Autoregressive, Integrative, Moving Average (ARIMA) Models

ARIMA is an acronym for autoregressive, integrative, moving average models. It is an approach to time-series analysis sometimes referred to as the [Page 77]Box-Jenkins approach. The three terms that compose the name are three different forms of serial dependency often found in time-series data. Because time-series data are repeated measures on the same case sequenced in time, each observation is not independent of the other observations in the sequence (i.e., serial dependency) resulting in correlated errors. This means that the data violate the assumptions of most standard traditional statistical tests like regression and analysis of variance (ANOVA). ARIMA models are stochastic in that they assume that the serial dependency is greatest among observations that are temporally proximate (e.g., values adjacent in a sequence), but that dependency lessens as the observations become further removed in time. ARIMA models generally assume that data values are at least interval level and each data point is equally spaced in time.

The logic behind ARIMA analysis is to first identify the form of serial dependency in the time-series data. Next, that serial dependency is removed from the time-series data through a process called prewhitening, leaving a white noise process that is free of serial dependency. This is done, not only to eliminate the problem of correlated errors, but also because if two time series have similar temporal patterns, this can produce a spurious association between two variables that may not be the result of the influence of one variable on another. Once the time series is a white noise process (i.e., each value in the series is statistically independent from other values in the same series, with a mean of 0 and constant variance across the series), the researcher can examine its association with other contemporaneous time series representing other variables or forecast future values.

In mass communication research, ARIMA has been applied to agenda setting research as well as other applications. In interpersonal research, it has been used to examine the mutual adaptation of dyadic partners during conversations. This entry discusses both univariate ARIMA and bivariate ARIMA modeling.