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I am trying to model a data series using ARIMA model. The series seems non stationary because the acf decays very gradually.Even after differencing two times, the values of p and q are coming as high as 115 and 120.On differencing for 3rd time , values of p and q are under 10.So is it fine to take higher values of d (as in 3 or more) or should I interpret that higher values of p and q indicate that ARIMA model is not well suited for my series.

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    $\begingroup$ What is the periodicity of your data (yearly, monthly, daily,...)? Are you taking regular differences or are also considering differences of seasonal order? $\endgroup$ – javlacalle Jan 19 '15 at 11:08
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    $\begingroup$ What strategy are you using to select the values of p and q? The statement "are coming as high as" is a bit vague. $\endgroup$ – Graeme Walsh Jan 19 '15 at 11:33
  • $\begingroup$ @javlacalle :basically I am trying to model a tripping event at a power system.And the observations that I have are the values of frequency against time. Each frequency sample is taken at an interval of 40 mili seconds. Is that what you mean by periodicity?? $\endgroup$ – Sharda Tripathi Jan 20 '15 at 11:37
  • $\begingroup$ @ Graeme Walsh : I am selecting the values of p and q from the partial auto correlation plot and auto correlation plot respectively.So p and q here are basically the value of lag where pacf and acf goes below the confidence interval of 95%. $\endgroup$ – Sharda Tripathi Jan 20 '15 at 11:40
  • $\begingroup$ After differencing calculate standard deviation and try to simulate $ARIMA(0,d,0)$ ($d$ being the number of times you differenced the data) model with innovations being white gaussian noise standard deviation calculated from date as above. Do some 100 simulations and see whether your data looks like anything similar. I suspect that it will look nothing like this, since $ARIMA(0,d,0)$ models for $d>1$ behave quite erraticaly. $\endgroup$ – mpiktas Jan 20 '15 at 12:53

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