What are the most typical graphs for an auto-correlation function?

Replies to This Discussion

Permalink Reply by AJAY OHRI on August 23, 2008 at 10:11am

look at the tutorial on spss trends within the spss tutorial

...it has the most lucid explanation on auto corelation graphs

▶ Reply to This

Permalink Reply by Brian J. Fox on February 14, 2009 at 12:41pm

In order to use an auto-correlation function the data series must be weakly stationary. This means that it have a very fast exponential decay. If there is not a quick decay then there is presence of long memory in the data. Typical a decay that goes to zero by no more than 10-15 lag. There will often be evidence of thickness in the tails which is know as leptokurtic. You can you use the excess kurtosis check to test for the thickness of the tails. Often in financial data there will be thiuckness in the tails because of how the data was measured. In order to have a weak form stationary data series the first two moments must be constant, the data must come from a normal distribution and there also must be serial correlation in the data. I recommend reading Analysis of Financial Time Series by Ruey S. Tsay.

▶ Reply to This

Permalink Reply by Arun on May 14, 2009 at 2:19am

As long as a process in not stationary, I think the ACF will look thick. Dying down within the first few lags are signs of stationarity. Also, to really check if the process is stationary or not, I think the IACF and the PACF graphs greatly help in finding the predominant memory lags that add to the tail. So, in the process, when we take differences of the respective lags, we should be able to end up with a rather fast decreasing exponential!

I have also seen instances of the ACF, being alternatively correlated (positive & negative). So it all depends on how the correlation is in the series, and how long the lag effects are in place.

▶ Reply to This

Permalink Reply by Jan Theodore Galkowski on June 28, 2009 at 3:58pm

Then what techniques are available for analyzing non-stationary time series? Are the SSA techniques (SVDs of windowed autocovariance and others) the way to go?

▶ Reply to This