Value-at-risk forecasting based on Gaussian mixture ARMA–GARCH model

In this paper, we develop a new forecasting algorithm for value-at-risk (VaR) based on ARMA–GARCH (autoregressive moving average–generalized autoregressive conditional heteroskedastic) models whose innovations follow a Gaussian mixture distribution. For the parameter estimation, we employ the conditional least squares and quasi-maximum-likelihood estimator (QMLE) for ARMA and GARCH parameters, respectively. In particular, Gaussian mixture parameters are estimated based on the residuals obtained from the QMLE of GARCH parameters. Our algorithm provides a handy methodology, spending much less time in calculation than the existing resampling and bias-correction method developed in Hartz et al. [Accurate value-at-risk forecasting based on the normal-GARCH model, Comput. Stat. Data Anal. 50 (2006), pp. 3032–3052]. Through a simulation study and a real-data analysis, it is shown that our method provides an accurate VaR prediction.     

A comparison of six methods of analysing row-column designs with inter-block information

Six methods of obtaining estimates of treatment effects in a row-column design are considered. Five methods use estimates of inter-row and inter-column variation, and the remaining method is Ordinary Least Squares. Using simulation, these methods are examined to see which are most appropriate for minimising the sum of the squared differences between the estimates of the elementary treatment contrasts and their true values. Recommendations are made of which methods to use.     

ADJUSTING RESIDUALS IN ESTIMATION OF DISPERSION EFFECTS

This paper studies a method of adjusting the ordinary least squares residuals, when estimating and comparing dispersions, at various levels of factors in a replicated factorial experiment. Using a general dispersion model, theoretical results demonstrate the benefits of the method of adjusting residuals. An illustrative example is included.     

A note on the likelihood-ratio statistic under model misspecification

Following Viraswami and Reid (1996), higher-order results under model misspecification are obtained for the likelihood-ratio statistic and the adjusted likelihood-ratio statistic, for the case of a scalar parameter. An improved version of the adjusted likelihood-ratio statistic is suggested.     

Monitoring distributional changes of squared residuals in GARCH models

Change point monitoring for distributional changes in time-series models is an important issue. In this article, we propose two monitoring procedures to detect distributional changes of squared residuals in GARCH models. The asymptotic properties of our monitoring statistics are derived under both the null of no change in distribution and the alternative of a change in distribution. The finite sample properties are investigated by a simulation.     

Economic and economic-statistical designs of the T2 control charts with SVSSI sampling scheme

Recent studies have shown that the adaptive T² chart with two different sampling interval and three sample sizes (SVSSI) shows a good performance in detecting small to large shifts in the process mean. This paper investigates the economic and economic statistical designs of the SVSSI T² charts. We use the Markov chain approach to developing the cost model proposed by Costa and Rahim (Journal of applied statistics 2001; 28: 875–885). A genetic algorithm approach is used to find the optimal solutions. Using numerical examples, we illustrate the performance of the proposed model and compare the statistical, economic, and economic statistical designs of the SVSSI T² chart with respect to the economic and statistical criteria. Furthermore, we compare the performance of the SVSSI T² chart with the other T² control schemes.     

Average run lengths for cusum control charts applied to residuals

A common approach to building control charts for autocorrelated data is to apply classical SPC to the residuals from a time series model of the process. However, Shewhart charts and even CUSUM charts are less sensitive to small shifts in the process mean when applied to residuals than when applied to independent data. Using an approximate analytical model, we show that the average run length of a CUSUM chart for residuals can be reduced substantially by modifying traditional chart design guidelines to account for the degree of autocorrelation in the data.     

On the sensitivity to non-normality of a test for outliers in linear models

In this note we use the class of exponential power distributions to assess the robustness to non-normality of the test for outliers based on the maximum absolute studentized residual. We find that the significance levels can be quite markedly affected by even moderate departures from normality of the error distribution in a regression model when the sample size is moderately large.     

Leverage and Influence Diagnostics for Spatial Point Processes

Abstract. For a spatial point process model fitted to spatial point pattern data, we develop diagnostics for model validation, analogous to the classical measures of leverage and influence in a generalized linear model. The diagnostics can be characterized as derivatives of basic functionals of the model. They can also be derived heuristically (and computed in practice) as the limits of classical diagnostics under increasingly fine discretizations of the spatial domain. We apply the diagnostics to two example datasets where there are concerns about model validity.     

Goodness-of-Fit Statistics for General Linear Regression Equations in the Presence of Replicated Responses

Goodness-of-fit statistics for general multiple-linear-regression equations are reviewed for the case of replicated responses. A modification of the coefficient of determination is recommended. This statistic has 1.0 as its achievable upper bound and has the coefficient of determination as a special case. It indicates more effectively how close a general-linear-regression equation is relative to the best possible one and is particularly useful when the purpose is to ascertain whether higher-order terms of a given set of explanatory variables are required. Other goodness-of-fit statistics that take into account the variation within replicated responses are reviewed. An illustration example is presented.