Extracting a common stochastic trend: Theory with some applications
This paper investigates the statistical properties of estimators of the parameters and unobserved series for state space models with integrated time series. In particular, we derive the full asymptotic results for maximum likelihood estimation using the Kalman filter for a prototypical class of such models--those 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 inference is valid for this class of models. The models we explicitly consider comprise a special-yet useful-class of models that may be employed to extract the common stochastic trend from multiple integrated time series. Such 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 this class of models extracting a common stochastic trend from three sets of time series involving short- and long-term interest rates, stock return volatility and trading volume, and Dow Jones stock prices.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
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.:
- Kwiatkowski, Denis & Phillips, Peter C. B. & Schmidt, Peter & Shin, Yongcheol, 1992.
"Testing the null hypothesis of stationarity against the alternative of a unit root : How sure are we that economic time series have a unit root?,"
Journal of Econometrics,
Elsevier, vol. 54(1-3), pages 159-178.
- Kwiatkowski, D. & Phillips, P.C.B. & Schmidt, P., 1990. "Testing the Null Hypothesis of Stationarity Against the Alternative of Unit Root : How Sure are we that Economic Time Series have a Unit Root?," Papers 8905, Michigan State - Econometrics and Economic Theory.
- Denis Kwiatkowski & Peter C.B. Phillips & Peter Schmidt, 1991. "Testing the Null Hypothesis of Stationarity Against the Alternative of a Unit Root: How Sure Are We That Economic Time Series Have a Unit Root?," Cowles Foundation Discussion Papers 979, Cowles Foundation for Research in Economics, Yale 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.
- 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.
- Tom Doan, "undated". "RATS programs to replicate Gonzalo and Granger JBES 1995 paper," Statistical Software Components RTZ00074, Boston College Department of Economics.
- Gonzalo, J. & Granger, C., 1992. "Estimation of Common Long-Memory Components in Cointegrated Systems," Papers 4, Boston University - Department of Economics.
- Park, Joon Y & Phillips, Peter C B, 2001.
"Nonlinear Regressions with Integrated Time Series,"
Econometric Society, vol. 69(1), pages 117-161, January.
- 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.
- Joon Y. Park & Peter C.B. Phillips, 1998. "Nonlinear Regressions with Integrated Time Series," Cowles Foundation Discussion Papers 1190, Cowles Foundation for Research in Economics, Yale University.
- 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).
- Yoosoon Chang & Joon Park, 2002. "On The Asymptotics Of Adf Tests For Unit Roots," Econometric Reviews, Taylor & Francis Journals, vol. 21(4), pages 431-447.
- Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Heiko Ebens, 2000.
"The Distribution of Stock Return Volatility,"
Center for Financial Institutions Working Papers
00-27, Wharton School Center for Financial Institutions, University of Pennsylvania.
- 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.
- Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-155, January.
- 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.
- 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.
- Engle, Robert & Granger, Clive, 2015.
"Co-integration and error correction: Representation, estimation, and testing,"
Publishing House "SINERGIA PRESS", vol. 39(3), pages 106-135.
- Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, vol. 55(2), pages 251-276, March.
- 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.
- Gallant, A Ronald & Rossi, Peter E & Tauchen, George, 1992. "Stock Prices and Volume," Review of Financial Studies, Society for Financial Studies, vol. 5(2), pages 199-242.
- 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.
- 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.
- Andersen, Torben G & Bollerslev, Tim, 1998. "Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 885-905, November.
- Park, Joon Y, 1992. "Canonical Cointegrating Regressions," Econometrica, Econometric Society, vol. 60(1), pages 119-143, January.
- 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.
- Thomas J. Sargent, 1978. "A note on maximum likelihood estimation of the rational expectations model of the term structure," Staff Report 26, Federal Reserve Bank of Minneapolis.
- Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
When requesting a correction, please mention this item's handle: RePEc:eee:econom:v:150:y:2009:i:2:p:231-247. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Shamier, Wendy)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.