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Nonparametric estimation of time-varying covariance matrix in a slowly changing vector random walk model

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  • Feng, Yuanhua
  • Yu, Keming

Abstract

A new multivariate random walk model with slowly changing parameters is introduced and investigated in detail. Nonparametric estimation of local covariance matrix is proposed. The asymptotic distributions, including asymptotic biases, variances and covariances of the proposed estimators are obtained. The properties of the estimated value of a weighted sum of individual nonparametric estimators are also studied in detail. The integrated effect of the estimation errors from the estimation for the difference series to the integrated processes is derived. Practical relevance of the model and estimation is illustrated by application to several foreign exchange rates.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 1597.

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Date of creation: 2006
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Handle: RePEc:pra:mprapa:1597

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Keywords: Multivariate time series; slowly changing vector random walk; local covariance matrix; kernel estimation; asymptotic properties; forecasting;

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  1. Feng, Yuanhua, 2004. "Simultaneously Modeling Conditional Heteroskedasticity And Scale Change," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 20(03), pages 563-596, June.
  2. Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 61(2), pages 247-64, April.
  3. Ait-Sahalia, Yacine, 1996. "Nonparametric Pricing of Interest Rate Derivative Securities," Econometrica, Econometric Society, Econometric Society, vol. 64(3), pages 527-60, May.
  4. Wei Biao Wu, 2003. "Nonparametric estimation of large covariance matrices of longitudinal data," Biometrika, Biometrika Trust, Biometrika Trust, vol. 90(4), pages 831-844, December.
  5. Beran, Jan & Feng, Yuanhua, 2002. "SEMIFAR models--a semiparametric approach to modelling trends, long-range dependence and nonstationarity," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 40(2), pages 393-419, August.
  6. Wolfgang HÄRDLE & A. TSYBAKOV & L. YANG, 1996. "Nonparametric Vector Autoregression," SFB 373 Discussion Papers 1996,61, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  7. Bollerslev, Tim & Engle, Robert F & Wooldridge, Jeffrey M, 1988. "A Capital Asset Pricing Model with Time-Varying Covariances," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 96(1), pages 116-31, February.
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