普通似然及经验似然情况下的结点问题

本文在普通似然及经验似然情况下,分别对数据无结点和有结点的情况做了计算,得出在普通似然及经验似然问题中,有结点与无结点情况完全相同的结论。     

A new energy model to capture the behavior of energy price processes

Owing to the vague fluctuation of energy prices from time to time, a new energy model, which considers both the mean-reverting behavior and the long memory property, is proposed in this paper. Since the problem of estimating parameters, in discrete time for this model, plays a central role in forecast inference, the problem of estimating the unknown parameters has been dealt with for the fractional Ornstein–Uhlenbeck process observed discretely. The asymptotic properties of these estimates are also provided. The numerical simulation results confirm the theoretical analysis and show that our method is effective. To show how to apply our approach in realistic contexts, an empirical study of energy in China, namely Daqing crude oil, is presented. The empirical results seem reasonable when compared to the real data.     

Calibration Weighting Methods for Complex Surveys

This paper presents a careful investigation of the three popular calibration weighting methods: (i) generalised regression; (ii) generalised exponential tilting and (iii) generalised pseudo empirical likelihood, with a major focus on computational aspects of the methods and some empirical evidences on calibrated weights. We also propose a simple weight trimming method for range‐restricted calibration. The finite sample behaviour of the weights obtained by the three calibration weighting methods and the effectiveness of the proposed weight trimming method are examined through limited simulation studies.     

Small-sample Properties of Panel Spatial Autoregressive Models: Comparison of the Bayesian and Maximum Likelihood Methods

Abstract

This article considers autoregressive (SAR) models. We method to estimate the parameters of likelihood (ML) method. Our Bayesian by the Monte Carlo studies. We found the efficient as the ML estimators.     

Proportional Odds Models with High‐Dimensional Data Structure

The proportional odds model is the most widely used model when the response has ordered categories. In the case of high‐dimensional predictor structure, the common maximum likelihood approach typically fails when all predictors are included. A boosting technique pomBoost is proposed to fit the model by implicitly selecting the influential predictors. The approach distinguishes between metric and categorical predictors. In the case of categorical predictors, where each predictor relates to a set of parameters, the objective is to select simultaneously all the associated parameters. In addition, the approach distinguishes between nominal and ordinal predictors. In the case of ordinal predictors, the proposed technique uses the ordering of the ordinal predictors by penalizing the difference between the parameters of adjacent categories. The technique has also a provision to consider some mandatory predictors (if any) that must be part of the final sparse model. The performance of the proposed boosting algorithm is evaluated in a simulation study and applications with respect to mean squared error and prediction error. Hit rates and false alarm rates are used to judge the performance of pomBoost for selection of the relevant predictors.     

Full versus quasi MLE for ARMA-GARCH models with infinitely divisible innovations

We compare the backtesting performance of ARMA-GARCH models with the most common types of infinitely divisible innovations, fit with both full maximum likelihood estimation (MLE) and quasi maximum likelihood estimation (QMLE). The innovation types considered are the Gaussian, Student’s t, α-stable, classical tempered stable (CTS), normal tempered stable (NTS) and generalized hyperbolic (GH) distributions. In calm periods of decreasing volatility, MLE and QMLE produce near identical performance in forecasting value-at-risk (VaR) and conditional value-at-risk (CVaR). In more volatile periods, QMLE can actually produce superior performance for CTS, NTS and α-stable innovations. While the t-ARMA-GARCH model has the fewest number of VaR violations, rejections by the Kupeic and Berkowitz tests suggest excessively large forecasted losses. The α-stable, CTS and NTS innovations compare favourably, with the latter two also allowing for option pricing under a single market model.     

Distribution of parallel exchange rates in African countries

This paper investigates the distribution of parallel exchange rates in African countries using exploratory data analysis techniques and model fitting. Stable laws are fitted to empirical distributions using the maximum likelihood estimation method. Empirical evidence supports the stable hypothesis these distributions are positively skewed and have tails that are much heavier than Gaussian counterparts. The stable hypothesis is further supported by the “converging variance test,” which suggests that these distributions have infinite variance.     

Robust estimation of models of Engel curves

Both standard and robust methods are used here to estimate models of Engel curves for three household commodities, namely, food, transport, and tobacco and alcohol in Canada. The income elasticities of demand computed from the various methods differ significantly for the transport and tobacco-alcohol consumption where there are obvious outliers and zero expenditures problem. Robust estimators point to lower income elasticities and have better performance than the standard LS and Tobit estimator. These results are analyzed in the light of the information on finite-sample performance obtained in a previous Monte Carlo study. First version received: July 2000/Final version received: July 2001 RID="*" ID="*"  I wish to thank Victoria Zinde-Walsh, John Galbraith, Clint Coakley, two anonymous referees and an associate editor for helpful comments. I would also like to thank Anastassia Khouri for kindly providing the 1992 Family Expenditure Survey of Canada data.     

Statistical Methodologies for the Market Risk Measurement

This paper classifies statistical methodologies available for the marketrisk measurement. With the help of the weighted likelihood, a broad class ofnon-normal distributions, which are not generally considered so far, areapplied to possibly hetero-scedastic financial variables. The approach is compared with popular procedures such as GARCH and J. P. Morgan's using daily dataof 12 financial variables.