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Local inference for locally stationary time series based on the empirical spectral measure


  • Dahlhaus, Rainer


The time varying empirical spectral measure plays a major role in the treatment of inference problems for locally stationary processes. The properties of the empirical spectral measure and related statistics are studied -- both when its index function is fixed or when dependent on the sample size. In particular we prove a general central limit theorem. Several applications and examples are given including semiparametric Whittle estimation, local least squares estimation and spectral density estimation.

Suggested Citation

  • Dahlhaus, Rainer, 2009. "Local inference for locally stationary time series based on the empirical spectral measure," Journal of Econometrics, Elsevier, vol. 151(2), pages 101-112, August.
  • Handle: RePEc:eee:econom:v:151:y:2009:i:2:p:101-112

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    References listed on IDEAS

    1. Dahlhaus, Rainer & Neumann, Michael H., 2001. "Locally adaptive fitting of semiparametric models to nonstationary time series," Stochastic Processes and their Applications, Elsevier, vol. 91(2), pages 277-308, February.
    2. G. P. Nason & R. Von Sachs & G. Kroisandt, 2000. "Wavelet processes and adaptive estimation of the evolutionary wavelet spectrum," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 271-292.
    3. Kim, Woocheol, 2001. "Nonparametric kernel estimation of evolutionary autoregressive processes," SFB 373 Discussion Papers 2001,103, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    4. Sakiyama, Kenji & Taniguchi, Masanobu, 2004. "Discriminant analysis for locally stationary processes," Journal of Multivariate Analysis, Elsevier, vol. 90(2), pages 282-300, August.
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    Cited by:

    1. Gadea Rivas, María Dolores & Gonzalo, Jesús, 2017. "Trends in distributional characteristics : Existence of global warming," UC3M Working papers. Economics 24121, Universidad Carlos III de Madrid. Departamento de Economía.
    2. Matteo Barigozzi & Marc Hallin & Stefano Soccorsi, 2019. "Time-Varying General Dynamic Factor Models and the Measurement of Financial Connectedness," Working Papers ECARES 2019-09, ULB -- Universite Libre de Bruxelles.
    3. Rasmus Tangsgaard Varneskov, 2011. "Flat-Top Realized Kernel Estimation of Quadratic Covariation with Non-Synchronous and Noisy Asset Prices," CREATES Research Papers 2011-35, Department of Economics and Business Economics, Aarhus University.
    4. Ruprecht Puchstein & Philip Preuß, 2016. "Testing for Stationarity in Multivariate Locally Stationary Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(1), pages 3-29, January.
    5. Roueff, François & von Sachs, Rainer, 2011. "Locally stationary long memory estimation," Stochastic Processes and their Applications, Elsevier, vol. 121(4), pages 813-844, April.
    6. Efstathios Paparoditis & Philip Preuß, 2016. "On Local Power Properties of Frequency Domain-based Tests for Stationarity," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(3), pages 664-682, September.
    7. Inder Tecuapetla-Gómez & Michael Nussbaum, 2012. "On large deviations in testing simple hypotheses for locally stationary Gaussian processes," Statistical Inference for Stochastic Processes, Springer, vol. 15(3), pages 225-239, October.
    8. Roueff, François & von Sachs, Rainer & Sansonnet, Laure, 2016. "Locally stationary Hawkes processes," Stochastic Processes and their Applications, Elsevier, vol. 126(6), pages 1710-1743.
    9. repec:bla:jtsera:v:38:y:2017:i:2:p:204-224 is not listed on IDEAS
    10. Philip Preuss & Mathias Vetter & Holger Dette, 2013. "Testing Semiparametric Hypotheses in Locally Stationary Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(3), pages 417-437, September.


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