Extracting a Common Stochastic Trend:Theories with Some Applications
AbstractThis paper investigates the statistical properties of the Kalman filter for state space models including integrated time series. In particular, we derive the full asymptotics of maximum likelihood estimation for some prototypical class of such models, i.e., the models with a single latent common stochastic trend. Indeed, we establish the consistency and asymptotic mixed normality of the maximum likelihood estimator and show that the conventional method of infer- ence is valid for this class of models. The models considered explicitly in the paper comprise a special, yet useful, class of models that we may use to extract the common stochastic trend from multiple integrated time series. As we show in the paper, the models can be very useful to obtain indices that represent fluctuations of various markets or common latent factors that affect a set of economic and financial variables simultaneously. Moreover, our derivation of the asymptotics of this class makes it clear that the asymptotic Gaussianity and the validity of the conventional inference for the maximum likelihood procedure extends to a larger class of more general state space models involving integrated time series. Finally, we demonstrate the utility of the state space model by ex- tracting a common stochastic trend in three empirical analyses: interest rates, return volatility and trading volume, and Dow Jones stock prices.
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Bibliographic InfoPaper provided by Department of Economics, University of Missouri in its series Working Papers with number 0507.
Length: 38 pgs.
Date of creation: 15 Oct 2005
Date of revision: 18 Aug 2005
state space model; Kalman filter; common stochastic trend; maximum likelihood estimation; stock price index; interest rates; return volatility and trading volume.;
Other versions of this item:
- Chang, Yoosoon & Miller, J. Isaac & Park, Joon Y., 2005. "Extracting a Common Stochastic Trend: Theories with Some Applications," Working Papers 2005-06, Rice University, Department of Economics.
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
- C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Campbell, John Y & Shiller, Robert J, 1987.
"Cointegration and Tests of Present Value Models,"
Journal of Political Economy,
University of Chicago Press, vol. 95(5), pages 1062-88, October.
- John Y. Campbell & Robert J. Shiller, 1986. "Cointegration and Tests of Present Value Models," Cowles Foundation Discussion Papers 785, Cowles Foundation for Research in Economics, Yale University.
- Campbell, John & Shiller, Robert, 1987. "Cointegration and Tests of Present Value Models," Scholarly Articles 3122490, Harvard University Department of Economics.
- John Y. Campbell & Robert J. Shiller, 1986. "Cointegration and Tests of Present Value Models," NBER Working Papers 1885, National Bureau of Economic Research, Inc.
- Joon Y. Park & J. Isaac Miller, 2004.
"Nonlinearity, Nonstationarity, and Thick Tails: How They Interact to Generate Persistency in Memory,"
Econometric Society 2004 North American Summer Meetings
597, Econometric Society.
- Miller, J. Isaac & Park, Joon Y., 2010. "Nonlinearity, nonstationarity, and thick tails: How they interact to generate persistence in memory," Journal of Econometrics, Elsevier, vol. 155(1), pages 83-89, March.
- J. Isaac Miller & Joon Y. Park, 2008. "Nonlinearity, Nonstationarity, and Thick Tails: How They Interact to Generate Persistency in Memory," Working Papers 0801, Department of Economics, University of Missouri.
- Danny Quah, 1991.
"The Relative Importance of Permanent and Transitory Components: Identi- fication and Some Theoretical Bounds,"
NBER Technical Working Papers
0106, National Bureau of Economic Research, Inc.
- Quah, Danny, 1992. "The Relative Importance of Permanent and Transitory Components: Identification and Some Theoretical Bounds," Econometrica, Econometric Society, vol. 60(1), pages 107-18, January.
- Danny Quah, 1988. "The Relative Importance of Permanent and Transitory Components: Identification and Some Theoretical Bounds," Working papers 498, Massachusetts Institute of Technology (MIT), Department of Economics.
- Danny Quah, 1991. "The Relative Importance of Permanent and Transitory Components: Identification and Some Theoretical Bounds," FMG Discussion Papers dp126, Financial Markets Group.
- Karpoff, Jonathan M., 1987. "The Relation between Price Changes and Trading Volume: A Survey," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(01), pages 109-126, March.
- Foster, F Douglas & Viswanathan, S, 1995. "Can Speculative Trading Explain the Volume-Volatility Relation?," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(4), pages 379-96, October.
- Thomas J. Sargent, 1978.
"A note on maximum likelihood estimation of the rational expectations model of the term structure,"
26, Federal Reserve Bank of Minneapolis.
- Sargent, Thomas J., 1979. "A note on maximum likelihood estimation of the rational expectations model of the term structure," Journal of Monetary Economics, Elsevier, vol. 5(1), pages 133-143, January.
- BAUWENS, Luc & DEPRINS, Dominique & VANDEUREN, Jean-Pierre, 1997. "Modelling interest rates with a cointegrated VAR-GARCH model," CORE Discussion Papers 1997080, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Jeff Fleming & Chris Kirby & Barbara Ostdiek, 2006. "Stochastic Volatility, Trading Volume, and the Daily Flow of Information," The Journal of Business, University of Chicago Press, vol. 79(3), pages 1551-1590, May.
- Gonzalo, J. & Granger, C., 1992.
"Estimation of Common Long-Memory Components in Cointegrated Systems,"
4, Boston University - Department of Economics.
- Gonzalo, Jesus & Granger, Clive W J, 1995. "Estimation of Common Long-Memory Components in Cointegrated Systems," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(1), pages 27-35, January.
- Modigliani, Franco & Shiller, Robert J, 1973. "Inflation, Rational Expectations and the Term Structure of Interest Rates," Economica, London School of Economics and Political Science, vol. 40(157), pages 12-43, February.
- Chang-Jin Kim & Charles R. Nelson, 1999. "State-Space Models with Regime Switching: Classical and Gibbs-Sampling Approaches with Applications," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262112388, December.
- repec:fth:louvco:9780 is not listed on IDEAS
- Joon Y. Park & Peter C. B. Phillips, 1999.
"Nonlinear Regressions with Integrated Time Series,"
Working Paper Series
no6, Institute of Economic Research, Seoul National University.
- Tauchen, George E & Pitts, Mark, 1983. "The Price Variability-Volume Relationship on Speculative Markets," Econometrica, Econometric Society, vol. 51(2), pages 485-505, March.
- Hafer, R. W. & Kutan, Ali M. & Su Zhou, 1997. "Linkage in EMS term structures: evidence from common trend and transitory components," Journal of International Money and Finance, Elsevier, vol. 16(4), pages 595-607, August.
- Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
- Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, vol. 55(2), pages 251-76, March.
- Hai, Weike & Mark, Nelson C & Wu, Yangru, 1997. "Understanding Spot and Forward Exchange Rate Regressions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 12(6), pages 715-34, Nov.-Dec..
- Tara Sinclair & Sinchan Mitra, 2008.
"Output Fluctuations in the G-7: An Unobserved Components Approach,"
2008-04, The George Washington University, Institute for International Economic Policy.
- Mitra, Sinchan & Sinclair, Tara M., 2012. "Output Fluctuations In The G-7: An Unobserved Components Approach," Macroeconomic Dynamics, Cambridge University Press, vol. 16(03), pages 396-422, June.
- Sinchan Mitra & Tara M. Sinclair, . "Output Fluctuations in the G-7: An Unobserved Components Approach," MRG Discussion Paper Series 2509, School of Economics, University of Queensland, Australia.
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