By G. S. Maddala
Time sequence research has gone through many adjustments in the course of fresh years with the appearance of unit roots and cointegration. This textbook through G. S. Maddala and In-Moo Kim relies on a winning lecture application and gives a complete evaluate of those themes in addition to structural swap. G. S. Maddala is among the so much uncommon writers of graduate and undergraduate econometrics textbooks this present day and Unit Roots, Cointegration and Structural swap represents an important contribution that would be of curiosity either to experts and graduate and undergraduate scholars.
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Additional resources for Unit Roots, Cointegration, and Structural Change (Themes in Modern Econometrics)
Example text
9 Unit root tests As discussed earlier, the question of whether to detrend or to difference a time series prior to further analysis depends on whether the time series is trend-stationary (TSP) or difference-stationary (DSP). If the series is trend-stationary, the data generating process (DGP) for yt can be written as Vt = 7o + 7i* + et where t is time and et is a stationary ARM A process. If it is differencestationary, the DGP for yt can be written as yt = a0 + yt-i + et where et is again a stationary ARMA process.
If the time series is DSP and we treat it as TSP, this is a case of underdifferencing. If the time series is TSP, but we treat it as DSP, we have a case of overdifferencing. However, the serial correlation properties of the resulting errors from the misspecified processes need to be considered. e. Ayt = (3Axt + et this implies that yt = a + (3xt + ut where ut = et+et-\-\ is serially correlated and nonstationary. e. yt = a + f)xt + vt this implies that Ayt = (3Axt +vt -vt-i The errors follow a noninvertible moving-average process.
6666. , 13 recursively. This method can be used whether the roots are real or complex. 1 shows a plot of this correlogram. 4 Autoregressive moving-average (ARMA) processes We will now discuss models that are combinations of the AR and MA models. These are called ARM A models. ie t -i + • • • + Pqet- 16 Basic concepts Lags Fig. 1. Correlogram of an AR(2) model where St is a purely random process with mean zero and variance a2. The motivation for these methods is that they lead to parsimonious representations of higher-order AR(oo) or MA(oo) processes.