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

51 NTU Management Review Vol. 30 No. 3 Dec. 2020 with n variables in X t and T observations, BIC(p) = Ln |Ω p | + Ln (T) T pn 2 , where Ω p is the covariance matrix of the VAR(p) residuals. An information criterion measures the distance of the model being considered from the true but unobserved model. I do not consider other criteria, such as the Akaike criterion (AIC) (Akaike, 1974) or Hannan-Quinn criterion (HQIC) (Hannan and Quinn, 1979), because the AIC asymptotically overestimates p. While the HQIC and BIC consistently estimate p, the BIC is widely applied in the literature (Zivot and Wang, 2006). 2.5 Estimation Problems Khanthavit (2017) cautioned that weather studies suffered from the endogeneity problem and the incorrect fixed-effect assumption. The endogeneity problem results from the fact that weather variables are measured with errors, and some significant weather variables are omitted from the regressions. The fixed-effect assumption is incorrect because the sample period is long, and the structural relationship of the weather with stock returns changes over time. In this study, the endogeneity problem will not adversely affect the estimation because a VAR model is designed to describe the relationship of endogenous variables. As a result, it solves the endogeneity problems due to measurement errors and omitted variables. My concern relates to the incorrect fixed-effect assumption. The sample is long, covering a period of 26 years. To mitigate the effects of incorrect assumption, I follow Khanthavit (2017) to estimate the model using sample periods of one year at a time. 2.6 Hypothesis Tests 2.6.1 Significant Weather Effects and Time Behaviors If weather effects exist, the impulse response Θ j 2,1 of the return on day t + j to the weather shock η W t must be significantly different from zero for some j. Under the null hypothesis of Θ j 2,1 = 0, the Wald statistic is a chi-square variable of 1 degree of freedom. I check for the temporary weather effects by the reverse signs of significant Θ j 2,1 and Θ k>j 2,1 . The test for significant permanent effects is the significance test for the infinite sum lim J↑∞ Σ J j=0 Θ j 2,1 . I approximate lim J↑∞ Σ J j=0 Θ j 2,1 by Σ J=249 j=0 Θ j 2,1 . Setting J larger than 249, totaling 250 days from days 0 to 249, does not improve the statistic. The Wald statistic for the null hypothesis Σ J=249 j=0 Θ j 2,1 = 0 is a chi-square variable with 1 degree of freedom. The Wald statistics are computed based on analytical standard errors. Griffiths and Lütkepohl (1990)