Building Econometric Models



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Ch9 slides

Chapter 9

  • ‘Introductory Econometrics for Finance’ © Chris Brooks 2013

An Excursion into Non-linearity Land

  • ‘Introductory Econometrics for Finance’ © Chris Brooks 2013
  • Motivation: the linear structural (and time series) models cannot explain a number of important features common to much financial data
  • - leptokurtosis
  • - volatility clustering or volatility pooling
  • - leverage effects
  •  
  • Our “traditional” structural model could be something like:
  • yt = 1 + 2x2t + ... + kxkt + ut, or more compactly y = X + u
  •  We also assumed that ut  N(0,2).

A Sample Financial Asset Returns Time Series

  • ‘Introductory Econometrics for Finance’ © Chris Brooks 2013
  • Daily S&P 500 Returns for August 2003 – August 2013

Non-linear Models: A Definition

  • ‘Introductory Econometrics for Finance’ © Chris Brooks 2013
  • Campbell, Lo and MacKinlay (1997) define a non-linear data generating process as one that can be written
  • They also give a slightly more specific definition as
  • yt = g(ut-1, ut-2, …)+ ut2(ut-1, ut-2, …)
  • where g is a function of past error terms only and 2 is a variance term.
  • Models with nonlinear g(•) are “non-linear in mean”, while those with nonlinear 2(•) are “non-linear in variance”.

Types of non-linear models

  • ‘Introductory Econometrics for Finance’ © Chris Brooks 2013
  • The linear paradigm is a useful one.
  • Many apparently non-linear relationships can be made linear by a suitable transformation.
  • On the other hand, it is likely that many relationships in finance are intrinsically non-linear.
  • There are many types of non-linear models, e.g.
  • - ARCH / GARCH
  • - switching models
  • - bilinear models

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