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Comparative Study of Portmanteau Tests for the Residuals Autocorrelation in ARMA Models
Samir K. Safi,
Alaa A. Al-Reqep
Issue:
Volume 2, Issue 1, February 2014
Pages:
1-13
Received:
7 November 2013
Published:
10 December 2013
Abstract: The portmanteau statistic for testing the adequacy of an autoregressive moving average (ARMA) model is based on the first m autocorrelations of the residuals from the fitted model. We consider some of portmanteau tests for univariate linear time series such as Box and Pierce [2], Ljung and Box [9], Monti [12], Peña and Rodríguez [13 and 14], Generalized Variance Test (Gvtest) by Mahdi and McLeod [11] and Fisher [4]. We conduct an extensive computer simulation time series data, to make comparison among these tests. We consider different model parameters for small, moderate and large samples to examine the effect of lag m on the power of the selected tests, and determine the most powerful test for ARMA models. The similar portmanteau tests models was evaluated for the real data set on electricity consumption in Khan Younis, Palestine (April 2009 - May 2013). We found that, portmanteau tests have the highest values of power for large sample data (N = 500) comparing to small and moderate samples (N = 50 and 200). We found that the portmanteau tests are sensitive to the chosen for m value. Indeed there are loss of the power values for lags m ranging from m = 5 to 20, where Box-Pierce, Ljung-Box and Monti tests have more power loss than the other selected tests. The power loss reaches its minimum values for large sample data comparing to small and moderate samples. In addition, the results of the simulation study and real data analysis showed that the most powerful tests varies between Gvtest and Fisher tests.
Abstract: The portmanteau statistic for testing the adequacy of an autoregressive moving average (ARMA) model is based on the first m autocorrelations of the residuals from the fitted model. We consider some of portmanteau tests for univariate linear time series such as Box and Pierce [2], Ljung and Box [9], Monti [12], Peña and Rodríguez [13 and 14], Gener...
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Fuzzy Goal Programming to Optimization the Multi-Objective Problem
Azzabi Lotfi,
Ayadi Dorra,
Bachar Kaddour,
Kobi Abdessamad
Issue:
Volume 2, Issue 1, February 2014
Pages:
14-19
Received:
13 November 2013
Published:
20 February 2014
Abstract: Many present-day problems are multi-objective in nature and their solution requires consideration of conflicting objectives. Usually, they have a number of potentially Pareto-optimal solutions. An extensive knowledge of the problem is required in discriminating between solutions, eliminating the unwanted ones and accepting the required solution(s) by a decision making process. It is well known that multi-objective optimization model had found a lot of important applications in decision making problems such as in economics theory, management science and engineering design. Because of these applications, a lot of literatures have been published to study optimality conditions, duality theories and topological properties of solutions of multi-objective optimization problems. In the case of optimization problems, the idea of regularizing a problem by adding a strongly convex term to the objective function can actually be treated back at least. The regularization technique proved to be an invaluable tool in the solution of ill-posed problems, and an enormous amount of work has been devoted to its study. In this paper, a Multi-objective Optimization Problems formulation based on a Goal Programming Methods solves the multi-objective problem which can tackle relatively large test systems. This method is based on optimization of the most preferred objective and considering the other objectives as constraints.
Abstract: Many present-day problems are multi-objective in nature and their solution requires consideration of conflicting objectives. Usually, they have a number of potentially Pareto-optimal solutions. An extensive knowledge of the problem is required in discriminating between solutions, eliminating the unwanted ones and accepting the required solution(s) ...
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Robust Covariance Estimator for Small-Sample Adjustment in the Generalized Estimating Equations: A Simulation Study
Masahiko Gosho,
Yasunori Sato,
Hisao Takeuchi
Issue:
Volume 2, Issue 1, February 2014
Pages:
20-25
Received:
21 January 2014
Published:
20 February 2014
Abstract: The robust or sandwich estimator is common to estimate the covariance matrix of the estimated regression parameter for generalized estimating equation (GEE) method to analyze longitudinal data. However, the robust estimator would underestimate the variance under a small sample size. We propose an alternative covariance estimator to the robust estimator to improve the small-sample bias in the GEE method. Our proposed estimator is a modification of the bias-corrected covariance estimator proposed by Pan (2001, Biometrika88, 901—906) for the GEE method. In a simulation study, we compared the proposed covariance estimator to the robust estimator and Pan's estimator for continuous and binominallongitudinal responses for involving 10—50 subjects. The test size of Wald-type test statistics for the proposed estimator is relatively close to the nominal level when compared with those for the robust estimator and the Pan's approach.
Abstract: The robust or sandwich estimator is common to estimate the covariance matrix of the estimated regression parameter for generalized estimating equation (GEE) method to analyze longitudinal data. However, the robust estimator would underestimate the variance under a small sample size. We propose an alternative covariance estimator to the robust estim...
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Mathematical Problem Appearing in Industrial Lumber Drying: A Review
Issue:
Volume 2, Issue 1, February 2014
Pages:
26-30
Received:
21 February 2014
Published:
20 March 2014
Abstract: This article is a review of our work on the modeling of lumber drying that we have started in 2003. We consider a lumber drying process in a kiln chamber where from mathematical point of views, this is an initial and boundary value problem. The Moisture Content (MC) is measured at the center of the lumber by applying a nail that thousands times of the pore size of the wood. This leads to apply macro modeling for the diffusion process of the water inside the lumber. MC acts as the state variable u of the thickness x and time t. The state variable satisfies a diffusion equation. The Equilibrium Moisture Content (EMC) of the air acts as the boundary condition. We report the progress on mathematical modeling and compared the results with data from industry.
Abstract: This article is a review of our work on the modeling of lumber drying that we have started in 2003. We consider a lumber drying process in a kiln chamber where from mathematical point of views, this is an initial and boundary value problem. The Moisture Content (MC) is measured at the center of the lumber by applying a nail that thousands times of ...
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Modelling and Forecasting Malaria Mortality Rate using SARIMA Models (A Case Study of Aboh Mbaise General Hospital, Imo State Nigeria)
Ekezie Dan Dan,
Opara Jude,
Okenwe Idochi
Issue:
Volume 2, Issue 1, February 2014
Pages:
31-41
Received:
30 January 2014
Published:
20 March 2014
Abstract: This paper examined the modeling and forecasting malaria mortality rate using SARIMA Models. Among the most effective approaches for analysing time series data is the method propounded by Box and Jenkins, the Autoregressive Integrated Moving Average (ARIMA). In this paper, we employed Box-Jenkins methodology to build ARIMA model for malaria mortality rate for the period January 1996 to December 2013 with a total of 216 data points. The model obtained in this paper was used to forecast monthly malaria mortality rate for the upcoming year 2014. The forecasted results will help Government and medical professionals to see how to maintain steady decrease of malaria mortality in other to combat the predicted rise in mortality rate envisaged in some months.
Abstract: This paper examined the modeling and forecasting malaria mortality rate using SARIMA Models. Among the most effective approaches for analysing time series data is the method propounded by Box and Jenkins, the Autoregressive Integrated Moving Average (ARIMA). In this paper, we employed Box-Jenkins methodology to build ARIMA model for malaria mortali...
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