This paper provides a means of accurately simulating explosive autoregressive processes, and uses this method to analyse the distribution of the likelihood ratio test statistic for an explosive second order autoregressive process. Nielsen (2001) has shown that for the asymptotic distribution of the likelihood ratio unit root test statistic in a higher order autoregressive model, the assumption ...

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...

We consider a single-server queueing system. The arrival process is modelled as a Poisson process while the service times of the consecutive customers constitute a sequence of autoregressive random variables. Our interest into autoregressive service times comes from the need to capture temporal correlation of the channel conditions on wireless network links. If these fluctuations are slow in co...

Fast methods are presented for identifying a multivariate autoregressive model that is appropriate to represent large, potentially high-dimensional time series data as they occur, e.g., in geophysical applications. The algorithms are based on the concept of least-squares estimation, which is known to yield consistent and asymptotically unbiased coeecient matrix estimates that also perform well ...

Proactive management holds the promise of taking corrective actions in advance of service disruptions. Achieving this goal requires predictive models so that potential problems can be anticipated. Our approach builds on previous research in which HTTP operations per second are studied in a web server. As in this prior work, we model HTTP operations as two subprocesses, a (deterministic) trend s...

A weakly stationary process with summable partial autocorrelations is proved to have one-sided autoregressive and moving average representations. Sums of autocorrelations and alternating autocorrelations are expressed as products of simple rational functions of partial autocorrela-tions. A general bound for sums of squared autocorrelations in terms of partial autocorrelations is also obtained.

The authors give easy-to-check sufficient conditions for the geometric ergodicity and the finiteness of the moments of a random process xt = φ(xt−1, . . . , xt−p)+ tσ(xt−1, . . . , xt−q) in which φ : IR → IR, σ : IR → IR and ( t) is a sequence of independent and identically distributed random variables. They deduce strong mixing properties for this class of nonlinear autoregressive models with ...

This paper is concerned with a semiparametric partially linear regression model with unknown regression coefficients, an unknown nonparametric function for the non-linear component, and unobservable serially correlated random errors. The random errors are modeled by an autoregressive time series. We show that the distributions of the feasible semiparametric generalized least squares estimator o...

Value at risk (VaR) is the standard measure of market risk used by financial institutions. Interpreting the VaR as the quantile of future portfolio values conditional on current information, the conditional autoregressive value at risk (CAViaR) model specifies the evolution of the quantile over time using an autoregressive process and estimates the parameters with regression quantiles. Utilizin...

Often we are interested in the largest root of an autoregressive process. Available methods rely on inverting t-tests to obtain confidence intervals. However, for large autoregressive roots, t-tests do not approximate asymptotically uniformly most powerful tests and do not have optimality properties when inverted for confidence intervals. We exploit the relationship between the power of tests a...