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Continuous Weak Convergence and Stochastic Equicontinuity Results for Integrated Processes with an Application to the Estimation of a Regression Model

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  • Saikkonen, Pentti

Abstract

The concepts of continuous and uniform weak convergence and versions of stochastic equicontinuity are discussed in the context of integrated processes of order one. The considered processes depend on a parameter vector in a specific fashion which is relevant for integrated and cointegrated systems with non-linearities in parameters. The results of the paper can be applied to obtain asymptotic distributions of estimators and test statistics in such systems. In a correctly specified cointegrated Gaussian system, this can be done in a very convenient way. Combining the results of this paper with available general maximum likelihood estimation theories readily shows that the maximum likelihood estimator is asymptotically optimal with a mixed normal limiting distribution. The usefulness of this approach is demonstrated by analyzing a regression model with autoregressive moving average errors and strictly exogenous regressors which may be either integrated of order one, asymptotically stationary, or nonstochastic and bounded.

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  • Saikkonen, Pentti, 1993. "Continuous Weak Convergence and Stochastic Equicontinuity Results for Integrated Processes with an Application to the Estimation of a Regression Model," Econometric Theory, Cambridge University Press, vol. 9(2), pages 155-188, April.
    • Handle: RePEc:cup:etheor:v:9:y:1993:i:02:p:155-188_00
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    Cited by:

    1. Dietmar Bauer & Martin Wagner, 2002. "Asymptotic Properties of Pseudo Maximum Likelihood Estimates for Multiple Frequency I(1) Processes," Diskussionsschriften dp0205, Universitaet Bern, Departement Volkswirtschaft.
    2. Seo, Byeongseon, 1999. "Distribution theory for unit root tests with conditional heteroskedasticity1," Journal of Econometrics, Elsevier, vol. 91(1), pages 113-144, July.
    3. Pentti Saikkonen & Rickard Sandberg, 2016. "Testing for a Unit Root in Noncausal Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(1), pages 99-125, January.
    4. repec:zbw:bofrdp:2013_026 is not listed on IDEAS
    5. M. Hashem Pesaran & Yongcheol Shin, 2002. "Long-Run Structural Modelling," Econometric Reviews, Taylor & Francis Journals, vol. 21(1), pages 49-87.
    6. Julien Hambuckers & Li Sun & Luca Trapin, 2023. "Measuring tail risk at high-frequency: An $L_1$-regularized extreme value regression approach with unit-root predictors," Papers 2301.01362, arXiv.org.
    7. Bonham, Carl & Gangnes, Byron & Zhou, Ting, 2009. "Modeling tourism: A fully identified VECM approach," International Journal of Forecasting, Elsevier, vol. 25(3), pages 531-549, July.
    8. Pentti Saikkonen & Rickard Sandberg, 2016. "Testing for a Unit Root in Noncausal Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(1), pages 99-125, January.
    9. Allison Zhou & Carl Bonham & Byron Gangnes, 2007. "Modeling the supply and demand for tourism: a fully identified VECM approach," Working Papers 200717, University of Hawaii at Manoa, Department of Economics.
    10. Saikkonen, Pentti & Choi, In, 2000. "Cointegrating smooth transition regressions with applications to the Asian currency crisis," SFB 373 Discussion Papers 2000,98, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.

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