Components of Time Series, Seasonality and Pre-conditions

for Seasonal Adjustment

Anu PeltolaEconomic Statistics Section, UNECE

UNECE Workshop on Short-Term Statistics (STS) UNECE Workshop on Short-Term Statistics (STS) and Seasonal Adjustmentand Seasonal Adjustment14 – 17 March 2011, Astana, Kazakhstan

March 2011 UNECE Statistical Division Slide 2

Overview

Basic Concepts Components of Time Series Seasonality Pre-conditions for Seasonal Adjustment

March 2011 UNECE Statistical Division Slide 3

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)

new observation

old observation

x 100

March 2011 UNECE Statistical Division Slide 4

Components of Time Series

Seasonal adjustment is based on the idea that time series can be decomposed

The components are:SeasonalIrregularTrend

March 2011 UNECE Statistical Division Slide 5

Trend-Cycle Component

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Relation of ComponentsComponents of the Industrial Production Index of Kazakhstan

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March 2011 UNECE Statistical Division Slide 6

Seasonal Component

= Depicts systematic, calendar-related movements

has a similar pattern from year to yearrefers 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 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)

March 2011 UNECE Statistical Division Slide 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

March 2011 UNECE Statistical Division Slide 9

IPI – KazakhstanAn Example of the Components of Time Series

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March 2011 UNECE Statistical Division Slide 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)

March 2011 UNECE Statistical Division Slide 11

Seasonality

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Industrial production in Moldova, original series 2000-2008

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March 2011 UNECE Statistical Division Slide 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

March 2011 UNECE Statistical Division Slide 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

March 2011 UNECE Statistical Division Slide 14

Trading DaysSaturday

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 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

March 2011 UNECE Statistical Division Slide 16

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Moving HolidaysImpact of moving holidays to the number of working days

Ascension day Christmas moves between weekdays and weekend

March 2011 UNECE Statistical Division Slide 17

Working Days and Seasonality

Example of average working days in 2009 - 2011

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March 2011 UNECE Statistical Division Slide 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

March 2011 UNECE Statistical Division Slide 19

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• Presence of seasonality, moderate volatility• No major breaks in seasonal behaviour