Integrated modified OLS and fixed-b inference for seasonally cointegrated processes
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Date
2020
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Abstract
Many economic time series exhibit persistent seasonal patterns. One approach to model
this phenomenon is given by models including seasonal unit roots and, if several time series
are considered jointly, seasonal cointegration. For quarterly time series, e.g., unit roots may
be present at frequencies =2 and , in addition to the “standard unit root” at frequency
zero. Gregoir (2010) has extended the fully modified OLS estimator of Phillips and Hansen
(1990) from the cointegrating regression to the seasonally cointegrating regression case. In
this paper, we have a similar agenda, in that we undertake the corresponding extension for
the IM-OLS estimator of Vogelsang and Wagner (2014). The benefit of the seasonal IMOLS
estimator, or SIM-OLS estimator, is that it forms the basis not only for asymptotic
standard inference but also allows for fixed-b inference. The paper furthermore proposes a
test for seasonal cointegration at all unit root frequencies. Note here that the cointegrating
spaces in general differ across frequencies and have to be estimated separately for each
frequency. The theoretical analysis is complemented by a simulation study.
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Keywords
seasonal cointegration, cointegration test, fixed-b inference, SIM-OLS, seasonal unit roots