ECONOMETRIC ANALYSIS OF CONTINUOUS TIME MODELS: A SURVEY OF PETER PHILLIPS’S WORK AND SOME NEW RESULTS

Econometric analysis of continuous time models has drawn the attention of Peter Phillips for 40 years, resulting in many important publications by him. In these publications he has dealt with a wide range of continuous time models and the associated econometric problems. He has investigated problems from univariate equations to systems of equations, from asymptotic theory to finite sample issues, from parametric models to nonparametric models, from identification problems to estimation and inference problems, and from stationary models to nonstationary and nearly nonstationary models. This paper provides an overview of Peter Phillips’ contributions in the continuous time econometrics literature. We review the problems that have been tackled by him, outline the main techniques suggested by him, and discuss the main results obtained by him. Based on his early work, we compare the performance of three asymptotic distributions in a simple setup. Results indicate that thein-fillasymptotics significantly outperforms thelong-spanasymptotics and thedoubleasymptotics.

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A nondegenerate Vuong test and post selection confidence intervals for semi/nonparametric models

Quantitative Economics ◽

10.3982/qe1312 ◽

2020 ◽

Vol 11 (3) ◽

pp. 983-1017

Author(s):

Zhipeng Liao ◽

Xiaoxia Shi

Keyword(s):

Model Selection ◽

Size Control ◽

Parametric Models ◽

Model Parameters ◽

Local Alternatives ◽

Finite Sample ◽

Inference Procedure ◽

Uniform Size ◽

Nonparametric Models ◽

Asymptotic Size

This paper proposes a new model selection test for the statistical comparison of semi/non‐parametric models based on a general quasi‐likelihood ratio criterion. An important feature of the new test is its uniformly exact asymptotic size in the overlapping nonnested case, as well as in the easier nested and strictly nonnested cases. The uniform size control is achieved without using pretesting, sample‐splitting, or simulated critical values. We also show that the test has nontrivial power against all n ‐local alternatives and against some local alternatives that converge to the null faster than n . Finally, we provide a framework for conducting uniformly valid post model selection inference for model parameters. The finite sample performance of the nondegenerate test and that of the post model selection inference procedure are illustrated in a mean‐regression example by Monte Carlo.

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Diagnosing Multivariate Continuous-Time Models with Application to Affine Term Structure Models

SSRN Electronic Journal ◽

10.2139/ssrn.858724 ◽

2005 ◽

Cited By ~ 2

Author(s):

Bin Chen ◽

Yongmiao Hong

Keyword(s):

Term Structure ◽

Continuous Time ◽

Affine Term Structure ◽

Affine Term Structure Models ◽

Term Structure Models ◽

Continuous Time Models

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Continuous-Time Models in Corporate Finance, Banking, and Insurance

10.2307/j.ctvc774r0 ◽

2018 ◽

Cited By ~ 1

Author(s):

Santiago Moreno-Bromberg ◽

Jean-Charles Rochet

Keyword(s):

Corporate Finance ◽

Continuous Time ◽

Continuous Time Models

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Statistical Inference for the Beta Coefficient

Risks ◽

10.3390/risks7020056 ◽

2019 ◽

Vol 7 (2) ◽

pp. 56 ◽

Cited By ~ 1

Author(s):

Taras Bodnar ◽

Arjun K. Gupta ◽

Valdemar Vitlinskyi ◽

Taras Zabolotskyy

Keyword(s):

Confidence Interval ◽

Empirical Study ◽

Crucial Role ◽

Risk Measure ◽

Statistical Test ◽

Asymptotic Distributions ◽

Finite Sample ◽

Benchmark Portfolio ◽

Beta Coefficient ◽

Theoretical Results

The beta coefficient plays a crucial role in finance as a risk measure of a portfolio in comparison to the benchmark portfolio. In the paper, we investigate statistical properties of the sample estimator for the beta coefficient. Assuming that both the holding portfolio and the benchmark portfolio consist of the same assets whose returns are multivariate normally distributed, we provide the finite sample and the asymptotic distributions of the sample estimator for the beta coefficient. These findings are used to derive a statistical test for the beta coefficient and to construct a confidence interval for the beta coefficient. Moreover, we show that the sample estimator is an unbiased estimator for the beta coefficient. The theoretical results are implemented in an empirical study.

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