Multivariate control charts based on Bayesian state space models

This paper develops a new multivariate control charting method for vector autocorrelated and serially correlated processes. The main idea is to propose a Bayesian multivariate local level model, which is a generalization of the Shewhart-Deming model for autocorrelated processes, in order to provide the predictive error distribution of the process and then to apply a univariate modified EWMA control chart to the logarithm of the Bayes' factors of the predictive error density versus the target error density. The resulting chart is proposed as capable to deal with both the non-normality and the autocorrelation structure of the log Bayes' factors. The new control charting scheme is general in application and it has the advantage to control simultaneously not only the process mean vector and the dispersion covariance matrix, but also the entire target distribution of the process. Two examples of London metal exchange data and of production time series data illustrate the capabilities of the new control chart.Comment: 19 pages, 6 figure

Optimal Cost-Effective Maintenance Policy for a Helicopter Gearbox Early Fault Detection under Varying Load

Most of the existing fault detection methods rarely consider the cost-optimal maintenance policy. A novel multivariate Bayesian control approach is proposed, which enables the implementation of early fault detection for a helicopter gearbox with cost minimization maintenance policy under varying load. A continuous time hidden semi-Markov model (HSMM) is employed to describe the stochastic relationship between the unobservable states and observable observations of the gear system. Explicit expressions for the remaining useful life prediction are derived using HSMM. Considering the maintenance cost in fault detection, the multivariate Bayesian control scheme based on HSMM is developed; the objective is to minimize the long-run expected average cost per unit time. An effective computational algorithm in the semi-Markov decision process (SMDP) framework is designed to obtain the optimal control limit. A comparison with the multivariate Bayesian control chart based on hidden Markov model (HMM) and the traditional age-based replacement policy is given, which illustrates the effectiveness of the proposed approach

Forecasting inflation with an uncertain output gap

The output gap (measuring the deviation of output from its potential) is a crucial concept in the monetary policy framework, indicating demand pressure that generates inflation. The output gap is also an important variable in itself, as a measure of economic fluctuations. However, its definition and estimation raise a number of theoretical and empirical questions. This paper evaluates a series of univariate and multivariate methods for extracting the output gap, and compares their value added in predicting inflation. The multivariate measures of the output gap have by far the best predictive power. This is in particular interesting, as they use information from data that are not revised in real time. We therefore compare the predictive power of alternative indicators that are less revised in real time, such as the unemployment rate and other business cycle indicators. Some of the alternative indicators do as well, or better, than the multivariate output gaps in predicting inflation. As uncertainties are particularly pronounced at the end of the calculation periods, assessment of pressures in the economy based on the uncertain output gap could benefit from being supplemented with alternative indicators that are less revised in real time.Output gap, real time indicators, forecasting, Phillips curve

Bayesian Model Selection for Beta Autoregressive Processes

We deal with Bayesian inference for Beta autoregressive processes. We restrict our attention to the class of conditionally linear processes. These processes are particularly suitable for forecasting purposes, but are difficult to estimate due to the constraints on the parameter space. We provide a full Bayesian approach to the estimation and include the parameter restrictions in the inference problem by a suitable specification of the prior distributions. Moreover in a Bayesian framework parameter estimation and model choice can be solved simultaneously. In particular we suggest a Markov-Chain Monte Carlo (MCMC) procedure based on a Metropolis-Hastings within Gibbs algorithm and solve the model selection problem following a reversible jump MCMC approach

Portfolio choice and estimation risk : a comparison of Bayesian approaches to resampled efficiency

Estimation risk is known to have a huge impact on mean/variance (MV) optimized portfolios, which is one of the primary reasons to make standard Markowitz optimization unfeasible in practice. Several approaches to incorporate estimation risk into portfolio selection are suggested in the earlier literature. These papers regularly discuss heuristic approaches (e.g., placing restrictions on portfolio weights) and Bayesian estimators. Among the Bayesian class of estimators, we will focus in this paper on the Bayes/Stein estimator developed by Jorion (1985, 1986), which is probably the most popular estimator. We will show that optimal portfolios based on the Bayes/Stein estimator correspond to portfolios on the original mean-variance efficient frontier with a higher risk aversion. We quantify this increase in risk aversion. Furthermore, we review a relatively new approach introduced by Michaud (1998), resampling efficiency. Michaud argues that the limitations of MV efficiency in practice generally derive from a lack of statistical understanding of MV optimization. He advocates a statistical view of MV optimization that leads to new procedures that can reduce estimation risk. Resampling efficiency has been contrasted to standard Markowitz portfolios until now, but not to other approaches which explicitly incorporate estimation risk. This paper attempts to fill this gap. Optimal portfolios based on the Bayes/Stein estimator and resampling efficiency are compared in an empirical out-of-sample study in terms of their Sharpe ratio and in terms of stochastic dominance