1. Introduction to Nonlinear Models From Ruey. S. Tsay’s slides

2. What is nonlinear Model?

3. General Concepts of Nonlinear Models

4. TAR Model

5. TAR Example

6. TAR Properties Asymmetry in rising and declining patterns, The mean of xt is not zero even though there is no constant term in the model, The lag-1 coefficient may be greater than 1 in absolute value.

7. Markov switching model

8. Nonparametric Methods The essence of nonparametric methods is smoothing.  Consider two financial variable Y and X, which are related by Y t =m(X t )+a t  Suppose X=x, we have independent observations, y 1, …y T, The the data become Y t =m(X t )+a t, t=1, …, T  Taking average (AVG) AVG(Y t )=m(x)+AVG(a t )

9. Nonparametric Estimation Methods Kernel Regression  Key issue: bandwidth selection Neural Networks  Selection of hidden layers