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
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