**[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.

**[notes]**

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:

_{}

where

_{}

and

_{}

The Add-In is written in VBA.

**[related links]**

All links will be open in a new window

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.

screenshot of hp-filter add-in

**[download]**

for downloading click on the filename

File: **setup_web-reg_correlogram.exe
**Filesize:

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