5 VAR与协整.pdf

VAR • VAR • VAR • VAR 2006-1-4 VAR • 1980Simsvector autoregressive model 2006-1-4 1 1. VAR • y 1t y 2t1VAR y = c + π y + π y + u 1, t 1 11.1 1, t-1 12.1 2, t-1 1t y = c + π y + π y + u 2, t 2 21.1 1, t-1 22.1 2, t-1 2t 2 • u1 t, u2 t ∼ IID (0, σ ), Cov(u1 t, u2 t) = 0 y c ⎡π π ⎤ u ⎡ ⎤ ⎡ ⎤ 11.1 12.1 ⎡y ⎤ ⎡ ⎤ 1t 1 1,t −1 1t • ⎢ ⎥= ⎢ ⎥+ ⎢ ⎥⎢ ⎥+ ⎢ ⎥ y 2t c ⎣π21.1 π22.1 ⎦ y 2,t −1 u 2t ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ 2 ⎡y ⎤ ⎡π π ⎤ u 1t 11.1 12.1 ⎡ ⎤ c 1t ⎡ ⎤ • Y = ⎢ ⎥, c = 1 , Π = ⎢π π ⎥ , u = ⎢ ⎥ , t y ⎢ ⎥ 1 ⎣ 21.1 22.1 ⎦ t u2t ⎣ 2t ⎦ c ⎣ ⎦ ⎣ ⎦ 2 • Y = c + Π Y + u (5.1) t 1 t-1 t 2006-1-4 •NkVAR •Y = c + Π Y + Π Y + … + Π Y + u , u ∼IID (0, Ω) t 1 t-1 2 t-2 k t-k t