Abdelwahed Trabelsi

Benchmarking of Economic Time Series

Abstract This article develops a statistical model-based approach to the benchmarking problem. Benchmarking is done when data from a monthly sample survey are combined with data from an annual census for the purpose of improving the survey estimates. Previous authors have used numerical analysis techniques to derive methods to perform benchmarking. This article formulates the benchmarking problem in a statistical framework and uses modern times series methods to derive a solution. This solution is based in part upon the statistical properties of the time series being benchmarked and upon the properties of the survey errors associated with that time series. The article makes use of the theory of signal extraction that has been derived for nonstationary time series. Two common types of benchmarking problems are studied in greater detail. The results of the theory derived in the article are illustrated by an example.

Predictive performance of conditional Extreme Value Theory in Value-at-Risk estimation

This paper conducts a comparative evaluation of the predictive performance of various Value-at-Risk (VaR) models. Special emphasis is paid to two methodologies related to the Extreme Value Theory (EVT): The Peaks Over Threshold (POT) and the Block Maxima (BM). We apply both unconditional and conditional EVT models to management of extreme market risks in stock markets. They are applied on daily returns of the BVMT and CAC 40 indices with the intention to compare the performance of various estimation methods on markets with different capitalisation and trading practices. The results we report demonstrate that conditional POT EVT method produces the most accurate forecasts of extreme losses both for standard and more extreme VaR quantiles. The conditional block maxima EVT method is less accurate.

Intelligent Monitoring System for Intensive Care Units

We address in the present paper a medical monitoring system designed as a multi-agent based approach. Our system includes mainly numerous agents that act as correlated multi-agent sub-systems at the three layers of the whole monitoring infrastructure, to avoid non informative alarms and send effective alarms at time. The intelligence in the proposed monitoring system is provided by the use of time series technology. In fact, the capability of continuous learning of time series from the physiological variables allows the design of a system that monitors patients in real-time. Such system is a contrast to the classical threshold-based monitoring system actually present in the Intensive Care Units (ICUs) which causes a huge number of irrelevant alarms.

Measure of financial risk using conditional extreme value copulas with EVT margins

In this paper we propose a method to estimate the value-at-risk (VaR) of a portfolio based on a combination of time series, extreme value theory and copula fitting. Given multivariate financial data, we use a univariate ARMA-GARCH model for each return series. We then fit a generalized Pareto distribution to the tails of the residuals to model the distributions of marginal residuals, followed by a bivariate extreme value copula fitting, which is used to estimate portfolio VaR via simulation. As a first step, this method is applied to two portfolios, each composed of two indexes. As a second step, we extend the method to portfolios based on three indexes. In this case dependence between residuals is modeled by using trivariate nested copulas. The reported results demonstrate that conditional extremevalue copula methods provide a better representation of the dependence structure of multivariate data and produce the most accurate estimates of risk, both for standard and for more extreme VaR quantiles. Comparatively, traditional univariate and multivariate methods result in significantly less accurate risk estimates for most cases. In the context of the international financial crises in the year 2008, the predictive performance of all models decreases significantly. Only copula methods provide acceptable VaR predictions.

A Benchmarking Approach to Forecast Combination

This article is concerned with the development of a statistical model-based approach to optimally combine forecasts derived from an extrapolative model, such as an autoregressive integrated moving average (ARIMA) time series model, with forecasts of a particular characteristic of the same series obtained from independent sources. The methods derived combine the strengths of all forecasting approaches considered in the combination scheme. The implications of the general theory are investigated in the context of some commonly encountered seasonal ARIMA models. An empirical example to illustrate the method is included.

Bench-Marking Time Series with Reliable Bench-Marks

This paper investigates the implications for the signal extraction bench-marking method when the bench-marks are observed without error and when the variance of the survey errors is relatively small. Conditions under which the solutions of several numerical bench-marking approaches are optimal are derived. It is shown that these numerical methods are particular cases of the signal extraction method. Comparisons between the numerically derived methods and the signal extraction method are made in the light of a particular survey

Fractionally integrated time varying GARCH model

This paper introduces the new FITVGARCH model to describe both long memory and structural change behaviour in the volatility process by allowing for time varying dynamic structure in the conditional variance. The parameters of the conditional variance in the FIGARCH model are allowed to change smoothly over time. We derive an LM-type test for parameter constancy of the FIGARCH model against the alternative of time dependent parameters. Simulation analysis shows that both empirical size and power of the constancy test are quite good. An empirical application to the stock market volatility indicates that this new class of model seems to outperform the FIGARCH model in the description of the daily NASDAQ composite index returns.

The impact of global financial crisis on the dependence structure of equity markets and on risk management

In this work, we use a time varying copula model to investigate the impact of the global financial crisis on dependence between US and each of six major stock markets and on risk management strategies. The model is implemented with an AR-GARCH-t for the marginal distribution and the extreme value copula for the joint distribution, which allow taking into account non-linear dependence, tails behaviour and their development over time. We investigate whether there are significant changes in the time-varying dependence structure of market and in VaR and ES measures especially during global financial crises period. Empirical results show that market dependences between US, European and Brazilian markets tend to increase considerably during crisis period and this increase started around the beginning of 2008. In the other hand, market volatility registered record levels around the end of 2008 due to the increase of the degree of uncertainty in this period. As a consequence, investors will allow more amounts to cover against negative evolution of portfolio value.

Optimal dynamic hedging strategy with futures oil markets via FIEGARCH-EVT copula models

The goal of this paper is to evaluate the hedging strategies performance of a range of copula and traditional methods for three spot and futures oil markets: WTI crude oil, propane and heating oil. Our contribution is two-fold. First, we model dependence structure between spot and futures oil markets using copula theory applied to bivariate standardised residuals data obtained from two fitted univariate FIEGARCH models. To take in consideration the presence of extremes, we model residuals by a generalised Pareto distribution (GPD). This procedure permits to simultaneously capturing asymmetric non-linear behaviour, dependence structure, long memory and occurrence of extreme events. Second, we use this method with different Archimedean copulas functions (Joe, Frank, bb1, bb2, bb6, and Gumbel) to investigate hedging performance and the efficiency of copula methods in risk reduction and return improvement. Empirical results show that copulas methods perform better than tradition hedging strategies in terms of return and variance. bb6 copula provide the best performed hedge ratios for both WTI crude oil and propane markets while Frank copula prove effective risk reducers compared with other copulas and traditional methods for heating oil market.

Time Series Analysis and Outlier Detection in Intensive Care Data

In intensive care units, clinical information systems record a huge number of variables in the purpose of using them in medical decision making. Those variables are controlled by alarm systems based on fixed thresholds. This kind of systems produce alerts each time that a sudden shift as outlier, level change point or trend occurs and exceeds the threshold. In practice, we can see that a big number of alarms are false; this is due to the presence of non-symptomatic outliers. In this paper we aim to present some methods that can be helpful to detect this kind of outliers. And later, they can be used in the development of intelligent alarm systems