By K. Patterson
This ebook supplies an authoritative review of the literature on non-stationarity, integration and unit roots, offering path and suggestions. It additionally offers precise examples to teach how the innovations should be utilized in useful events and the pitfalls to avoid.
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Additional info for A Primer for Unit Root Testing
3 Random vector case We are typically interested in the outcomes of several random variables together rather than a single random variable. For example, interest may focus on whether the prices of two financial assets are related, suggesting we consider two random variables x1 and x2, and the relationship between them. More generally, define an n-dimensional random vector as the collection of n random variables: x = ( x1 , x 2 , .! 11) where each of the xj is a real-valued random variable. For simplicity assume that each random variable is defined on the measurable space (ᑬ, B).
58) is that, in the limit, there is no need for the integral over X1 ʦ A, because the set A collapses to a single point. The end result is simple enough and does have the same form as the discrete case. 59) 36 A Primer for Unit Root Testing where f(X1 = a) > 0.
One is to redefine the conditional probability as a limit and the second is to go directly to the concept of a conditional expectation without first defining a conditional distribution or conditional density function. The solution outlined here is of the former kind and follows Mittelhammer (1996); for an earlier reference see Feller (1966). The second approach is adopted in more advanced treatments, where the emphasis is on a measure-theoretic approach; the interested reader may like to consult Davidson (1994, chapter 10) and Billingsley (1995, chapter 6).
A Primer for Unit Root Testing by K. Patterson