# Non seasonal and seasonal parameters of this time-series

Cross Validated Asked by StatsMonkey on July 27, 2020

The ACF and PACF of a stationary timeseries "myts" is as given below:

> myts
[,1]  [,2]  [,3] [,4]  [,5]  [,6] [,7] [,8]  [,9] [,10] [,11] [,12] [,13] [,14] [,15]
ACF  -0.18 -0.11 -0.15 0.11 -0.31  0.03 0.54 0.00 -0.20 -0.12  0.07 -0.22 -0.01  0.38  0.14
PACF -0.18 -0.15 -0.21 0.02 -0.37 -0.16 0.53 0.14 -0.04 -0.05 -0.09  0.00 -0.11  0.02  0.20
[,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26] [,27] [,28] [,29] [,30]
ACF  -0.31  0.06 -0.03 -0.07 -0.15  0.40 -0.06 -0.15 -0.06  0.04 -0.09 -0.06  0.15  0.00 -0.03
PACF -0.18  0.24 -0.01 -0.01  0.02 -0.09 -0.18 -0.05 -0.12 -0.05  0.02  0.04 -0.18 -0.07  0.18
[,31] [,32] [,33] [,34] [,35] [,36] [,37] [,38] [,39] [,40] [,41] [,42] [,43] [,44] [,45]
ACF  -0.07  0.06 -0.07  0.01  0.02  0.05 -0.09  0.04 -0.01 -0.01 -0.05  0.05 -0.04 -0.01 -0.01
PACF -0.03 -0.06  0.04  0.01  0.03 -0.03 -0.02 -0.02  0.02  0.01 -0.09  0.05  0.04 -0.11 -0.09
[,46] [,47] [,48] [,49] [,50] [,51] [,52]
ACF   0.01  0.00  0.01  0.00 -0.01  0.00  0.00
PACF -0.02 -0.08 -0.03  0.02  0.06 -0.08  0.09


I read this and auto.arima(rawts) suggests ARIMA(0,1,0)(1,0,1)[7]. But I would like to know from ACF/PACF plots.

I found weekly season pattern in ACF. There are significant positive spikes in the ACF plot at lag 7,14 and 21. I assume ACF tails off and PACF Cuts off at lag 7. But I am unable to choose the parameters. Is it ARIMA(p=0,d=1,q=1)(P=1,D=0,Q=0)[7]….?

May I know what SARIMA parameters (p,d,q and P,D,Q)can be chosen based on the these ACF and PACF plots?

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