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Lecture Introductory econometrics for finance – Chapter 9: Modelling volatility and correlation

In this chapter, you will learn how to: Discuss the features of data that motivate the use of GARCH models, explain how conditional volatility models are estimated, test for ‘ARCH-effects’ in time series data, produce forecasts from GARCH models, contrast various models from the GARCH family,. | Chapter 9 Modelling volatility and correlation ‘Introductory Econometrics for Finance’ c Chris Brooks 2013 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 – volatility clustering or volatility pooling – leverage effects • Our “traditional” structural model could be something like: y = β1 + β2 x2 + . . . + βk xkt + u or more compactly y = X β + u. • We also assumed that ut ∼ N(0, σ 2 ). ‘Introductory Econometrics for Finance’ c Chris Brooks 2013 2 A Sample Financial Asset Returns Time Series Daily S&P 500 Returns for August 2003 – August 2013 ‘Introductory Econometrics for Finance’ c Chris Brooks 2013 3 Non-linear Models: A Definition • Campbell, Lo and MacKinlay (1997) define a non-linear data generating process as one that can be written yt = f (ut , ut−1 , ut−2 , . . .) where ut is an iid error term and f is a non-linear function. • They also give a slightly more specific definition as yt = g (ut−1 , ut−2 , . . .) + ut σ 2 (ut−1 , ut−2 , . . .) where g is a function of past error terms only and σ 2 is a variance term. • Models with nonlinear g (•) are “non-linear in mean”, while those with nonlinear σ(•)2 are “non-linear in variance”. ‘Introductory Econometrics for Finance’ c Chris Brooks 2013 4 Types of non-linear models • 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 ‘Introductory Econometrics for Finance’ c Chris Brooks .