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

49 NTU Management Review Vol. 30 No. 3 Dec. 2020 2. Methodology 2.1 The Vector Autoregressive Model Let X t = W t r t be a (2 × 1) vector of the demeaned weather variable W t and stock return r t on day t. The reduced-form VAR(p) model describes the dynamic of X t by relating it linearly with its p lags, as shown in equation (1). X t = π 1 X t-1 + ... + π p X t-p + ε t , (1) where π i is the (2 × 2) matrix of the coefficients for X t-1 , and ε t is a (2 × 1) vector of the error terms. ε t has a zero-mean vector and a Ω covariance matrix. In weather studies, weather necessarily is the exogenous variable, and the relationship of the weather with the stock return is well described by a structural VAR (SVAR) model. I choose the linear VAR in equation (1) because it is implied by the SVAR (Enders, 2015). Linear VARs are powerful and reliable tools in data description (Stock and Watson, 2001). The relationship between weather and stock returns can be nonlinear. The nonlinear VAR models, e.g., vector threshold autoregressive, vector smooth transition autoregressive, and vector Markov-switching autoregressive models, are more flexible and better describe the nonlinear relationship (Hubrich and Teräsvirta, 2013). Nevertheless, the nonlinear pattern should show in long estimation samples. In this study, equation (1) will be estimated annually. For short samples, linear VAR should be able to approximate the relationship even though the long-sample relationship is nonlinear. Time paths of the impulse responses of returns to structural shocks of weather variables in a linear VAR model exhibit how weather affects return over time. The impulse responses are crucial information required to identify the temporary and permanent parts of the weather effects. Permanent effects are measured by the significant infinite sum of the impulse responses, whereas reverse signs of the significant impulse responses in early days suggest temporary effects. Although the methodology of Lee et al. (2002) can identify temporary and permanent weather effects, the identification is implied. Moreover, it is possible that the methodology misses the permanent effects resulting from the price adjustment process (Wermers, 1999). The temporary and permanent weather effects identified by the time paths are exact and the permanent effects from the price adjustment process can still be observed.