Compute the autocorrelation for an external time Series and the autocorrelation for the same series filtered by a first order process.

Description

The autocovariance at a given lag is calculated

                               n
                             -----
                              \    x(i)
                     xMean =   )   ----
                              /     n
                             -----
                             i = 1


                            n - lag
                             -----
                              \
                               )    (x(i) - xMean) (x(i + lag) - xMean)
                              /
                             -----
                             i = 1
  autocovariance(lag) = ------------------------------------------------
                                            n-1

The autocovariance at zero lag  is the estimated variance. The autocorrelation
is the autocovariance normalized by the variance.

                            autocovariance(lag)
   autocorrelation(lag) = -----------------
                            autocovariance( 0 )

Upper Panel: A time series of Gaussianly distributed random numbers with mean=0, variance=4.
Lower Panel: The autocovariance function (black) and the autocorrelation function (red) are plotted as functions of the lag.

Equations

None.

The equations for this model may be viewed by running the JSim model applet and clicking on the Source tab at the bottom left of JSim's Run Time graphical user interface. The equations are written in JSim's Mathematical Modeling Language (MML). See the Introduction to MML and the MML Reference Manual. Additional documentation for MML can be found by using the search option at the Physiome home page.