1. Working with Planning
  2. Predictive Planning Forecasting and Statistical Descriptions
  3. ARIMA Time-series Forecasting Methods

ARIMA Time-series Forecasting Methods

Autoregressive integrated moving average (ARIMA) forecasting methods were popularized by G. E. P. Box and G. M. Jenkins in the 1970s. These techniques, often called the Box-Jenkins forecasting methodology, have the following steps:

  1. Model identification and selection

  2. Estimation of autoregressive (AR), integration or differencing (I), and moving average (MA) parameters

  3. Model checking

ARIMA is a univariate process. Current values of a data series are correlated with past values in the same series to produce the AR component, also known as p. Current values of a random error term are correlated with past values to produce the MA component, q. Mean and variance values of current and past data are assumed to be stationary, unchanged over time. If necessary, an I component (symbolized by d) is added to correct for a lack of stationarity through differencing.

In a nonseasonal ARIMA(p,d,q) model, p indicates the number or order of AR terms, d indicates the number or order of differences, and q indicates the number or order of MA terms. The p, d, and q parameters are integers equal to or greater than 0.

Cyclical or seasonal data values are indicated by a seasonal ARIMA model of the format:

SARIMA(p,d,q)(P,D,Q)(t)

The second group of parameters in parentheses are the seasonal values. Seasonal ARIMA models consider the number of time periods in a cycle. For a year, the number of time periods (t) is 12.

Note:

In Predictive Planning charts, tables, and reports, seasonal ARIMA models do not include the (t) component, although it is still used in calculations.

Predictive Planning ARIMA models do not fit to constant datasets or datasets that can be transformed to constant datasets by nonseasonal or seasonal differencing. Because of that feature, all constant series, or series with absolute regularity such as data representing a straight line or a saw-tooth plot, do not return an ARIMA model fit.

Estimation of ARIMA Model Coefficients

For a given ARIMA model, Predictive Planning uses the unconditional least square method to estimate model coefficients. Instead of using matrix algebra, a simpler iterative scheme is used (Box, G. E. P., Jenkins, G. M., and Reinsel, G. C. Time Series Analysis: Forecasting and Control. 4th ed. Hoboken, NJ: John Wiley & Sons. 2008.).