Which of the following statement is correct?

1. If autoregressive parameter (p) in an ARIMA model is 1, it means that there is no auto-correlation in the series. 2. If moving average component (q) in an ARIMA model is 1, it means that there is auto-correlation in the series with lag 1. 3. If integrated component (d) in an ARIMA model is 0, it means that the series is not stationary.

Solution

Autoregressive component: AR stands for autoregressive.  Autoregressive parameter is denoted by p.  When p =0, it means that there is no auto-correlation in the series.  When p=1, it means that the series auto-correlation is till one lag.

Integrated: In ARIMA time series analysis, integrated is denoted by d.  Integration is the inverse of differencing.  When d=0, it means the series is stationary and we do not need to take the difference of it.  When d=1, it means that the series is not stationary and to make it stationary, we need to take the first difference.  When d=2, it means that the series has been differenced twice.  Usually, more than two time difference is not reliable.

Moving average component: MA stands for moving the average, which is denoted by q.  In ARIMA, moving average q=1 means that it is an error term and there is auto-correlation with one lag.