# An Alternative Semiparametric Regression Approach to Nonlinear Duration Modeling: Theory and Practice

60 Pages Posted: 18 Sep 2010

See all articles by Jiti Gao

## Jiti Gao

Monash University - Department of Econometrics & Business Statistics

## Pipat Wongsaart

University of Western Australia; University of Adelaide

## David E. Allen

School of Mathematics and Statistics, The University of Sydney; Financial Research Network (FIRN); Department of Finance; School of Business and Law, Edith Cowan University

Date Written: September 15, 2010

### Abstract

This paper puts forward an alternative semiparametric regression approach to a nonlinear ACD modeling. The semiparametric functional form of the dependence of the conditional intensity on past durations suggests that the model be called the Semiparametric ACD (SEMI-ACD) model. The development of the SEMI-ACD model relies on two important factors; namely (i) an iterative estimation algorithm, which is devised to address the latency problem arises because the conditional expectation of duration with respect to the past history is not observable in practice, and (ii) an adaptive estimation of a partially linear additive autoregressive process.

The theoretical study involves two fundamental issues. The first and by far the most important is the consistency of the estimation algorithm. Results will be exhibited for a variety of modes of consistency.

Furthermore, to enrich the statistical rigor of the SEMI-ACD estimation procedure, the asymptotic properties of the semiparametric estimators are established under the conditions of the algorithm consistency. These asymptotic results are presented in conjunction with simulated examples which illustrate a robust finite-sample performance of the model. Finally, the paper applies the SEMI-ACD procedure to model the price duration process of the \\$US/\\$EUR exchange rate.

Keywords: Dependent point process, duration, hazard rate and random measure, irregularly spaced high frequency data, semiparametric time series

JEL Classification: C14, C41, F31

Suggested Citation

Gao, Jiti and Wongsaart, Pipat and Allen, David Edmund, An Alternative Semiparametric Regression Approach to Nonlinear Duration Modeling: Theory and Practice (September 15, 2010). Available at SSRN: https://ssrn.com/abstract=1677752 or http://dx.doi.org/10.2139/ssrn.1677752

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