Paper 454-2013

THE BOX-JENKINS METHODOLOGY FOR TIME SERIES MODELS THERESA HOANG DIEM NGO, WARNER BROS. ENTERTAINMENT GROUP, BURBANK, CA

ABSTRACT

A time series is a set of values of a particular variable that occur over a period of time in a certain pattern. The most common patterns are increasing or decreasing trend, cycle, seasonality, and irregular fluctuations (Bowerman, O’Connell, and Koehler 2005). To model a time series event as a function of its past values, analysts identify the pattern with the assumption that the pattern will persist in the future. Applying the Box-Jenkins methodology, this paper emphasizes how to identify an appropriate time series model by matching behaviors of the sample autocorrelation function (ACF) and partial autocorrelation function (PACF) to the theoretical autocorrelation functions. In addition to model identification, the paper examines the significance of the parameter estimates, checks the diagnostics, and validates the forecasts.

INTRODUCTION

This paper is an introduction to applied time series modeling for analysts who have minimum experience in model building, but are not very familiar with time series models. It would help to have a basic understanding of regression analysis such as simple linear regression or multiple regressions. The challenge of modeling is to diagnose the problem and decide on an appropriate model to help answer the real-world questions. It takes experience to develop an ability to formulate appropriate statistical models and to interpret the results, but this paper gives a head start on practicing these techniques.

NON-SEASONAL BOX-JENKINS MODEL IDENTIFICATION

Before identifying the pattern, the time series values must be stationary where its mean and variance are constant through time. The constant mean and variance can be achieved by removing the pattern caused by the time dependent autocorrelation. Besides looking at the plot of the time series values over time to determine stationary or non-stationary, the sample autocorrelation function (ACF) also gives visibility to the data. If the ACF of the time series values either cuts off or dies down fairly quickly (Figure 1(a)), then the time series values should be considered stationary. On the other hand, if the ACF of the time series values either cuts off or dies down extremely slowly (Figure 1(b)), then it should be considered non-stationary. In general, if the original time series values are nonstationary and non-seasonal, perform the first or second differencing transformation on the original data will usually produce stationary time series values.