An autoregressive integrated moving average (ARIMA) model is one of the most general classes of models used for forecasting a time series which can be made stationary by differencing. A stationary time serieshas no trend, and has consistent movement or variation around the mean. Furthermore, its short term variability and autocorrelation (correlation between the current observation and past observations) is consistent throughout time. An ARIMA model can be viewed as a “filter” that tries to separate the true signal in the time series from random noise. The signal is then used to forecast future observations to obtain forecasts.

An ARIMA model consists of 3 parameters specified as (p,d,q). A Seasonal ARIMA model consists of 6 parameters specified as (p,d,q)(P,D,Q). In an ARIMA model, each value for (p,d,q)(P,D,Q) is generally a whole number integer value. Here p represents the autoregressive structure of the nonseasonal time series component, d consists of the nonseasonal difference component, and q consists of the nonseasonal moving average component. P, D, and Q represent the seasonal versions of the same components. An ARIMA model will consist of either 3 or 6 of these parameters depending on the instrument being forecast and the individual properties of that series. These components are specified by looking at autocorrelation function plots for the moving average component (Q, q) of the time series and partial autocorrelation function plots (P, p) of the time series and resulting residuals. The differencing parameters (D, d) will be used if necessary to make the series stationary. The appropriate autoregressive and moving average parameter values can be determined by addressing the autocorrelation and partial autocorrelation function plots of the instrument and model residuals. Information regarding these plots are presented in Section 6. Both ARIMA and seasonal ARIMA models are estimated for each instrument as necessary.

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