The unece organizes with the financial support of the World Bank

Seasonal Adjustment Approach

Pre-Treatment of Time Series

• = 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:

• Φ(B) = (1+ Φ1B + … + ΦpBp)(1+ Φ1Bs + …+ ΦPBs×P)

• δ(B) = (1-B)d(1-Bs)D

•