# A list of common time series tests?

I am reviewing my time series knowledge and looking for a document that has the commonly-used time series tests, what they are used for, how to use them, etc. e.g. Augmented Dickey–Fuller test, PACF tests, etc.

I found a wikipedia page of common statistical tests, but I am looking for a list of such that is specific for time series analysis.

http://en.wikipedia.org/wiki/Statistical_hypothesis_testing#Common_test_statistics

Thanks!

• Why not just refer to one of the many available textbooks on time series? They should provide descriptions of most of the tests that you aare interested in. Jun 18, 2012 at 3:42

I think the Time Series task view in R and this list of time series functions will get you most of the way there.

Just read the corresponding documentation to learn how to use them. As Michael mentioned, there are many books that describe these methods in depth.

http://cran.r-project.org/doc/contrib/Ricci-refcard-ts.pdf

http://cran.r-project.org/web/views/TimeSeries.html

To clarify, ACF and PACF are not statistical tests. The ouput of the autocorrelation function (ACF) and partial autocorrelation (PACF) functions help you decide whether you want to model a time series using an autoregressive (AR) model, a moving average (MA) model, or an autoregressive moving average model (ARMA, a linear combination of AR and MA models). Furthermore, the behavior of the ACF and PACF help you determine the parameters of these models. For instance, if your ACF drops off sharply after two lags and your PACF drops off after one lag for a particular time series, you might want to use an MA(2), AR(1), or an ARMA(1,2) to model your time series. (You may also model time series using auto regressive integrated moving average, or ARIMA models.) Once you have modeled a time series several different ways, you can inspect the AIC value to help you decide between models. The AIC takes into account goodness of fit and model simplicity. Generally, the smaller the AIC, the better. In R, you can build models using the arima() function, and evaluate their performance using the tsdiag() function.

Here is a link to the website of a helpful timeseries textbook: http://www.stat.pitt.edu/stoffer/tsa3/

• This seems to imply that time series analysis and ARIMA modelling are one and the same. That's presumably a matter of accident or particular choice of examples. Jul 30, 2013 at 17:25
• No, ARIMA modeling is only a part of time series analysis. I was just pointing out that ACF and PACF weren't statistical tests. Jul 30, 2013 at 20:03
• Quite so. In fact, large areas of modern time series analysis pay no attention to ARIMA at all. Jul 30, 2013 at 20:04