Profit From Your Forecasting Software

CHAPTER 5Box-Jenkins ARIMA Models

5.1 INTRODUCTION

The Box-Jenkins method is a relatively advanced approach to short-term forecasting that exploits the autocorrelations between observations at different points in time to produce forecasts. Like exponential smoothing, it is a univariate method, so it only uses data in the sales history to produce its forecasts. The method involves a formal series of steps, which include identifying a tentative model and then using a battery of diagnostic tests to assess the model's adequacy. However, some software packages will automatically identify and fit the most appropriate model for you. Later, we will look at why Box-Jenkins models are also called ARMA or ARIMA models; but first, we'll explore the models that are appropriate when we have a sales history that is described as stationary.

5.2 STATIONARITY

Stationary time series are sales histories that have an underlying structure that does not change over time. For example, their underlying mean and their variability remain the same. There are a number of ways of assessing whether series are stationary, but we can gain an initial idea by looking at the graph of the series. In Figure 5.1, the upward-sloping series is nonstationary – clearly, the mean level of sales gets larger over time. The “flat” series is stationary – the underlying mean level of sales does not change over time. The series in Figure 5.2 is not stationary. Its underlying mean is the same, but its variability increases ...