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Efficient Iterative Maximum Likelihood Estimation of High-Parameterized Time Series Models

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  • Nikolaus Hautsch
  • Ostap Okhrin
  • Alexander Ristig

Abstract

We propose an iterative procedure to efficiently estimate models with complex log-likelihood functions and the number of parameters relative to the observations being potentially high. Given consistent but inefficient estimates of sub-vectors of the parameter vector, the procedure yields computationally tractable, consistent and asymptotic efficient estimates of all parameters. We show the asymptotic normality and derive the estimator's asymptotic covariance in dependence of the number of iteration steps. To mitigate the curse of dimensionality in high-parameterized models, we combine the procedure with a penalization approach yielding sparsity and reducing model complexity. Small sample properties of the estimator are illustrated for two time series models in a simulation study. In an empirical application, we use the proposed method to estimate the connectedness between companies by extending the approach by Diebold and Yilmaz (2014) to a high-dimensional non-Gaussian setting.

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Bibliographic Info

Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2014-010.

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Length: 34 pages
Date of creation: Jan 2014
Date of revision:
Handle: RePEc:hum:wpaper:sfb649dp2014-010

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Keywords: Multi-Step estimation; Sparse estimation; Multivariate time series; Maximum likelihood estimation; Copula;

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  1. repec:sae:ecolab:v:16:y:2006:i:2:p:1-2 is not listed on IDEAS
  2. Francis X. Diebold & Kamil Yilmaz, 2011. "On the Network Topology of Variance Decompositions: Measuring the Connectedness of Financial Firms," NBER Working Papers 17490, National Bureau of Economic Research, Inc.
  3. Robert Tibshirani, 2011. "Regression shrinkage and selection via the lasso: a retrospective," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(3), pages 273-282, 06.
  4. Song, Peter X.K. & Fan, Yanqin & Kalbfleisch, John D., 2005. "Maximization by Parts in Likelihood Inference," Journal of the American Statistical Association, American Statistical Association, American Statistical Association, vol. 100, pages 1145-1158, December.
  5. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
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