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The Spatial Analysis of Time Series

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  • Joon Y. Park

Abstract

In this paper, we propose a method of analyzing time series in the spatial domain. The analysis is based on the inference on the local time and its expectation. Both for the stationary and nonstationary time series, the spatial distributions are provided by the local time, and some of their important characteristics can be examined through the investigation of the expected local time. The methodology developed in the paper for the analysis of the expected local time applies to both stationary and nonstationary time series. The expected local time, however, reduces to the density of the time invariant distribution if the underlying time series is stationary. Our analysis may therefore be regarded as an extension to the nonstationary time series of the usual distributional analysis for the stationary time series. Our approach is nonparametric, and imposes very weak and minimal conditions on the underlying time series. In particular, we allow for observations generated from a wide class of stochastic processes with stationary and mixing increments, or general markov processes including virtually all diffusion models used in practice. Proposed are several interesting applications of our methodology, such as forecast of spatial distribution, test of structural break in spatial domain, specification test in spatial domain, test of equality in spatial distribution and test of spatial dominance

Suggested Citation

  • Joon Y. Park, 2004. "The Spatial Analysis of Time Series," Econometric Society 2004 North American Winter Meetings 595, Econometric Society.
  • Handle: RePEc:ecm:nawm04:595
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    References listed on IDEAS

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    1. Oliver Linton & Esfandiar Maasoumi & Yoon-Jae Whang, 2002. "Consistent Testing for Stochastic Dominance: A Subsampling Approach," STICERD - Econometrics Paper Series 433, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    2. Bandi, Federico M., 2002. "Short-term interest rate dynamics: a spatial approach," Journal of Financial Economics, Elsevier, vol. 65(1), pages 73-110, July.
    3. Federico M. Bandi & Peter C. B. Phillips, 2003. "Fully Nonparametric Estimation of Scalar Diffusion Models," Econometrica, Econometric Society, vol. 71(1), pages 241-283, January.
    4. Peter P. Carr & Robert A. Jarrow, 2008. "The Stop-Loss Start-Gain Paradox and Option Valuation: A new Decomposition into Intrinsic and Time Value," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 4, pages 61-84 World Scientific Publishing Co. Pte. Ltd..
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    Cited by:

    1. Wang, Qiying & Phillips, Peter C.B., 2009. "Asymptotic Theory For Local Time Density Estimation And Nonparametric Cointegrating Regression," Econometric Theory, Cambridge University Press, vol. 25(03), pages 710-738, June.

    More about this item

    Keywords

    local time; expected local time; semimartingale; markov process; diffusion; bootstrap; sub-sampling.;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric 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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