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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 Overview Basic Concepts Components of Time Series Seasonality Pre-conditions for Seasonal Adjustment March 2011 UNECE Statistical Division Slide 2 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 new observation old observation x 100 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) March 2011 UNECE Statistical Division Slide 3 Components of Time Series Seasonal adjustment is based on the idea that time series can be decomposed The components are: Seasonal Irregular Trend March 2011 UNECE Statistical Division Slide 4 March 2011 UNECE Statistical Division Jul- 10 Jan-10 Jul- 09 Jan-09 Jul- 08 50 Jan-08 50 Jul- 07 60 Jan-07 60 Jul- 06 70 Jan-06 80 Jul- 05 100 Jan-05 110 Jul- 04 130 Jan-04 Irregular component Jul- 03 Jan-10 Jan-09 Jan-08 Jan-07 Jan-06 Jan-05 Jan-04 Jan-03 50 Jan-03 60 Jan-02 80 Jul- 02 120 Jan-02 90 Jan-01 90 Jul- 01 100 Jan-01 80 Jan-00 130 Jul- 00 Jan-10 Jan-09 Jan-08 Jan-07 Jan-06 Jan-05 Jan-04 Jan-03 Original component Jan-00 Jan-10 Jan-09 Jan-08 Jan-07 Jan-06 Jan-05 Jan-04 Jan-03 120 Jan-02 Jan-01 Jan-00 140 Jan-02 Jan-01 Jan-00 Index 2005=100 Relation of Components Components of the Industrial Production Index of Kazakhstan Seasonal component 120 110 110 100 70 70 60 50 Trend-Cycle Component 120 110 90 100 90 80 70 Slide 5 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 March 2011 UNECE Statistical Division Slide 6 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 nonsampling error (not necessarily random) March 2011 UNECE Statistical Division Slide 7 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 March 2011 UNECE Statistical Division Slide 8 IPI – Kazakhstan An Example of the Components of Time Series 140 120 110 100 90 80 70 60 Original March 2011 Seasonally adjusted UNECE Statistical Division Jul-10 Jan-10 Jul-09 Jan-09 Jul-08 Jan-08 Jul-07 Jan-07 Jul-06 Jan-06 Jul-05 Jan-05 Jul-04 Jan-04 Jul-03 Jan-03 Jul-02 Jan-02 Jul-01 Jan-01 Jul-00 50 Jan-00 Index 2005=100 130 Trend Slide 9 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: March 2011 The calendar Christmas and New Year Social habits (the holiday season), Business (quarterly provisional tax payments) and Administrative procedures (tax returns) UNECE Statistical Division Slide 10 Seasonality Industrial production in Moldova, original series 2000-2008 150 140 130 2000 2001 Index 2005=100 120 2002 2003 110 2004 100 2005 2006 90 2007 2008 80 70 60 1 March 2011 2 3 4 5 6 months 7 8 9 UNECE Statistical Division 10 11 12 Slide 11 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 March 2011 UNECE Statistical Division Slide 12 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 March 2011 UNECE Statistical Division Slide 13 Trading Days Saturday Source: Analysis of Daily Sales Data during the Financial Panic of 2008, John B. Taylor (Target Corporation’s sales) March 2011 UNECE Statistical Division Slide 14 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 March 2011 UNECE Statistical Division Slide 15 Moving Holidays Impact of moving holidays to the number of working days Ascension day Christmas moves between weekdays and weekend 25 average working days 20 15 2009 2010 2011 10 5 0 Jan March 2011 Feb Mar Apr May Jun Jul Aug Sep UNECE Statistical Division Oct Nov Dec Slide 16 Working Days and Seasonality Example of average working days in 2009 - 2011 25 average working days 20 15 2009 2010 2011 10 5 0 Jan March 2011 Feb Mar Apr May Jun Jul Aug Sep Oct UNECE Statistical Division Nov Dec Slide 17 Sudden Changes Outliers • • Trend breaks (level shifts) • • Extreme values with identifiable causes (strikes or extreme weather conditions) Part of irregular component 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 March 2011 UNECE Statistical Division Slide 18 Pre-conditions for Seasonal Adjustment 1. Good quality of raw data • • Strange values to be checked (zeros or outliers) Revision of errors with new acquired data 2. Length of time series 36/12 or 16/4 • At least 36 observations for monthly series and 16 observations for quarterly series needed 3. Consistent time series • • • To provide data according to a base year Use of comparable definitions and classifications Remove non-comparable changes 4. Solid structure • • March 2011 Presence of seasonality, moderate volatility No major breaks in seasonal behaviour UNECE Statistical Division Slide 19