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Econometric Analysis of Continuous Time Models: A Survey of Peter Phillips' Work and Some New Results

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  • Jun Yu

    (Sim Kee Boon Institute for Financial Economics, Singapore Management University)

Abstract

Econometric analysis of continuous time models has drawn the attention of Peter Phillips for nearly 40 years, resulting in many important publications by him. In these publications he has dealt with a wide range of continuous time models and econometric problems, from univariate equations to systems of equations, from asymptotic theory to nite sample issues, from parametric models to nonparametric models, from identi cation problems to estimation and inference problems, 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 two asymptotic distributions in a simple setup. Results indicate that the in- ll asymptotics signi cantly outperforms the long-span asymptotics.

Suggested Citation

  • Jun Yu, 2009. "Econometric Analysis of Continuous Time Models: A Survey of Peter Phillips' Work and Some New Results," Working Papers CoFie-04-2009, Singapore Management University, Sim Kee Boon Institute for Financial Economics.
    • Handle: RePEc:skb:wpaper:cofie-04-2009
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    Cited by:

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    2. H. Peter Boswijk & Jun Yu & Yang Zu, 2024. "Testing for an Explosive Bubble using High-Frequency Volatility," Working Papers 202402, University of Macau, Faculty of Business Administration.
    3. Wang, Xiaohu & Xiao, Weilin & Yu, Jun, 2023. "Modeling and forecasting realized volatility with the fractional Ornstein–Uhlenbeck process," Journal of Econometrics, Elsevier, vol. 232(2), pages 389-415.
    4. Jiang, Liang & Wang, Xiaohu & Yu, Jun, 2018. "New distribution theory for the estimation of structural break point in mean," Journal of Econometrics, Elsevier, vol. 205(1), pages 156-176.
    5. Zhou, Qiankun & Yu, Jun, 2015. "Asymptotic theory for linear diffusions under alternative sampling schemes," Economics Letters, Elsevier, vol. 128(C), pages 1-5.
    6. Yiu Lim Lui & Weilin Xiao & Jun Yu, 2022. "The Grid Bootstrap for Continuous Time Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(3), pages 1390-1402, June.
    7. Wang, Xiaohu & Yu, Jun, 2016. "Double asymptotics for explosive continuous time models," Journal of Econometrics, Elsevier, vol. 193(1), pages 35-53.
    8. Emma M. Iglesias & Garry D. A. Phillips, 2020. "Further Results on Pseudo‐Maximum Likelihood Estimation and Testing in the Constant Elasticity of Variance Continuous Time Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(2), pages 357-364, March.
    9. Tayanagi, Toshikazu & 田柳, 俊和 & Kurozumi, Eiji & 黒住, 英司, 2022. "In-fill asymptotic distribution of the change point estimator when estimating breaks one at a time," Discussion Papers 2022-03, Graduate School of Economics, Hitotsubashi University.
    10. Marcus J. Chambers & J. Roderick McCrorie & Michael A. Thornton, 2018. "Continuous Time Modelling Based on an Exact Discrete Time Representation," Springer Books, in: Kees van Montfort & Johan H. L. Oud & Manuel C. Voelkle (ed.), Continuous Time Modeling in the Behavioral and Related Sciences, chapter 0, pages 317-357, Springer.
    11. Zhan, Yaosong & Ling, Shiqing & Liu, Zhenya & Wang, Shixuan, 2025. "Modeling bimodal stock price dynamics by a parsimonious diffusion process," International Review of Financial Analysis, Elsevier, vol. 105(C).

    More about this item

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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