SPECTRAL RADIUS, KRONECKER PRODUCTS AND STATIONARITY

Jian Liu

Journal of Time Series Analysis, 1992, vol. 13, issue 4, 319-325

Abstract: Abstract. We provide a stochastic proof of the inequality ρ(A⊗A+B⊗B) ≥ρ(A⊗A), where ρ(M) denotes the spectral radius of any square matrix M, i.e. max{|eigenvalues| of M}, and M⊗N denotes the Kronecker product of any two matrices M and N. The inequality is then used to show that stationarity of the bilinear model will imply stationarity of the linear part, i.e. the linear ARMA model for r= 1 and q= 1. Furthermore, it is shown that stationarity of the subdiagonal model, i.e. the bilinear model with bij=0 for i

Date: 1992
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