We introduce GP-RLARX, a novel Gaussian Process (GP) model for robust system identification. Our approach draws inspiration from nonlinear autoregressive modeling with exogenous inputs (NARX) and it encapsulates a novel and powerful structure referred to as latent autoregression. This structure accounts for the feedback of uncertain values during training and provides a natural framework for fr...

We study a bootstrap method for stationary real-valued time series, which is based on the method of sieves. We restrict ourselves to autoregressive sieve bootstraps. Given a sample X1; : : : ; Xn from a linear process fXtgt2ZZ, we approximate the underlying process by an autoregressive model with order p = p(n), where p(n)!1; p(n) = o(n) as the sample size n!1. Based on such a model a bootstrap...

Nonstationary ARIMA processes and nearly nonstationary ARMA processes, such as autoregressive processes having a root of the AR polynomial close to the unit circle, have sample autocovariance and spectral properties that are, in practice, almost indistinguishable from those of a stationary longmemory process, such as a Fractionally Integrated ARMA (ARFIMA) process. Because of this, model misspe...

The preliminary unit root test has been found to be a useful tool for improving the accuracy of a one-step-ahead predictor and prediction interval for the first-order autoregressive process when an autoregressive coefficient is close to one. This paper applies the aforementioned concepts of the preliminary unit root test in order to improve the efficiency of prediction intervals for the Gaussia...

This paper proposes a simple class of threshold autoregressive model for purpose of forecasting daily maximum ozone concentrations in Southern California. Linear time series model has been widely considered in environmental modeling. However, this class of models fails to capture the nonlinearity in ozone process and the complexity of meteorological interactions with ozone. In this article, we ...

The risk-sensitive asset management problem with a finite horizon is studied under a financial market model having a Wishart autoregressive stochastic factor, which is positive-definite symmetric matrix-valued. This financial market model has the following interesting features: 1) it describes the stochasticity of the market covariance structure, interest rates, and the risk premium of the risk...

Consider a stationary, pth order autoregression fX n g satisfying whose innovation sequence fZ n g is iid with regularly varying tail probabilities of index ?. From p of the autore-gressive coeecients and then to estimate the residuals by and then to apply Hill's estimator to the estimated residuals. We show that from the point of asymptotic variance, the second procedure is superior.

This article investigates a Cautious Minimum Variance (CMV) control approach for controlling industrial process variability when the model parameters are estimated from data and subject to uncertainty. CMV control has a number of advantages over traditional robust control methods. It incorporates probabilistic, as opposed to deterministic, measures of parameter uncertainty, which are more consi...

We consider a time series model with autoregressive conditional heteroskedasticity that is subject to changes in regime. The regimes evolve according to a multistate latent Markov switching process with unknown transition probabilities, and it is the constant in the variance process of the innovations that is subject to regime shifts. The joint estimation of the latent process and all model par...