# Time Series Analysis: the Multiplicative Decomposition Method

**Topics:**Time series, Seasonal adjustment, Trend estimation

**Pages:**5 (1443 words)

**Published:**November 13, 2008

Table of Contents

Page

Abstract………………………………………………………………………………………………………………………………………….3 Introduction………………………………………………………………………………………………………………………...…4-5

Methodology: Multiplicative Decomposition……………………………………………….…5-7

Advantages/Disadvantages of Multiplicative Method………………………………7-8 Conclusion…………………………………………………………………………………………………………………………………..8

Abstract

One of the most essential pieces of information useful to compute sales, and the ability to forecast them is strategically important. Forecasts can provide useful information to cut costs, increase efficient use of resources, and improve the capability to compete in a frequently changing environment. This study tests complicated, yet simple to use time series models to forecast sales. The results will show that, with minor rearrangement of past sales data, easy-to-use time series models can accurately forecast gross sales .Forecasters often need to guesstimate doubtful quantities, but with restricted time and resources. Decomposition is a method for dealing with such problems by breaking down the estimation task down into a set of components that can be more readily estimated, and then combining the component estimates to generate an objective estimate. Estimators can effectively apply decomposition to either multiplicative or segmented forecasts, though multiplicative decomposition is especially sensitive to associated errors in component values. Decomposition is most used for highly unsure estimates, such as ones having a large numerical value or quantities. Decomposition should be used only when the estimation can make component estimates more accurately or more confidently than the target estimate.

Introduction

In today’s business world, businesses must strategically choose a methodology which is best suited for the company when unforeseeable haphazard’s cause economical disasters. In this case, a time series, the multiplicative decomposition method is used. According to Taylor (2007), a time series is a category of statistical techniques that uses historical data to predict future behavior. As for the Carlson/County department store case problem, this time series is a collection of observations of well defined data items obtained through repeated measurements over time. For instance, measuring the value of retail sales each month of the year would compromise a time series. This is because sales revenue is well defined, and consistently measured at equally space intervals. An observed time series can be decomposed into three components: the trend (long term), the seasonal (systematic, calendar related movements) and the irregular (unsystematic, short term fluctuations). The multiplicative decomposition method is a strategy that uses a multifactor (Yt = f (T,C,S,e) where Yt = actual value of the time series at time t f = mathematical function of T = trend, C = cyclical influences, S = seasonal influences and e = error (Hora, Dodd, & Hora, 1993). The trend component (T) in a time series is the long run general movement caused by long term economic, demographic, weather and technological movements. The cyclical is an influence of about three to nine years caused by economic, demographic, weather and technological changes in an industry or economy. The seasonal variations (S) are the result of weather and man-made conventions such as holidays. These can occur every year, month, week, or 24 hours. The error term (e) is simply the residual component of a time series that is not explained by T, C, and S. There are two types of decomposition models that can be used. They are the additive and the multiplicative decomposition models. Additive is expressed as Y = T + C + S + e and Multiplicative is expressed as Y = T*C*S*e. As you can see in the graph in the case problem, the determination of whether seasonal influences...

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