Multivariate Portmanteau (Ljung-Box) Test

Test if there is auto- and cross correlation in a multivariate vector series

MLBQTEST(X,LAGS) performs multivariate Portmanteau test.

h = mlbqtest(X,LAGS) returns returns a logical value (h) for LAGS with the rejection decision from conducting a multivariate Portmanteau test for joint cross-correlation in a multivariate series X.

h = mlbqtest(X,LAGS,ALPHA) specifies the significance level (default=0.05).

[h,pValue] = mlbqtest(~) returns the rejection decision and p-value for the hypothesis test.

[h,pValue,stat,cValue] = mlbqtest(~) additionally returns the test statistic (stat) and critical value (cValue) for the hypothesis test.

Input argument X: a multivariate time-series (T x k) with k assets and T times.

Test null hypothesis H0: all correlation coefficients are zero, i.e.. rho_1=rho_2=...rho_m=0, where m the lag
Alternative hypothesis H1: there are some coefficients are not zero.