Econometric theory and methods, Russell Davidson - Chapter 13 potx

... 1999, Russell Davidson and James G. MacKinnon Chapter 13 Methods for Stationary Time-Series Data 13. 1 Introduction Time-series data have special features that often require the use of special- ized ... a way Copyright c  1999, Russell Davidson and James G. MacKinnon 547 13. 3 Estimating AR, MA, and ARMA Models 563 limit and the factor of n −1 in expression (13. 47) an...

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... moments and the inverse of the matrix W  Ω 0 W. Equivalently, it is a quadratic form in n −1/2 W  (y − Xβ) and the inverse of n −1 W  Ω 0 W, since Copyright c  1999, Russell Davidson and James ... the Newey-West esti- mator, and shows that, in some circumstances, they may perform better than it does in finite samples. A different approach to HAC estimation is suggested by Andrew...

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... horizontally. Similarly, X 11 and X 21 have the same number of columns, and also X 12 and X 22 , as required for the submatrices to fit together vertically as well. Copyright c  1999, Russell Davidson and James ... of the error terms, if necessary spec- ifying parameters such as its mean and variance; • Use a random-number generator to generate the n successive and mutu- ally...

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... OC. Copyright c  1999, Russell Davidson and James G. MacKinnon 2.4 The Frisch-Waugh-Lovell Theorem 69 by looking again at Figure 2 .13, in which the constant ι plays the role of X 1 , and the centered ... least squares esti- mates, which we will refer to as the Frisch-Waugh-Lovell Theorem, or FWL Theorem for short. It was introduced to econometricians by Frisch and Waugh (1933), a...

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... regressors and their cross-products. Thus there should not be too much dependence between X ti X tj and X si X sj for s = t, and the variances of these quantities should not differ too much as t and ... (3.19) Copyright c  1999, Russell Davidson and James G. MacKinnon 3.6 Residuals and Error Terms 109 The consistency of ˆ β implies that ˆ u → u as n → ∞, but the finite-sample...

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... the Copyright c  1999, Russell Davidson and James G. MacKinnon 4.3 Some Common Distributions 131 the rest of this section, we therefore use lower-case letters to denote both random variables and the arguments ... no possible confusion. Copyright c  1999, Russell Davidson and James G. MacKinnon 4.3 Some Common Distributions 133 where z 1 , z 2 , and z 3 are mutually indep...

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... factor on the right-hand side tends to S −1 X  X as n → ∞, and the second factor, which is just v, tends to a random vector distributed as Copyright c  1999, Russell Davidson and James G. MacKinnon 5.3 ... may still seem strange that the lower and upper limits of (5 .13) depend, respectively, on the upper-tail and lower-tail quantiles of the t(n − k) distri- bution. This actuall...

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... include Bard (1974), Gill, Murray, and Wright (1981), Quandt (1983), Bates and Watts (1988), Seber and Wild (1989, Chapter 14), and Press et al. (1992a, 1992b, Chapter 10). There are many algorithms ... has mean 0, and the IID assumption in (6.02) is enough to allow us to apply a law of large numbers to that sum. It follows that the right-hand side, and therefore also the left...

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... matrix- weighted averages of the within-groups, or fixed-effects, estimator (7.85) and Copyright c  1999, Russell Davidson and James G. MacKinnon Chapter 7 Generalized Least Squares and Related Topics 7.1 Introduction If ... the 2 See Dufour, Gaudry, and Liem (1980) and Betancourt and Kelejian (1981). Copyright c  1999, Russell Davidson and James G. MacKinnon 300 Gener...

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... terms. Copyright c  1999, Russell Davidson and James G. MacKinnon 8.3 Instrumental Variables Estimation 313 It can be seen from this solution that p t and q t will depend on both u d t and u s t , and on every ... (1999), Donald and Newey (2001), Hahn and Hausman (2002), Kleibergen (2002), and Stock, Wright, and Yogo (2002). There remain many unsolved problems. Copyright...

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