Market Risk Analysis Volume II: Practical Financial Econometrics

II.7

Advanced Econometric Models

II.7.1 INTRODUCTION

A regression model is a tool that is rather like a pair of spectacles. Like spectacles, regression models allow you to see more clearly. Characteristics of the data that cannot be seen from simple graphs or by calculating basic sample statistics can be seen when we apply a regression model. Spectacles come in all shapes and sizes, and some are specifically designed to be worn for certain purposes. Likewise regression models come in many varieties and some models should only be applied to certain types of data. A standard multiple linear regression estimated using ordinary least squares (OLS) is like an ordinary pair of spectacles. It is fine when the data are in the right form and you do not want to see too much. But for special types of data we need to use a different type of model; for instance, when data are discrete we may use a probit or logit model. Also, like spectacles, some regression models are more powerful than others. For instance, non-linear regression, quantile regression, copula quantile regression or Markov switching regression models allow one to see far more than is possible using a simple linear regression.

We should always plot data before estimating a regression model. This is a golden rule that should never be overlooked. Forgetting to plot the data before prescribing and fitting the regression model is like an optician forgetting to do an eye test before prescribing the lenses and fitting the frames. A ...