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Vector Error Correction Models

In: New Introduction to Multiple Time Series Analysis

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  • Helmut Lütkepohl

    (European University Institute)

Abstract

As defined in Chapter 2, a process is stationary if it has time invariant first and second moments. In particular, it does not have trends or changing variances. A VAR process has this property if the determinantal polynomial of its VAR operator has all its roots outside the complex unit circle. Clearly, stationary processes cannot capture some main features of many economic time series. For example, trends (trending means) are quite common in practice. For instance, the original investment, income, and consumption data used in many previous examples have trends (see Figure 3.1). Thus, if interest centers on analyzing the original variables (or their logarithms) rather than the rates of change, it is necessary to have models that accommodate the nonstationary features of the data. It turns out that a VAR process can generate stochastic and deterministic trends if the determinantal polynomial of the VAR operator has roots on the unit circle. In fact, it is even sufficient to allow for unit roots (roots for z = 1) to obtain a trending behavior of the variables. We will consider this case in some detail in this chapter. In the next section, the effect of unit roots in the AR operator of a univariate process will be analyzed. Variables generated by such processes are called integrated variables and the underlying generating processes are integrated processes. Vector processes with unit roots are considered in Section 6.2. In these processes, some of the variables can have common trends so that they move together to some extent.

Suggested Citation

  • Helmut Lütkepohl, 2005. "Vector Error Correction Models," Springer Books, in: New Introduction to Multiple Time Series Analysis, chapter 6, pages 237-267, Springer.
  • Handle: RePEc:spr:sprchp:978-3-540-27752-1_6
    DOI: 10.1007/978-3-540-27752-1_6
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    References listed on IDEAS

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    1. Ralf Brüggemann & Helmut Lütkepohl, 2005. "Practical Problems with Reduced‐rank ML Estimators for Cointegration Parameters and a Simple Alternative," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 67(5), pages 673-690, October.
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    6. Benkwitz, Alexander & Lütkepohl, Helmut & Wolters, Jürgen, 2001. "Comparison Of Bootstrap Confidence Intervals For Impulse Responses Of German Monetary Systems," Macroeconomic Dynamics, Cambridge University Press, vol. 5(1), pages 81-100, February.
    7. Lütkepohl,Helmut & Krätzig,Markus (ed.), 2004. "Applied Time Series Econometrics," Cambridge Books, Cambridge University Press, number 9780521547871, December.
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    18. Lütkepohl,Helmut & Krätzig,Markus (ed.), 2004. "Applied Time Series Econometrics," Cambridge Books, Cambridge University Press, number 9780521839198, December.
    19. Vlaar, Peter J.G., 2004. "On The Asymptotic Distribution Of Impulse Response Functions With Long-Run Restrictions," Econometric Theory, Cambridge University Press, vol. 20(5), pages 891-903, October.
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    More about this item

    Keywords

    Unit Root; Forecast Error; Vector Error Correction Model; Deterministic Term; Cointegration Relation;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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