Testing VARMA Models for Nonlinearities Gauss file(s) stsm_varmab.g Matlab file(s) stsm_varmab.m Simulate T = 500 observations of the VARMA(1, 1) model set out in Exercise 7, using the population parameters given in Table 13.2.

(a) Use the simulated data to estimate the following nonlinear time series model y1,t = µ1 + φ1,1,1y1,t−1 + v1,t + ψ1,1,1v1,t−1 + ψ1,1,2v2,t−1 +δ1y1,t−1v1,t−1 y2,t = µ2 + φ1,2,2y2,t−1 + v2,t + ψ1,2,1v1,t−1 + ψ1,2,2v2,t−1 +δ2y2,t−1v2,t−1. The inclusion of the nonlinearities yields a multivariate bilinear model that is studied in greater detail in Chapter 19. Perform a test of multivariate bilinearity H0 : δ1 = δ2 = 0, using a LR test and a Wald test.

(b) Briefly discuss how you could make the multivariate test of bilinearity robust to nonnormality.