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[ACF, PACF and correlogram]

Characterizing a time series involves estimating not only a mean and standard deviation but also the correlations between observations separated in time. In the identification phase of the Box Jenkins procedure the empirical autocorrelation (ACF) as well as the partial autocorrelation function (PACF) are important tools.

The autocorrelation function measures the strength of relationship between  and . For example if  near to one, a “high” value of  will be followed by a “high” value tomorrow. The ACF is an important tool in identifying the order of moving average time series models.

Partial autocorrelations measures the strength of the relationship between observations in a time series controlling for the effect of intervening time periods. Specifically, partial autocorrelations are useful in identifying the order of autoregressive models.

The plots of ACF and PACF are called correlogram.

The Ljung-Box-statistic (Q-statistic) at lag k is a test statistic for the null hypothesis that there is no autocorrelation up to order k. The definition of it is:

 is asymptotically distributed as a with degrees of freedom equal to the number of autocorrelations.



The autocorrelation of a series  at lag  is estimated by:

where  is the sample mean of the time series.

The partial autocorrelation of a series  is estimated by:



The Add-In is written in VBA.

[related links]

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Xycoon, Time Series Analysis - ARIMA models - Basic Definitions and Theorems about ARIMA models (HTML)

mathworld, description of autocorrelation. (HTML)

Links to other sites from these pages are for information only and Kurt Annen accepts no responsibility or liability for access to, or the material on, any site which is linked from or to this site.

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for downloading click on the filename

File: setup_web-reg_correlogram.exe
Filesize: 582 kb

The correlogram Add-In was written by Kurt Annen. This program is freeware. But I would highly appreciate if you could give me credit for my work by providing me with information about possible open positions as an economist. My focus as an economist is on econometrics and dynamic macroeconomics. If you like the program, please send me an email.

[correlogram excel add-in ]
© 2005 Kurt Annen