Supplemental Material for ”Robust Generalized Empirical Likelihood for Heavy Tailed Autoregressions with Conditionally Heteroscedastic Errors”
نویسنده
چکیده
The following tables and figures report all results from the three simulation experiments in the main paper. In all cases the instruments are zt = [yt−1, yt−2] ′. Tables T.1-T.3 concern trimmed EL for each transform, based on weight Wt = 1/ ∏2 i=1(1 + y 2 t−i) 1/2. Tables T.4-T.6 concern trimmed CUE for each transform based on weightWt = 1/(1 + y2 t−1). In those cases the model estimated is AR(1) with i.i.d. t that is symmetrically P1.5, P2.5 or P4.5 distributed; or with GARCH t that has an i.i.d. error ut that is P2.5 or P4.5 distributed; or IGARCH t that has an i.i.d. error ut that is N(0, 1) distributed. Tables T.7-T.9 concern trimmed EL for each transform, based on the smaller weightWt = 1/ ∏2 i=1(1+ y2 t−i). The model is AR(1) with i.i.d. t that is symmetrically P.75, P1.5, or P2.5 distributed. Figures F.1-F.4 contain plots of confidence regions, bias, median, root mean squared error [rmse], and 95% coverage probabilities for EL estimates under simple trimming, for the AR model with an i.i.d. or GARCH error, and n ∈ {100, 500}. Figures F.5-F.8 contain related plots for the AR model with an i.i.d. error that may be very heavy tailed.
منابع مشابه
Robust Generalized Empirical Likelihood for heavy tailed autoregressions with conditionally heteroscedastic errors
We present a robust Generalized Empirical Likelihood estimator and confidence region for the parameters of an autoregression that may have a heavy tailed heteroscedastic error. The estimator exploits two transformations for heavy tail robustness: a redescending transformation of the error that robustifies against innovation outliers, and weighted least squares instruments that ensure robustness...
متن کاملLeast Tail-Trimmed Squares for In...nite Variance Autoregressions
We develop a robust least squares estimator for autoregressions with possibly heavy tailed errors. Robustness to heavy tails is ensured by negligibly trimming the squared error according to extreme values of the error and regressors. Tail-trimming ensures asymptotic normality and superp -convergence with a rate comparable to the highest achieved amongst M-estimators for stationary data. Moreov...
متن کاملBayesian Semiparametric Density Deconvolution in the Presence of Conditionally Heteroscedastic Measurement Errors.
We consider the problem of estimating the density of a random variable when precise measurements on the variable are not available, but replicated proxies contaminated with measurement error are available for sufficiently many subjects. Under the assumption of additive measurement errors this reduces to a problem of deconvolution of densities. Deconvolution methods often make restrictive and un...
متن کاملSupplemental Material for GEL Estimation for Heavy-Tailed GARCH Models with Robust Empirical Likelihood Inference
In the main paper we reported GELITT simulation bias over a grid of trimming fractiles {k ) n , k n }. We now repreat the simulation and fix either k ) n or k n , and report bias, mse, and test statistics. We use k ( ) n ∼ λn/ ln(n), λn and λ ln(n) each with k n ∼ .2 ln(n), and k n ∼ λn/ ln(n), λn and λ ln(n) each with k ( ) n ∼ .05n/ ln(n). We summarize the various λ’s and actual fractile valu...
متن کامل@bullet @bullet a Note on the Effect of Estimating Weights in Weighted Least Squares
• ABSTRACT We consider heteroscedastic linear models for which the variances are parametric functions of known regressors. Second order expansions are derived for a class of estimators which includes normal theory maximum likelihood and generalized least squares. The result is a fairly precise description of when conventional asymptotic variance formulae are optimistic; i.e., they underestimate...
متن کامل