt
Φ(B)δ(B)xt=θ(B)at
where
β is a vector of regression coefficients
yt denotes n regression variables
B is the backshift operator (Bkyt = yt-k )
Φ(B), δ(B), and θ(B) are finite polynomials in B
at is assumed a normal independently identically distributed (NIID) (0,σa2) white-noise innovation
The regression variables
The regression variables capture the deterministic components of the series. In TS, these can be of different type:
Calendar effects
Trading day effect
Easter effect
Leap-year effect
Holidays
Intervention variables generated by the program
Regression variables entered by the user
Outliers
The ARIMA model
Model-based-pre-adjustment identifies and fits an ARIMA model on the linearized series (cleaned from deterministic effects). The ARIMA model is composed of three components:
the stationary AR component (polynomial Φ(B))
the non-stationary AR component (polynomial δ(B))
the invertible MA component (polynomial θ(B))
For seasonal time series, the polynomials are given by:
