TIMCAI: An interactive program to assist in the identification of univariate nonseasonal nonmixed ARIMA time series

Abstract

The need for accurate statistical techniques in the interpretation of time-series data is crucial for many social-psychological studies. While many techniques have been proposed and debated, the technique initially proposed by Box and Tiao (1965) known as autoregres­ sive integrated moving average (ARIMA) modeling seems to show promise. While much has been written about the technique, there seems to be some reluctance on the part of the social-psychological community to use it when appropriate. One of the major reasons for this reluctance may be due to difficulties in the initial step of identify­ ing an appropriate ARIMA model. Other reasons for the reluctance have been discussed elsewhere (Brown, 1980; McCleary & Hay, 1980). The Box-Tiao approach is an iterative process encom­ passing several stages of development, with the initial step requiring a tentative model identification. This identification step basically relies on two statistics: (1) the autocorrelation function (AUCF) and (2) the partial autocorrelation function (PACF). Autocorrela­ tion refers to the correlations among successive data points separated by each different observation (lag) in the series. Partial autocorrelation refers to the autocorre­ lation of a series with the influence of previous time points partialed out. These two functions are calcu­ lated on the time-series data and generally supplied to the users as a correlogram, or a plot of the autocorrela­ tion and partial autocorrelation as a function of K lags. It is from an ocular analysis of the correlograms that a tentative ARIMA model may be identified. This ocular analytic technique basically compares the estimated AUCF and PACF with theoretical or expected functions, according to a variety of basic ARIMA models. Ambi­ guity in these estimated functions is then lessened by either placing an approximate 95% confidence band around each function (±2 standard errors) or by calcu­ lating a t-like statistic (Bowerman & O'Connell, 1979). The t-like statistic, for both functions, is simply the value of each AUCF and PACF over their respective standard errors at each lag period. The purpose of this software is to assist users in their ocular identification of an appropriate ARIMA model by providing statistically based decision support.