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Strict Stationarity Testing and GLAD Estimation of Double Autoregressive Models

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  • Guo, Shaojun
  • Li, Dong
  • Li, Muyi

Abstract

In this article we develop a tractable procedure for testing strict stationarity in a double autoregressive model and formulate the problem as testing if the top Lyapunov exponent is negative. Without strict stationarity assumption, we construct a consistent estimator of the associated top Lyapunov exponent and employ a random weighting approach for its variance estimation, which in turn are used in a t-type test. We also propose a GLAD estimation for parameters of interest, relaxing key assumptions on the commonly used QMLE. All estimators, except for the intercept, are shown to be consistent and asymptotically normal in both stationary and explosive situations. The nite-sample performance of the proposed procedures is evaluated via Monte Carlo simulation studies and a real dataset of interest rates is analyzed.

Suggested Citation

  • Guo, Shaojun & Li, Dong & Li, Muyi, 2018. "Strict Stationarity Testing and GLAD Estimation of Double Autoregressive Models," IRTG 1792 Discussion Papers 2018-049, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    • Handle: RePEc:zbw:irtgdp:2018049
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    Cited by:

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    2. Wang, Honglin & Yu, Fan & Zhou, Yinggang, 2018. "Property Investment and Rental Rate under Housing Price Uncertainty: A Real Options Approach," IRTG 1792 Discussion Papers 2018-051, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    3. Zhong, Wei & Liu, Xi & Ma, Shuangge, 2018. "Variable selection and direction estimation for single-index models via DC-TGDR method," IRTG 1792 Discussion Papers 2018-050, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    4. Xiaojia Bao & Qingliang Fan, 2020. "The impact of temperature on gaming productivity: evidence from online games," Empirical Economics, Springer, vol. 58(2), pages 835-867, February.
    5. Yatracos, Yannis G., 2018. "Residual'S Influence Index (Rinfin), Bad Leverage And Unmasking In High Dimensional L2-Regression," IRTG 1792 Discussion Papers 2018-060, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".

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    More about this item

    Keywords

    DAR model; GLAD estimation; Nonstationarity; Random weighting; Strict stationarity testing;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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