Generalized Regression

Linear regression is one of the most useful applications in the financial engineer’s tool-kit, but it suffers from a rather restrictive set of assumptions that limit its applicability in areas of research that are characterized by their focus on highly non-linear or correlated variables.  The latter problem, referred to as colinearity (or multicolinearity) arises very frequently in financial research, because asset processes are often somewhat (or even highly) correlated.  In a colinear system, one can test for the overall significant of the regression relationship, but one is unable to distinguish which of the explanatory variables is individually significant.  Furthermore, the estimates of the model paramaters, the weights applied to each explanatory variable, tend to be biased.

Over time, many attempts have been made to address this issue, one well-known example being ridge regression.  More recent attempts include lasso, elastic net and what I term generalized regression, which appear to offer significant advantages vs traditional regression techniques in situations where the variables are correlated.

In this note, I examine a variety of these technqiues and attempt to illustrate and compare their effectiveness.

You can downlaod a pdf here.

A Mathematica notebook is also available here.

 

About Jonathan

Dr Jonathan Kinlay is the Head of Quantitative Trading at Systematic Strategies, LLC, a systematic hedge fund that deploys high frequency trading strategies using news-based algorithms. Dr Kinlay, was the founder and General Partner of the Caissa Capital hedge fund, whose volatility arbitrage strategies were developed by Dr Kinlay’s investment research firm, Investment Analytics. Caissa, which managed $400M in assets, was ranked by FIMAT as the top performing fund in its class in 2004. Dr Kinlay went on to establish the Proteom Capital, whose statistical arbitrage strategies were based on pattern recognition techniques used in DNA sequencing. Dr Kinlay was formerly Global Head of Model Review at the US investment bank Bear Stearns. Dr Kinlay holds a PhD in economics and has held positions on the faculty at New York University Stern School of Business, Carnegie Mellon and Reading Universities. Dr Kinlay is a regular conference speaker and writer on investment research, hedge fund investing and quantitative finance. Kinlay was a member of England’s chess team that won gold in the World Student Olympiad in Mexico in 1978. He is the son of Fleet Street editor James Kinlay and father of British actress Antonia Kinlay.
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