Introduction to Nonlinear Models

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Introduction to Nonlinear Models

• From Ruey. S. Tsays slides

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What is nonlinear Model?
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General Concepts of Nonlinear Models
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TAR Model
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TAR Example
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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.

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Markov switching model
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Nonparametric Methods

• The essence of nonparametric methods is
  smoothing.
• Consider two financial variable Y and X, which
  are related by
• Ytm(Xt)at
• Suppose Xx, we have independent observations,
  y1, yT, The the data become
• Ytm(Xt)at, t1, , T
• Taking average (AVG)
• AVG(Yt)m(x)AVG(at)

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Nonparametric Estimation Methods

• Kernel Regression
• Key issue bandwidth selection
• Neural Networks
• Selection of hidden layers