Empirical Likelihood for Partial Parameters in ARMA Models with Infinite Variance

This paper proposes a profile empirical likelihood for the partial parameters in ARMA(p,q) models with infinite variance. We introduce a smoothed empirical log-likelihood ratio statistic. Also, the paper proves a nonparametric version of Wilks’s theorem. Furthermore, we conduct a simulation to illustrate the performance of the proposed method

Global self-weighted and local quasi-maximum exponential likelihood estimators for ARMA--GARCH/IGARCH models

This paper investigates the asymptotic theory of the quasi-maximum exponential likelihood estimators (QMELE) for ARMA--GARCH models. Under only a fractional moment condition, the strong consistency and the asymptotic normality of the global self-weighted QMELE are obtained. Based on this self-weighted QMELE, the local QMELE is showed to be asymptotically normal for the ARMA model with GARCH (finite variance) and IGARCH errors. A formal comparison of two estimators is given for some cases. A simulation study is carried out to assess the performance of these estimators, and a real example on the world crude oil price is given.Comment: Published in at http://dx.doi.org/10.1214/11-AOS895 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Are Output Fluctuations Transitory?

According to the conventional view of the business cycle, fluctuations in output represent temporary deviations from trend. The purpose of this paper is to question this conventional view. If fluctuations in output are dominated by temporary deviations from the natural rate of output, then an unexpected change in output today should not substantially change one's forecast of output in, say, ten or twenty years. Our examination of quarterly post-war United States data leads us to be skeptical about this implication. We find that a unexpected change in real GNP of one percent should change one's forecast by over one percent over a long horizon. While it is obviously imprudent to make definitive judgments regarding theories on the basis of one stylized fact alone, we believe that the great persistence of output shocks documented in this paper is an important and often neglected feature of the data that should more widely be used for evaluating theories of economic fluctuations.

GARCH TIME-SERIES MODELS: AN APPLICATION TO RETAIL LIVESTOCK PRICES

This article applies recent developments in time-series modeling to analyze the retail prices of beef, pork, and chicken. Specifically, generalized autoregressive conditional heteroscedasticity (GARCH) models were fitted to these data to determine if, unlike more traditional time-series models, the conditional variances of the underlying stochastic processes are nonconstant. The estimation results indicate that the constant conditional variances assumption can be rejected. Furthermore, ex post forecast intervals generated from the GARCH processes indicate that the forecasting accuracy of the estimated models has varied widely over time with substantial volatility occurring during the 1970s and early 1980s.Demand and Price Analysis, Livestock Production/Industries, Research Methods/ Statistical Methods,

Forecasting an ARIMA (0,2,1) using the random walk model with drift

In this paper we show that the random walk model with drift behaves like an ARIMA (0,2,1) when its parameter θ is greater but close to –1. Using the random walk for predicting future values of an ARIMA (0,2,1) process, we find out that when θ is not so close to –1, the performance of the prediction interval for the period forecast is not satisfactory. Particularly, for large, the achieved coverage, namely, the probability the prediction interval to include the future value is quite low. Even in the cases of large samples and small , although the random walk coverage approaches that of the ARIMA, the random walk produces wider prediction intervals. This picture changes when we forecast ARIMA (0,2,1) values for θ close to –1. The random walk should be preferred as it produces on average narrower confidence intervals, and its coverage is almost the same with the nominal coverage of the ARIMA (0,2,1).ARIMA; Random Walk; Monte Carlo Simulations

Time Series Analysis

We provide a concise overview of time series analysis in the time and frequency domains, with lots of references for further reading.time series analysis, time domain, frequency domain

Rank-based estimation for all-pass time series models

An autoregressive-moving average model in which all roots of the autoregressive polynomial are reciprocals of roots of the moving average polynomial and vice versa is called an all-pass time series model. All-pass models are useful for identifying and modeling noncausal and noninvertible autoregressive-moving average processes. We establish asymptotic normality and consistency for rank-based estimators of all-pass model parameters. The estimators are obtained by minimizing the rank-based residual dispersion function given by Jaeckel [Ann. Math. Statist. 43 (1972) 1449--1458]. These estimators can have the same asymptotic efficiency as maximum likelihood estimators and are robust. The behavior of the estimators for finite samples is studied via simulation and rank estimation is used in the deconvolution of a simulated water gun seismogram.Comment: Published at http://dx.doi.org/10.1214/009053606000001316 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org