Unit Root Tests in Time Series: Extensions and Developments by K. Patterson

By K. Patterson

Testing for a Unit Root is now a necessary a part of time sequence research however the literature at the subject is so huge that realizing the place to begin is tough even for the professional. This publication presents a fashion into the options of unit root checking out, explaining the pitfalls and nonstandard instances, utilizing sensible examples and simulation analysis.

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Sample text

023yt−1 The models estimated for each regime, together with their implied steady states, are as follows. 473 and this estimate is well inside . 69. 37, respectively, which suggest rejection of the null hypothesis of no temporal structural break. There are two variations on obtaining appropriate critical values. 95 and y0 ∼ N(0, 1/(1 − ϕ12 )), εt ∼ N(0, 1). 55, each slightly larger than in the case with a nonstochastic regressor. Lastly, the quantiles and p-values were obtained by bootstrapping the test statistic to allow for the possibility that the empirical distribution function is generated from a dependent or non-normal process.

For example, there have been 1,300 more citations of the seminal Dickey and Fuller (1979) article in less than 18 months. As in the case of Volume 1, appropriate prerequisites for this book include some knowledge of econometric theory at an intermediate or graduate level as, for example, in Davidson (2000), Davidson and Mackinnon (2004) or Greene (2011); also some exposure to the basic DF framework for testing for a unit root would be helpful, but this is now included in most introductory courses in econometrics (see, for example, Dougherty, 2011).

One possibility is to look for the greatest evidence against the null hypothesis of structural stability in the set , so that the chosen test statistic is the supremum of C, say Sup-C, over all possible breakpoints, with the breakpoint being estimated as that value of λb , , that is associated with Sup-C. This idea is associated with the work say λˆ = λmax b of Andrews (1993) and Andrews and Ploberger (1994), who also suggested the arithmetic average and the exponential average of the C values over the set .

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