Testing for white noise has been well studied in the literature of econometrics and statistics. For most of the proposed test statistics, such as the well-known Box–Pierce test statistic with fixed lag truncation number, the asymptotic null distributions are obtained under independent and identically distributed assumptions and may not be valid for dependent white noise. Because of recent popul...

A variational Bayesian autoregressive conditional heteroskedastic (VB-ARCH) model is presented. The ARCH class of models is one of the most popular for economic time series modeling. It assumes that the variance of the time series is an autoregressive process. The variational Bayesian approach results in an approximation to the full posterior distribution over ARCH model parameters, and provide...

A natural generalization of the ARCH (Autoregressive Conditional Heteroskedastic) process introduced in Engle (1982) to allow for past conditional variances in the current conditional variance equation is proposed. Stationarity conditions and autocorrelation structure for this new class of parametric models are derived. Maximum likelihood estimation and testing are also considered. Finally an e...

Any discussion on exchange rate movements and forecasting should include explanatory variables from both the current account and the capital account of the balance of payments. In this paper, we include such factors to forecast the value of the Indian rupee vis a vis the US Dollar. Further, factors reflecting political instability and lack of mechanism for enforcement of contracts that can affe...

We derive a local linear estimator of generalized impulse response (GIR) functions for nonlinear conditional heteroskedastic autoregressive processes and show its asymptotic normality. We suggest a plug-in bandwidth based on the derived asymptotically optimal bandwidth. A local linear estimator for the conditional variance function is proposed which has simpler bias than the standard estimator....

This paper derives asymptotic normality of a class of M-estimators in the generalized autoregressive conditional heteroskedastic ~GARCH! model+ The class of estimators includes least absolute deviation and Huber’s estimator in addition to the well-known quasi maximum likelihood estimator+ For some estimators, the asymptotic normality results are obtained only under the existence of fractional u...

We consider time series described by Markov chains that alternate periodically between different transition distributions, with conditional constraints involving unknown parameters. We obtain variance bounds and characterize efficient estimators for these parameters. Efficient estimators can be obtained as solutions of randomly weighted martingale estimating equations. Our model includes altern...