Threshold Estimation from a Generated Auxiliary Regression

With an Application to U.S. Stock Return

When?

Wednesday 10 October 2012, 16.00 to 17:30

Where?

40AD00

Open to:

Staff, Students, Public

Speaker:

Daniele Massacci (University of Surrey and EIEF)

Dr. Daniele Massacci (University of Surrey and EIEF)

"Threshold Estimation from Generated Auxiliary Regression: With an Application to U.S. Stock Return".

Abstract

This paper deals with the issue of inference on the threshold value in threshold regression models. This is a challenging problem, as least squares estimation delivers a n consistent estimator for the threshold value, where n is the size of the available sample: the resulting asymptotic distribution depends on a number of nuisance parameters, which make inference on the threshold value a nonstandard problem. This paper develops a n 1/2 asymptotically normally distributed estimator for the threshold value: as a consequence, inference can be based on standard testing procedures. The methodology we propose is based on a two-stage least squares estimator: in the first stage, the model’s parameters are estimated by least squares, and a n consistent estimator for the threshold value is produced; in the second stage, the threshold value is re-estimated by least squares from an auxiliary linear regression model in which the dependent variable is constructed as the sum between the first stage estimated threshold value and a generated error term. The proposed methodology produces a n1/2 asymptotically normally distributed estimator for the threshold value: the first stage estimator converges at a faster rate than the second stage estimator, and the former estimator does not affect the asymptotic distribution of the latter. The finite sample properties of the proposed estimator are assessed by Monte Carlo analysis, and the potential empirical usefulness is illustrated by an application to U.S. stock returns.