8-2 1 An Excursion into Non-linearity Land Motivation: the linear structural (and time series ) models cannot explain a number of important features common to much financial data leptokurtosis:尖峰性,厚尾 volatility clustering or volatility pooling波动性集群 较卖 age effects与价格同幅上升相比,价格大幅下降后,波动性上升 levers Our "traditional"structural model could be something like: y,= Bi+Bx2+.+ Bkrk+u, or y=XB+u We also assumed u,N(0, 08-2 1 An Excursion into Non-linearity Land • Motivation: the linear structural (and time series) models cannot explain a number of important features common to much financial data - leptokurtosis：尖峰性，厚尾 - volatility clustering or volatility pooling 波动性集群 - leverage effects 与价格同幅上升相比，价格大幅下降后，波动性上升 较多 • Our “traditional” structural model could be something like: yt = 1 + 2x2t + ... + kxkt + ut, or y = X + u. We also assumed ut  N(0, 2 )