The Adjustment of the Yule-Walker Relations in VAR Modeling: The Impact of the Euro on the Hong Kong Stock Market

Abstract

Vector autoregressive models are increasingly being used in the analysis of relationships within and between financial markets. In such models, there are circumstances that require zero entries in the coefficient matrices. Such circumstances can be particularly relevant in the context of markets with special characteristics, such as emerging economies. This paper shows that a direct extension of the use of the Yule-Walker relations for fitting vector autoregressive models with zero-non-zero patterned coefficient matrices is inconsistent with statistical procedures as the resultant estimated variance-covariance matrix of the white noise disturbance process becomes non-symmetric. This inconsistency can cause a breakdown when testing financial theory. The paper provides a consistent adjustment which fits with the theory. The practical use of the adjustment is demonstrated in a vector system comprising variables from the Hong Kong stock market and foreign exchange markets.

Keywords: foreign exchange market; time series; VAR models; Yule-Walker relations

JEL Classification: C13, C32, C63, G10, G15