ESTIMATING PARAMETERS IN AUTOREGRESSIVE MODELS IN NON-NORMAL SITUATIONS: ASYMMETRIC INNOVATIONS

The estimation of coefficients in a simple autoregressive model is considered in a supposedly difficult situation where the innovations have an asymmetric distribution. Two distributions, gamma and generalized logistic, are considered for illustration. Closed form estimators are obtained and shown to be efficient and robust. Efficiencies of least squares estimators are evaluated and shown to be very low. This work is an extension of that of Tiku, Wong and Bian [1] Tiku, M. L., Wong, W. K. and Bian, G. 1999. Time Series Models with Asymmetric Innovations. Commun. Stat.-Theory Meth., 28: 1131–1160.  [Google Scholar] who give solutions for a simple AR(1) model.

     

Testing for Heteroscedasticity and/or Autocorrelation in Longitudinal Mixed Effect Nonlinear Models with AR(1) Errors

The effect of influental observation son the parameter estimates of ordinary least squares regression models has received considerable a t t e n t i o n fn the last decade. However, very little attention has been given to the problem of influential observation sinthea naysis of variace . The purpose of this paper is to show by way of examples that in fluential observations can alter the conclusions of tests of hypotheses in the analysis of variance . Regression diagno stics for identifying both extreme points and out liers can be used toreveal potential data and design problems.     

Preliminary Estimation in Gaussian Stationary Processes

Preliminary estimation of the kth Lag autocorrelation function in the Gaussian stationary processes is considered. An estimation procedure is derived from the ratio of the sum filter and the difference filter. The performance of this estimator is compared to the sample estimator through a Monte Carlo study.     

RATES OF CONVERGENCE IN SEMI-PARAMETRIC MODELLING OF LONGITUDINAL DATA

We consider the problem of semi-parametric regression modelling when the data consist of a collection of short time series for which measurements within series are correlated. The objective is to estimate a regression function of the form E[Y(t) | x] =x'ß+μ(t), where μ(.) is an arbitrary, smooth function of time t, and x is a vector of explanatory variables which may or may not vary with t. For the non-parametric part of the estimation we use a kernel estimator with fixed bandwidth h. When h is chosen without reference to the data we give exact expressions for the bias and variance of the estimators for β and μ(t) and an asymptotic analysis of the case in which the number of series tends to infinity whilst the number of measurements per series is held fixed. We also report the results of a small-scale simulation study to indicate the extent to which the theoretical results continue to hold when h is chosen by a data-based cross-validation method.     

An autocorrelation criterion for bandwidth selection in nonparametric regression ∗

In this note, we propose a new method for selecting the bandwidth parameter in non-parametric regression. While standard criteria, such as cross-validation, are based on the true regression curve about which we know little, we propose a criterion which focuses on the true errors about which assumptions may be made. Our proposal is to choose the bandwidth for which the residuals are as uncorrelated as possible. We use the Box-Pierce statistic as the objective to be minimized. In doing so, the behaviour of our residuals will be close to that of the true errors under the hypothesis of independent errors. A simulation study shows that our method succeeds in capturing the main features of the regression curve, in the sense that the number of turning-points of the curve is correctly estimated most of the time.     

A simulation study and evaluation of multivariate forecast based control charts applied to ARMA processes

Much research had been performed in the area of control charting techniques for monitoring autocorrelated processes, especially regarding forecast based monitoring schemes. Forecast based monitoring schemes involve fitting an appropriate time-series model to the process, generating one step ahead forecast errors, and monitoring the forecast errors with traditional control charts. Another method introduced into the literature involves using multivariate control charts to monitor the ARMA derived one-step-ahead (OSA) and two-step-ahead (TSA) forecast errors. This article provides a broad simulation study and evaluation of the suggested multivariate approaches in regards to various ARMA(1,1) and AR(1) processes, and a comparison to their univariate counterparts.     

Cross validation of ridge regression estimator in autocorrelated linear regression models

ABSTRACT

In this paper, we investigated the cross validation measures, namely OCV, GCV and Cp under the linear regression models when the error structure is autocorrelated and regressor data are correlated. The best performed ridge regression estimator is obtained by getting the optimal ridge parameter so as to minimize these measures. A Monte Carlo simulation study is given to see how the optimal ridge parameter is affected by autocorrelation and the strength of multicollinearity.     

A Robust Test for Weak Instruments

This article deals with the estimation of continuous-time stochastic volatility models of option pricing. We argue that option prices are much more informative about the parameters than are asset prices. This is confirmed in a Monte Carlo experiment that compares two very simple strategies based on the different information sets. Both approaches are based on indirect inference and avoid any discretization bias by simulating the continuous-time model. We assume an Ornstein-Uhlenbeck process for the log of the volatility, a zero-volatility risk premium, and no leverage effect. We do not pursue asymptotic efficiency or specification issues; rather, we stick to a framework with no overidentifying restrictions and show that, given our option-pricing model, estimation based on option prices is much more precise in samples of typical size, without increasing the computational burden.