Clarifying Time Series Models: Autocorrelation and Seasonality in ARIMA Analysis

[logarithmic]

Can anyone help clarify a few things about telling the time series model used based on the (partial) autocorrelation graphs. For example, if I have to difference a series once to get the autocorrelation and partial correlation graph completely within the confidence bands, does that mean it's ARIMA(0,1,0)? What if without differencing, there is 1 spike at the start of both the partial autocorrelation and the autocorrelations graphs, is that ARIMA(1,0,1) or is it either AR(1) or MA(1)? Also, if I think there's seasonality in the model, how do I incorporate that into the ARIMA model?

 

[lippyka]

Based on the information you have provided, it is difficult to definitively answer your questions. Generally speaking, if you have to difference the series once to get the autocorrelation and partial correlation graphs within the confidence bands, then it is likely ARIMA(0,1,0). If you have one spike at the start of both the partial autocorrelation and autocorrelation graphs without differencing, then it could be either AR(1) or MA(1). To incorporate seasonality into an ARIMA model, you can use the SARIMA (Seasonal ARIMA) model. This model takes into account the seasonal component of the data in addition to the regular ARIMA parameters.