A model for a time series with a constant mean (taken as 0). Let x1, x2,…be successive values of the random variable X, measured at regular intervals of time and let ε1, ε2,…denote the corresponding random errors. A pth-order moving average model with parameters α1, α2,…, αp relates the value at time j (≥p+1) to the preceding p error values bySuch a model is written in brief as MA(p). The errors are presumed to be independent and to have mean 0 and hence the X-variables also have mean 0. Moving average models can also be expressed as autoregressive models. Models combining both type of process include ARMA models and ARIMA models.