Components of Time Series, Seasonality and Pre-conditions for Seasonal Adjustment

1. UNECE Workshop on Short-Term Statistics (STS) and Seasonal Adjustment 14 – 17 March 2011, Astana, Kazakhstan Components of Time Series, Seasonality and Pre-conditions for Seasonal Adjustment Anu Peltola Economic Statistics Section, UNECE

2. Overview • Basic Concepts • Components of Time Series • Seasonality • Pre-conditions for Seasonal Adjustment

3. new observation old observation x 100 Basic Concepts • Index comes from Latin and means a pointer, sign, indicator, list or register • A ratio that measures change • As per cent of a base value (base always 100) • Each observation is compared to the base value • Time series are a collection of observations, measured at equally spaced intervals • Stock series = at a point in time (discrete) • Flow series = period in time (continuous)

4. Components of Time Series • Seasonal adjustment is based on the idea that time series can be decomposed • The components are: • Seasonal • Irregular • Trend

5. Relation of Components Components of the Industrial Production Index of Kazakhstan Index 2005=100

6. Seasonal Component = Depicts systematic, calendar-related movements • has a similar pattern from year to year • refers to the periodic fluctuations within a year that re-occur in approximately the same way annually • Is removed in seasonal adjustment

7. Irregular Component = Depicts unsystematic, short term fluctuations • The remaining component after the seasonal and trend components have been removed • Certain specific outliers, such as those caused by strikes, also belong to this component • Sometimes called the residual component • May or may not be random with random effects (white noise) or artifacts of non-sampling error (not necessarily random)

8. Trend Component = Depicts the long-term movement in a series • A trend series is derived by removing the irregular influences from the seasonally adjusted series • A reflection of the underlying development • Typically due to influences such as population growth, technological development, inflation and general economic development • Sometimes referred to as the trend-cycle

9. IPI – KazakhstanAn Example of the Components of Time Series Index 2005=100

10. Causes of Seasonality = seasons e.g. holidays and consumption habits, which are related to the rhythm of the year • Warmth in summer and cold in winter BUT not extreme weather conditions (irregular component) • Seasonality reflects traditional behavior associated with: • The calendar • Christmas and New Year • Social habits (the holiday season), • Business (quarterly provisional tax payments) and • Administrative procedures (tax returns)

11. Seasonality Industrial production in Moldova, original series 2000-2008 Index 2005=100 months

12. Seasonal Effect = Intra-year fluctuations in the series that repeat • A seasonal effect is reasonably stable with respect to timing, direction and magnitude • The seasonal component of a time series is comprised of three main types of systematic calendar-related influences: • Seasonal influences • Trading day influences • Moving holiday influences

13. Trading Day Effect = The impact on the series, of the number and type of days in a particular month • Different days may have a different weight • A calendar month comprises four weeks (28 days) plus extra one, two or three days • Rarely an issue in quarterly data, since quarters have 90, 91 or 92 days

14. Trading Days Saturday Source: Analysis of Daily Sales Data during the Financial Panic of 2008, John B. Taylor (Target Corporation’s sales)

15. Moving Holidays = The impact on the series of holidays whose exact timing shifts from year to year • Examples of moving holidays: • Easter • Chinese New Year - where the exact date is determined by the cycles of the moon • Ramadan

16. Moving Holidays Impact of moving holidays to the number of working days Ascension day Christmas moves between weekdays and weekend

17. Working Days and Seasonality Example of average working days in 2009 - 2011

18. Sudden Changes • Outliers • Extreme values with identifiable causes (strikes or extreme weather conditions) • Part of irregular component • Trend breaks (level shifts) • The trend component suddenly increases or decreases in value • Often caused by changes in definitions (tax rate, reclassification) • Seasonal breaks • The seasonal pattern changes, e.g. due to a structural change caused by a crisis or administrative issues such as timing of invoicing

19. Pre-conditions for Seasonal Adjustment • Good quality of raw data • Strange values to be checked (zeros or outliers) • Revision of errors with new acquired data • Length of time series 36/12 or 16/4 • At least 36 observations for monthly series and 16 observations for quarterly series needed • Consistent time series • To provide data according to a base year • Use of comparable definitions and classifications • Remove non-comparable changes • Solid structure • Presence of seasonality, moderate volatility • No major breaks in seasonal behaviour