8 research outputs found
Convergence en loi d'intégrales stochastiques et estimateurs des moindres carrés de certains modèles statistiques instables
No full textLa motivation de cette thèse est d'étudier les lois asymptotiques des estimateurs des moindres carrés des paramètres de certains modèles linéaires instables plus généraux que les AR considérés par Chan Wei (1988) et ARMA par Truong-Van et Larramendy (1996). Comme les statistiques définissant ces estimateurs peuvent être considérés comme des intégrales stochastiques discrètes, nous avons commence "par mettre en place un outil d'étude asymptotique" : L'étude de la convergence en loi de certaines intégrales stochastiques discrètes, d'une part en nous inspirant des résultats de Kurtz et Protter (1991) sur la convergence en loi de semi-martingales et d'autre part en introduisant une nouvelle technique d'approximation différente de celle classique par des martingales. On a appliqué ensuite ces résultats de convergence en distribution à l'étude des lois asymptotiques des estimateurs des moindres carrés des paramètres AR des modèles ARMAX(p,r,q) avec q>0 et IARCH purement instablesIn many recent applications, statistics are under the form of discrete stochastic integrals. In this work, we establish a basic theorem on the convergence in distribution of a sequence of discrete stochastic integrals. This result extends earlier corresponding theorems in Chan & Wei (1988) and in Truong-van & Larramendy (1996). Its proof is not based on the classical martingale approximation technique, but from a derivation of Kurtz & Protter's theorem (1991) on the convergence in distribution of sequences of Itô stochastic integrals relative to two semi-martigales and another approximation technique. Furthermore, various applications to asymptotic statistics are also given, mainly those concerning least squares estimators for ARMAX(p,r,q) models and purely unstable integrated ARCH modelsTOULOUSE-INSA (315552106) / SudocSudocFranceF
Some Stochastic Functional Differential Equations with Infinite Delay: A Result on Existence and Uniqueness of Solutions in a Concrete Fading Memory Space
No full textThis paper is devoted to existence and uniqueness of solutions for some stochastic functional differential equations with infinite delay in a fading memory phase space.</jats:p
Number of Volatility Regimes in the Muscat Securities Market Index in Oman Using Markov-Switching GARCH Models
No full textThe predominant approach for studying volatility is through various GARCH specifications, which are widely utilized in model-based analyses. This study focuses on assessing the predictive performance of specific GARCH models, particularly the Markov-Switching GARCH (MS-GARCH). The primary objective is to determine the optimal number of regimes within the MS-GARCH framework that effectively captures the conditional variance of the Muscat Securities Market Index (MSMI). To achieve this, we employ the Akaike Information Criterion (AIC) to compare different MS-GARCH models, estimated via Maximum Likelihood Estimation (MLE). Our findings indicate that the chosen models consistently exhibit at least two regimes across various GARCH specifications. Furthermore, a validation using the Value at Risk (VaR) confirms the accuracy of volatility forecasts generated by the selected models
Comparison of methods in estimating Weibull parameters for wind energy applications
No full text
Purpose
The purpose of this study is to select the most accurate and the most efficient method in estimating Weibull parameters at Agadir region in Morocco.
Design/methodology/approach
In this paper, Weibull distribution is used to model the wind speed in hourly time series format. Since several methods are used to adjust the Weibull distribution to the measured data, in reporting and analyzing the easiest and the most effective method, seven methods have been investigated, namely, the graphical method (GM), the maximum likelihood method (MLM), the empirical method of Justus (EMJ), the empirical method of Lysen (EML), the energy pattern factor method (EPFM), Mabchour’s method (MMab) and the method of moments (MM).
Findings
According to the statistical analysis tools (the coefficient of determination, root mean square error and chi-square test), it was found that for five months, the MLM presents more efficiency, and for four months, EMJ is ranked first and it is ranked second for February. To select only one method, the selected methods (MLM and EMJ) were compared by calculating the error in estimating the power density using Weibull distribution adjusted by those methods. The average error was found to be −0.51 and −4.56 per cent for MLM and EMJ, respectively.
Originality/value
This investigation is the first of its kind for the studied region. To estimate the available wind power at Agadir in Morocco, investors can directly use MLM to determine the Weibull parameters at this site.
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Wind speed distribution modeling for wind power estimation: Case of Agadir in Morocco
No full text To estimate a wind turbine output, optimize its dimensioning, and predict the economic profitability and risks of a wind energy project, wind speed distribution modeling is crucial. Many researchers use directly Weibull distribution basing on a priori acceptance. However, Weibull does not fit some wind speed regimes. The goal of this work is to model the wind speed distribution at Agadir. For that, we compare the accuracy of four distributions (Weibull, Rayleigh, Gamma, and lognormal) which have given good results in this yield. The goodness-of-fit tests are applied to select the effective distribution. The obtained results explain that Weibull distribution is fitting the histogram of observations better than the other distributions. The analysis deals with comparing the error in estimating the annual wind power density using the examined distributions. It was found that Weibull distribution presents minimum error. Thus, wind energy assessors in Agadir can use directly Weibull distribution basing on a scientific decision made via statistical tests. Moreover, assessors worldwide can use the followed methodology to model their wind speed measurements. </jats:p
The impact of two independent gaussian white noises on the behavior of a stochastic epidemic model
No full textThe aim of this paper is to investigate a stochastic SIS (Susceptible, Infected, Susceptible) epidemic model in which the disease transmission coefficient and the death rate are subject to random disturbances. Using the convergence theorem for local martingales and solving the Fokker-Planck equation associated with the one-dimensional stochastic differential equation, we demonstrate that the disease will almost surely persist in the mean. In the case of global asymptotic stability of the endemic equilibrium for a SIS deterministic epidemic model, we formulate suitable conditions guaranteeing that the stochastic SIS model has a unique ergodic stationary distribution. Furthermore, we deal with the exponential extinction of the disease. Finally, some numerical simulations are provided to illustrate the obtained analytical results
