臺大管理論叢 NTU Management Review VOL.30 NO.3

Time Paths of Weather-Induced Mood Effects on Stock Returns 50 2.2 Impulse Responses Let A be a (2 × 2) lower triangular matrix such that AA T = Ω. The model in equation (1) implies the triangular structural VAR(p) model in equation (2) (Sims, 1980). A -1 X t = A -1 π 1 X t-1 + ... +A -1 π p X t-p + η t , (2) where η t = η W t η r t is the (2 × 1) vector of uncorrelated and orthogonal structural shocks. η t has an identity covariance matrix. The η W t and η r t shocks are the information brought into the system by W t and r t , respectively. Because A is a lower triangular matrix, A -1 is one as well. Equation (2) imposes the recursive causal ordering from W t to r t . I impose this structure because stock returns cannot cause weather conditions. The Wold representation of X t based on the model in equation (2) is given by X t = Θ 0 η t + Θ 1 η t-1 + Θ 2 η t-2 + Θ 3 η t-3 + ... , (3) where Θ 0 = A, Θ j = Ψ j A, Ψ j>0 = Σ p s=1 Ψ j-s π s , and Ψ 0 is an identity matrix (Zivot and Wang, 2006). Θ j 2,1 , which is the (2,1) th element of matrix Θ j , is the impulse response of the return r t+j to the structural shock η W t . The time path of Θ j 2,1 offers useful information for analyzing the behaviors of weather effects. Permanent weather effects are measured by the significant, infinite sum lim J↑∞ Σ J j=0 Θ j 2,1 . I conclude that temporary effects exist if, for some j and k, Θ j 2,1 is significant and if Θ k>j 2,1 is also significant and has the opposite sign. 2.3 Model Estimation I estimate the coefficient matrices π i = 1,...,p of the reduced-from model in equation (1) using the seemingly unrelated regression equations (SUR) technique. The covariance matrix Ω is estimated by the covariance matrix of the VAR residuals. The SUR system links the weather variable W t and stock return r t by the fact that their errors are correlated. This system yields a full covariance matrix of the coefficients for all the variables in X t . 2.4 Lag Selection The lag order p is unknown. I chose the lag order by the VAR(p * ) model that gives the minimum Bayesian information criterion (BIC) (Schwarz, 1978). For a VAR(p) model