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Time Series Models with a Common Stochastic Variance for Analysing Economic Time Series

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Author Info
Siem Jan Koopman () (Faculty of Economics and Business Administration, Vrije Universiteit Amsterdam)
Charles S. Bos () (Faculty of Economics and Business Administration, Vrije Universiteit Amsterdam)

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Abstract

The linear Gaussian state space model for which the common variance is treated as a stochastic time-varying variable is considered for the modelling of economic time series. The focus of this paper is on the simultaneous estimation of parameters related to the stochastic processes of the mean part and the variance part of the model. The estimation method is based on maximum likelihood and it requires the subsequent uses of the Kalman filter to treat the mean part and sampling techniques to treat the variance part. This approach leads to the evaluation of the exact likelihood function of the model subject to simulation error. The standard asymptotic properties of maximum likelihood estimators apply as a result. A Monte Carlo study is carried out to investigate the small-sample properties of the estimation procedure. We present two illustrations which are concerned with the modelling and forecasting of two U.S. macroeconomic time series: inflation and industrial production.

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Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 02-113/4.

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Date of creation: 12 Nov 2002
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Handle: RePEc:dgr:uvatin:20020113

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Web page: http://www.tinbergen.nl/

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Related research
Keywords: Autoregressive integrated moving average Importance sampling Industrial production Inflation Kalman filer Monte Carlo simulation Simulation smoothing State space Stochastic volatility Unobserved components time series.

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Find related papers by JEL classification:
C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Statistical Simulation Methods
C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models
C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
E23 - Macroeconomics and Monetary Economics - - Macroeconomics: Consumption, Saving, Production, Employment, and Investment - - - Production
E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation

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  2. Siem Jan Koopman & Neil Shephard, 2002. "Testing the Assumptions Behind the Use of Importance Sampling," Economics Papers 2002-W17, Economics Group, Nuffield College, University of Oxford. [Downloadable!]
  3. Jurgen A Doornik & Henrik Hansen, . "An omnibus test for univariate and multivariate normalit," Economics Papers W4&91., Economics Group, Nuffield College, University of Oxford. [Downloadable!]
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  5. Sandmann, Gleb & Koopman, Siem Jan, 1998. "Estimation of stochastic volatility models via Monte Carlo maximum likelihood," Journal of Econometrics, Elsevier, vol. 87(2), pages 271-301, September. [Downloadable!] (restricted)
  6. Siem Jan Koopman & Neil Shephard & Jurgen A. Doornik, 1999. "Statistical algorithms for models in state space using SsfPack 2.2," Econometrics Journal, Royal Economic Society, vol. 2(1), pages 107-160.
    Other versions:
  7. Kloek, Tuen & van Dijk, Herman K, 1978. "Bayesian Estimates of Equation System Parameters: An Application of Integration by Monte Carlo," Econometrica, Econometric Society, vol. 46(1), pages 1-19, January. [Downloadable!] (restricted)
  8. Ghysels, E. & Harvey, A. & Renault, E., 1996. "Stochastic Volatility," Cahiers de recherche 9613, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
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  9. Ord, J.K. & Koehler, A. & Snyder, R.D., 1995. "Estimation and Prediction for a Class of Dynamic Nonlinear Statistical Models," Monash Econometrics and Business Statistics Working Papers 4/95, Monash University, Department of Econometrics and Business Statistics.
  10. Christoffersen, Peter F, 1998. "Evaluating Interval Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-62, November.
  11. Andrew Harvey & Siem Jan Koopman, 2000. "Signal extraction and the formulation of unobserved components models," Econometrics Journal, Royal Economic Society, vol. 3(1), pages 84-107.
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  12. Danielsson, Jon, 1994. "Stochastic volatility in asset prices estimation with simulated maximum likelihood," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 375-400. [Downloadable!] (restricted)
  13. Gallant, A. Ronald & Hsieh, David & Tauchen, George, 1997. "Estimation of stochastic volatility models with diagnostics," Journal of Econometrics, Elsevier, vol. 81(1), pages 159-192, November. [Downloadable!] (restricted)
  14. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 1994. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 371-89, October.
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  15. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July. [Downloadable!] (restricted)
  16. Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Blackwell Publishing, vol. 61(2), pages 247-64, April. [Downloadable!] (restricted)
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