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The residual of a seasonal_decompose (from python's statsmodels) yields the following ACF and PACF plots

ACF

PACF

The sampling frequency of the time series is hourly, so the ACF plot hints at daily (24 hour) seasonality, which is leaking from the seasonal_decomposition (I haven't been able to find a decomposition that doesn't leak some of this seasonality).

Anyway, I need to move forward and model this residual. However the SARIMAs I have so far used with orders (3,0,0)(0,0,4,24) haven't been doing very well. I see as a rule of thumb people take the significant ACF peaks to stand for MA orders, and significant PACF peaks to stand for AR orders, but I don't know the theoretical motivation behind that rule. Do you have any suggestions for how to capture this signal? It is normally distributed.

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interpreting the observed ACF and PACF an trying to match them to a candidate ARIMA model requires that the data under analysis

has no

1) step/level shifts 2) deterministic time trends 3) pulses 4) seasonal pulses

AND

that the resultant AIMA model has constant parameters and constant error variance over time

thus one needs to simultaneously consider factors 1-4 along with an ACF and PACF to form a useful model.

You probably want to include 23 hourly indicators and closely examine the residuals for your arma model. Hourly data offers the possibility of using deterministic structure. You may find the need for level/step shift indicators and/or time trends to capture additional deterministic structure. How many observations do you have ? Perhaps you should post your data.

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  • $\begingroup$ If you are happy with my answer , please accept it and close the question $\endgroup$ – IrishStat Aug 15 '19 at 8:00

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