This paper investigates regression quantiles (RQ) for unstable autoregressive models. The uniform Bahadur representation of the RQ process is obtained. The joint asymptotic distribution of the RQ process is derived in a unified manner for all types of characteristic roots on or outside the unit...

This paper investigates the asymptotic theory for a vector ARMA-GARCH model. The conditions for the strict stationarity, ergodicity, and the higherorder moments of the model are established. Consistency of the quasi- maximum likelihood estimator (QMLE) is proved under only the second-order...

Empirical factor demand analysis typically involves making a choice from among several competing non-nested functional forms. Each of the commonly used factor demand systems, such as Translog, Generalized Leontief, Quadratic, and Generalized McFadden, can provide a valid and useful empirical...

This paper investigates some structural properties of a family of GARCH processes. A simple sufficient condition for the existence of the alpha delta-order stationary solution of the processes is derived, where alpha belongs to (0,1] and delta 0. The solution is strictly stationary and ergodic,...

This paper provides a review of some recent theoretical results for time series models with GARCH errors, and is directed towards practitioners. Starting with the simple ARCH model and proceeding to the GARCH model, some results for stationary and nonstationary ARMA-GARCH are summarized. Various...

Least squares (LS) and maximum likelihood (ML) estimation are considered for unit root processes with GARCH (1, 1) errors. The asymptotic distributions of LS and ML estimators are derived under the condition alpha + beta 1. The former has the usual unit root distribution and the latter is a...

Prior to the recent Asian currency and economic crises, tourism from Asia had rapidly become Australia's major tourism export industry. Tourists from Singapore, which is Australia's fifth major market, represented 6% of international tourist arrivals to Australia in 1996. The average annual...

This paper examines stationary and nonstationary time series by formally testing for the presence of unit roots and seasonal unit roots prior to estimation, model selection and forecasting. Various Box-Jenkins Autoregressive Integrated Moving Average (ARIMA) models are estimated over the period...

This paper investigates several empirical issues regarding quasimaximum likelihood estimation of Smooth Transition Autoregressive (STAR) models with GARCH errors, specifically STAR-GARCH and STAR-STGARCH. Convergence, the choice of different algorithms for maximising the likelihood function, and...

This paper considers adaptive estimation in nonstationary autoregressive moving average models with the noise sequence satisfying a generalised autoregressive conditional heteroscedastic process. The locally asymptotic quadratic form of the log-likelihood ratio for the model is obtained. It is...