By Yacine Ait-Sahalia, Lars Peter Hansen
This number of unique articles-8 years within the making-shines a vivid gentle on contemporary advances in monetary econometrics. From a survey of mathematical and statistical instruments for realizing nonlinear Markov methods to an exploration of the time-series evolution of the risk-return tradeoff for inventory industry funding, famous students Yacine AГЇt-Sahalia and Lars Peter Hansen benchmark the present nation of data whereas individuals construct a framework for its development. no matter if within the presence of statistical uncertainty or the confirmed merits and boundaries of worth in danger versions, readers will realize that they could set few constraints at the price of this long-awaited volume.
- Presents a huge survey of present research-from neighborhood characterizations of the Markov technique dynamics to monetary industry buying and selling activity
- Contributors contain Nobel Laureate Robert Engle and best econometricians
- Offers a readability of strategy and rationalization unavailable in different monetary econometrics collections
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Extra resources for Handbook of Financial Econometrics, Vol. 1: Tools and Techniques
Sample text
The GEL framework leads to a better understanding of the properties of the moment-based estimators and allows for more powerful test procedures, more e¢ cient estimation of density and distribution functions and improved bootstrap methods. In this chapter, we review the construction of nonparametric likelihood and discuss its relation to e¢ cient estimation of density and distribution functions. Then, we extend this method to models de…ned by moment restrictions and develop the generalized empirical likelihood framework.
L. Horowitz (1996) Bootstrap critical values for tests based on generalized-method-of-moments estimators. Econometrica, 64, 891–916. P. (1982) Large sample properties of generalized method of moments estimators. Econometrica, 50, 1029–1054. , J. Heaton and A. Yaron (1996) Finite-sample properties of some alternative GMM estimators. Journal of Business and Economic Statistics, 14, 262–280. J. Hodrick (1980) Forward exchange rates as optimal predictors of future spot rates. Journal of Political Economy, 88, 829–853.
0 and n ! 1: Standard Approaches to Estimation and Statistical Inference Let us denote 2 K = and RK = Z Z 23 u2 K (u) du 2 K (u) du: These two constants depend only on the chosen kernel, and are assumed to be …nite. 1 assuming < 1. Note that may or may not be zero. We also assume continuity and boundedness of g(x); g 0 (x); g 00 (x); f (x) and f 0 (x) everywhere except possibly at a …nite number of points. Consider the di¤erence between the estimate and the estimand: g^(a) g(a) = r^1 (a) + r^2 (a) ; f^ (a) where n 1X r^1 (a) = ei Kb (xi n i=1 a) ; n r^2 (a) = 1X (g(xi ) n i=1 g(a)) Kb (xi a) ; n 1X Kb (xi f^ (a) = n i=1 a) : The denominator f^ (a) is called the Nadaraya–Watson density estimator of the regressor density f (x) at x = a: It is straightforward to show that this estimator is consistent for f (a).