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I am doing a study on time series data. In a lot of examples, ARIMA model is used to forecast a time series data. On what basis ARIMA model chosen to predict a time series is my primary doubt.

Is ADF(Dickey–Fuller test) or Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test is used to justify the reason for choosing ARIMA model?

In few cases ARIMA model chosen based on the stationary data, ADF having a parameter p-value to show the time series data as stationary. In that case, what can be the minimum possible p-value to decide the data as stationary?

And is there any other better ways to decide which model can be used to forecast the time series data apart from ARIMA.

Any suggestions are highly appreciated. Thanks in advance.

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  • $\begingroup$ It is not clear what you want to know. Try to focus your question in a way that will be helpful. $\endgroup$ – Michael Chernick Apr 18 '17 at 16:41
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    $\begingroup$ ADF and KPSS test for unit root/stationarity. This issue is separate from model selection/order selection. $\endgroup$ – Taylor Apr 19 '17 at 0:00
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Decide what is the "best model" depends on the analyst criteria as well as performance metrics.

If you are starting you can check the site: https://www.otexts.org/fpp/8/7

auto.arima function from forecast package in R can help you with the initial step. It creates several models and retrieves the best, according to AIC (Akaike Information Criterion) statistic.

The AIC (which is indeed very similar to BIC) bases on two key concepts:

  • Accuracy of the model
  • Complexity of the model.

In general terms, more parameters (more variables) tend to provide more accuracy but incurring in overfitting.

For example, an Arima(3,0,1) is more complex than Arima(1,0,1).

AIC intends to be a good trade-off between complexity and accuracy.

This concept applies to other predictive models if you build a random forest model you will pick those few variables (complexity) that maximize the prediction (accuracy)

To check if the time series if stationary check this full example: http://www.statosphere.com.au/check-time-series-stationary-r/

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