Extracting a Common Stochastic Trend:Theories with Some Applications
J. Miller (),
Yoosoon Chang () and
Joon Park ()
No 507, Working Papers from Department of Economics, University of Missouri
This 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.
Keywords: state space model; Kalman filter; common stochastic trend; maximum likelihood estimation; stock price index; interest rates; return volatility and trading volume. (search for similar items in EconPapers)
JEL-codes: C13 C32 (search for similar items in EconPapers)
Date: 2005-10-15, Revised 2005-08-18
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Published in Journal of Econometrics 2009
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Working Paper: Extracting a Common Stochastic Trend: Theories with Some Applications (2005)
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Persistent link: https://EconPapers.repec.org/RePEc:umc:wpaper:0507
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