Previously, quality control and improvement researchers discussed multivariate control charts for independent processes and univariate control charts for autocorrelated processes separately. We combine the two topics and propose vector autoregressive (VAR) control charts for multivariate autocorrelated processes. In addition, we estimateAR(p) models instead ofARMAmodels for the systematic cause...

In this study the proper orthogonal decomposition (POD) methodology to model reduction is applied to construct a reduced-order control space for simple advection-diffusion equations. Several 4D-Var data assimilation experiments associated with these models are carried out in the reduced control space. Emphasis is laid on the performance evaluation of an adaptive POD procedure, with respect to t...

Determining contributions by sub-portfolios or single exposures to portfolio-wide economic capital for credit risk is an important risk measurement task. Often economic capital is measured as Valueat-Risk (VaR) of the portfolio loss distribution. For many of the credit portfolio risk models used in practice, the VaR contributions then have to be estimated from Monte Carlo samples. In the contex...

This paper investigates limit theory for the likelihood analysis of an I(2) cointegrated vector autoregressive (VAR) model in the presence of deterministic shifts. A log likelihood ratio (logLR) test statistic for integration indices is considered, and it is demonstrated that the asymptotic distribution of the statistic is given in the form of a generalised Dicky-Fuller type distribution. A log...

We propose a Bayesian stochastic search approach to selecting restrictions for Vector Autoregressive (VAR) models. For this purpose, we develop a Markov Chain Monte Carlo (MCMC) algorithm that visits high posterior probability restrictions on the elements of both the VAR regression coefficients and the error variance matrix. Numerical simulations show that stochastic search based on this algori...

The implementation of appropriate statistical techniques for monitoring conditional VaR models, i.e, backtesting, reported by institutions is fundamental to determine their exposure to market risk. Backtesting techniques are important since the severity of the departures of the VaR model from market results determine the penalties imposed for inadequate VaR models. In this paper we make six con...

The Basel III Accord requires that banks and other Authorized Deposit-taking Institutions (ADIs) communicate their daily risk forecasts to the appropriate monetary authorities at the beginning of each trading day, using one of a range of alternative risk models to forecast Value-at-Risk (VaR). The risk estimates from these models are used to determine the daily capital charges (DCC) and associa...

Vector Auto-regressive (VAR) models are useful for analyzing temporal dependencies among multivariate time series, known as Granger causality. There exist methods for learning sparse VAR models, leading directly to causal networks among the variables of interest. Another useful type of analysis comes from clustering methods, which summarize multiple time series by putting them into groups. We d...