Forecasting

NCSS Statistical Software

NCSS.com

Chapter 469

Decomposition

Forecasting

Introduction

Classical time series decomposition separates a time series into five components: mean, long-range trend,

seasonality, cycle, and randomness. The decomposition model is

Value = (Mean) x (Trend) x (Seasonality) x (Cycle) x (Random).

Note that this model is multiplicative rather than additive. Although additive models are more popular in other

areas of statistics, forecasters have found that the multiplicative model fits a wider range of forecasting situations.

Decomposition is popular among forecasters because it is easy to understand (and explain to others). While

complex ARIMA models are often popular among statisticians, they are not as well accepted among forecasting

practitioners. For seasonal (monthly, weekly, or quarterly) data, decomposition methods are often as accurate as

the ARIMA methods and they provide additional information about the trend and cycle which may not be

available in ARIMA methods.

Decomposition has one disadvantage: the cycle component must be input by the forecaster since it is not

estimated by the algorithm. You can get around this by ignoring the cycle, or by assuming a constant value. Some

forecasters consider this a strength because it allows the forecaster to enter information about the current business

cycle into the forecast.

Decomposition Method

The basic decomposition method consists of estimating the five components of the model

X t = UTt Ct S t Rt

where

Xt

denotes the series or, optionally, log of series.

U

Tt

denotes the mean of the series.

denotes the linear trend.

Ct

denotes cycle.

St

denotes season.

Rt

denotes random error.

t

denotes the time period.

We will now take you through the steps used by the program to perform a decomposition of a time series. Most of

this information is from Makridakis (1978), chapter 15.

469-1

© NCSS, LLC. All Rights Reserved.

NCSS Statistical Software

NCSS.com

Decomposition Forecasting...