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    Extracting a Common Stochastic Trend: Theory with Some Applications

    Chang, Yoosoon
    Miller, J. Isaac
    Park, Joon Y.
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    [PDF] ExtractingCommonStochasticTrend.pdf (922.9Kb)
    Date
    2008
    Format
    Working Paper
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    Abstract
    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.
    URI
    http://hdl.handle.net/10355/2632
    Part of
    Working papers (Department of Economics);WP 05-07
    Part of
    Economics publications
    Citation
    Department of Economics, 2008
    Collections
    • Economics publications (MU)

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