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)

Arguments

Series1	Vector of observations of the first univariate time series for which crosscorr computes or plots the sample cross-correlation function (XCF). The last element of Series1 contains the most recent observation.
Series2	Vector of observations of the second univariate time series for which crosscorr computes or plots the sample XCF. The last element of Series2 contains the most recent observation.
nLags	(optional) Positive, scalar integer indicating the number of lags of the XCF to compute. If nLags = [] or is not specified, crosscorr computes the XCF at lags 0, ±1, ±2, ..., ±T, where T = min([20, min([length(Series1), length(Series2)])-1]).
nSTDs	(optional) 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 not specified, the default is 2 (i.e., approximate 95 percent confidence interval).

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.

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

Example

Create a random sequence of 100 Gaussian deviates, and a delayed version lagged by four samples. Compute the XCF, and then plot it to see the XCF peak at the fourth lag.

randn('state',100)              % Start from a known state.
x           = randn(100,1);     % 100 Gaussian deviates, N(0,1).
y           = lagmatrix(x, 4);  % Delay it by 4 samples.
y(isnan(y)) = 0;                % Replace NaNs with zeros.
[XCF, Lags, Bounds] = crosscorr(x,y);  % Compute the XCF with
                                       % 95 percent confidence.
[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 =

    0.2000
   -0.2000

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

See Also
autocorr, parcorr

filter (in the online MATLAB Function Reference)

autocorr

garchar