# Determine paramaters for SARIMA model

I have the following timeseries with a frequency of 12 (months). Since there is both a trend and seasonality, I differenced the timeseries. To determine the parameters p, q, P and Q for the SARIMA(p, 1, q)(P, 1, Q)_12 model, I look at the ACF and PACF of the differenced timeseries, shown below.

Now how do I determine the values for p, q, P and Q? I am having trouble reading the ACF and PACF. My guess is parameter P is 0 because the PACF does not show spikes at lag 24 and parameter Q is 2 because the ACF shows 2 spikes after lag 0, 12 and 24. Am I correct so far? About parameters p and q I am clueless.

As a note: auto.arima() gives a SARIMA(1,1,2)(0,1,2)_12 model.

• Post your data... – Tom Reilly Jan 4 '19 at 19:22
• @TomReilly why? My question is about how to interpret the ACF and PACF plots shown in the question... – Stan Jan 5 '19 at 8:25
• The ACF and the PACF are summaries and often fail to correctly identify 1) the need and kind of differencing required 2) the AR and MA structure 3) the confounding ( and confusing ) presence of Pulses , Seasonal Pulses, Step/Level shifts and Local time Trends 3) The need for either Power transforms or wighted estimation to deal with non-constant error variance 4) the presence of time varying parameters . The interpretation ( what u are asking for) can be confused and confusing if 1,3,4, and 5 are in play. – IrishStat Jan 6 '19 at 20:05
• See @AdamO's insightful response to this question stats.stackexchange.com/questions/317734/… "The correlogram should be calculated from residuals using a model that controls for intervention administration, otherwise the intervention effects are taken to be Gaussian noise, underestimating the actual autoregressive effect." – IrishStat Jan 6 '19 at 20:11