GARCH Toolbox™

crosscorr - Plot or return computed sample cross-correlation function

Syntax

crosscorr(Series1,Series2,nLags,nSTDs) [XCF,Lags,Bounds] = crosscorr(Series1,Series2,nLags,nSTDs)

Description

crosscorr(Series1,Series2,nLags,nSTDs) computes and plots the sample cross-correlation function (XCF) between two univariate, stochastic time series. To plot the XCF sequence without the confidence bounds, set nSTDs = 0.
[XCF,Lags,Bounds] = crosscorr(Series1,Series2,nLags,nSTDs) computes and returns the XCF sequence.

Input Arguments

`Series1`	Column vector of observations of the first univariate time series for which `crosscorr` computes or plots the sample cross-correlation function (XCF). The last row of `Series1` contains the most recent observation.
`Series2`	Column vector of observations of the second univariate time series for which `crosscorr` computes or plots the sample XCF. The last row of `Series2` contains the most recent observation.
`nLags`	Positive scalar integer indicating the number of lags of the XCF to compute. If `nLags = []` or is unspecified, `crosscorr` computes the XCF at lags , where T `=` `min([20,min([length(Series1),` `length(Series2)])-1])`.
`nSTDs`	Positive scalar indicating the number of standard deviations of the sample XCF estimation error to compute, if `Series1` and `Series2` are uncorrelated. If `nSTDs = []` or is unspecified, the default is `2` (that is, approximate 95 percent confidence interval).

Output Arguments

`XCF`	Sample cross-correlation function between `Series1` and `Series2`. `XCF` is a vector of length `2(nLags)+1`, which corresponds to lags . The center element of `XCF` contains the 0th lag cross correlation.
`Lags`	Vector of lags corresponding to `XCF`(`nLags`, ..., +`nLags`).
`Bounds`	Two-element vector indicating the approximate upper and lower confidence bounds, assuming that `Series1` and `Series2` are completely uncorrelated.

Examples

Example 1

Create a time-series column vector of 100 Gaussian deviates:

randn('state', 100)      % Start from a known state
x = randn(100, 1);       % 100 Gaussian deviates, N(0, 1)

Create a delayed version of the vector, lagged by four samples:
```
y = lagmatrix(x, 4);    % Delay it by 4 samples
```

Compute the XCF, and then plot it to see the XCF peak at the fourth lag:

y(isnan(y)) = 0;
[XCF, Lags, Bounds] = crosscorr(x, y);
[Lags, XCF]
ans =
  -20.0000   -0.0210
  -19.0000   -0.0041
  -18.0000    0.0661
  -17.0000    0.0668
  -16.0000    0.0380
  -15.0000   -0.1060
  -14.0000    0.0235
  -13.0000    0.0240
  -12.0000    0.0366
  -11.0000    0.0505
  -10.0000    0.0661
   -9.0000    0.1072
   -8.0000   -0.0893
   -7.0000   -0.0018
   -6.0000    0.0730
   -5.0000    0.0204
   -4.0000    0.0352
   -3.0000    0.0792
   -2.0000    0.0550
   -1.0000    0.0004
         0   -0.1556
    1.0000   -0.0959
    2.0000   -0.0479
    3.0000    0.0361
    4.0000    0.9802
    5.0000    0.0304
    6.0000   -0.0566
    7.0000   -0.0793
    8.0000   -0.1557
    9.0000   -0.0128
   10.0000    0.0623
   11.0000    0.0625
   12.0000    0.0268
   13.0000    0.0158
   14.0000    0.0709
   15.0000    0.0102
   16.0000   -0.0769
   17.0000    0.1410
   18.0000    0.0714
   19.0000    0.0272
   20.0000    0.0473

Bounds
Bounds =
    0.2000
   -0.2000
crosscorr(x, y)        % Use the same example, but plot the XCF 
                       % sequence. Note the peak at the 4th lag.

Example 2

See Example: Analysis and Estimation Using the Default Model.