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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Lütkepohl, H. (2005). Vector Error Correction Models. In: New Introduction to Multiple Time Series Analysis. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27752-1_6
Download citation
DOI: https://doi.org/10.1007/978-3-540-27752-1_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40172-8
Online ISBN: 978-3-540-27752-1
eBook Packages: Business and EconomicsEconomics and Finance (R0)