Süleyman Günay

A new model selection strategy in artificial neural networks

In recent years, artificial neural networks have been used for time series forecasting. Determining architecture of artificial neural networks is very important problem in the applications. In this study, the problem in which time series are forecasted by feed forward neural networks is examined. Various model selection criteria have been used for the determining architecture. In addition, a new model selection strategy based on well-known model selection criteria is proposed. Proposed strategy is applied to real and simulated time series. Moreover, a new direction accuracy criterion called modified direction accuracy criterion is discussed. The new model selection strategy is more reliable than known model selection criteria.

Improving weighted information criterion by using optimization

Although artificial neural networks (ANN) have been widely used in forecasting time series, the determination of the best model is still a problem that has been studied a lot. Various approaches available in the literature have been proposed in order to select the best model for forecasting in ANN in recent years. One of these approaches is to use a model selection strategy based on the weighted information criterion (WIC). WIC is calculated by summing weighted different selection criteria which measure the forecasting accuracy of an ANN model in different ways. In the calculation of WIC, the weights of different selection criteria are determined heuristically. In this study, these weights are calculated by using optimization in order to obtain a more consistent criterion. Four real time series are analyzed in order to show the efficiency of the improved WIC. When the weights are determined based on the optimization, it is obviously seen that the improved WIC produces better results.

Bayesian model selection in ARFIMA models

Various model selection criteria such as Akaike information criterion (AIC; Akaike, 1973), Bayesian information criterion (BIC; Akaike, 1979) and Hannan-Quinn criterion (HQC; Hannan, 1980) are used for model specification in autoregressive fractional integrated moving average (ARFIMA) models. Classical model selection criteria require to calculate both model parameters and order. This kind of approach needs much time. However, in the literature, there are proposed methods which calculate model parameters and order at the same time such as reversible jump Markov chain Monte Carlo (RJMCMC) method, Carlin and Chib (CC) method. In this paper, we proposed two new methods that are using RJMCMC method. The proposed methods are compared with classical methods by a simulation study. We obtained that our methods outperform classical methods in most cases.

A New Approach to Robust Partial Least Squares Regression Analysis

Abstract— Partial Least Squares Regression (PLSR) is a linear regression technique developed to relate many independent variables to one or several dependent variables. Robust methods are introduced to reduce or remove the effects of outlying data points. In the previous studies in robust PLSR field it has been mentioned that if the sample covariance matrix is properly robustified further robustification of the linear regression steps of the PLS1 algorithm (PLSR with univariate dependent variable) becomes unnecessary. Therefore, the purpose of this study is to propose a new approach to robust PLSR based on statistical procedures for covariance matrix robustification by selecting the well-known S-estimators. Both simulation results and an analysis on a real data set, which is used in robust PLSR literature frequently, showing the effectiveness, success in fitting to regular data points and predictive power of the new proposed robust PLSR method.

Advances in Time Series Forecasting

In the literature, many models based on fuzzy systems have been utilized to solve various real world problems from different application areas. One of this areas is time series forecasting. Successful forecasting results have been obtained from fuzzy time series forecasting models in many studies. To determine the best fuzzy time series model among possible forecasting models is a vital decision. In order to evaluate fuzzy time series forecasting models, conventional performance measures such as root mean square error or mean absolute percentage error have been widely utilized in the literature. However, the nature of fuzzy logic is not taking into consideration when such conventional criteria are employed since these criteria are computed over crisp values. When fuzzy time series forecasting models are evaluated, using criteria which work based on fuzzy logic characteristics is wiser. Therefore, Aladag and Turksen [2] suggested a new performance measure which is calculated based on membership values to evaluate fuzzy systems. It is called as membership value based performance measure. In this study, a novel distance measure is firstly defined and a new membership value based performance measure based on this new distance measure is proposed. The proposed criterion is also applied to real world time series in order to show the applicability of the suggested measure.

A New Approach to Least Median of Squares and Regression Through the Origin

When the regression model passes through the origin, PROGRESS algorithm fails to find the exact minimum least median of squares (LMS). Therefore Barreto and Maharry (2006) proposed a new algorithm for finding the true LMS. In this paper, a new method is introduced to find the LMS solution, when the intercept is suppressed and regression model includes at most two unknown parameters, in the case of an odd number of data points.

A simulation study for the comparison of two popular robust PLSR methods: RSIMPLS and PRM with a robust PCR method in the presence of outliers

Classical Principal Component Regression (CPCR) and Partial Least Squares Regression (PLSR) both fit a linear relationship between two sets of variables. Both of these two methods could be used in case of number of regressors p smaller than number of observations n (p n). The responses are usually low-dimensional whereas the regressors are very numerous compared to the number of observations. They are the most popular regression techniques that they offer a good solution because they first reduce the dimensionality of the design matrix. SIMPLS algorithm is the leading PLSR algorithm because of its speed, efficiency and results are easier to interpret. However, both of the CPCR and SIMPLS yield unreliable results when the data set contains outlying observations. Therefore, Hubert and Vanden Branden (2003) have been proposed the robust versions of these methods: robust PCR (RPCR) and a robust PLSR (RPLSR) method: RSIMPLS. Moreover, Serneels et al. (2005) have been proposed Partial Robus...

Fuzzy approach for group sequential test

Buckleys approach (Buckley (2004), (2005), (2006)) uses sets of confidence intervals by taking into consideration both of the uncertainty and impreciseness of concepts that produce triangular shaped fuzzy numbers for the estimator. This approach produces fuzzy test statistics and fuzzy critical values in hypothesis testing. In addition, the sample size is fixed for this test. When data comes sequentially, however, it is not suitable to study with a fixed sample size test. In such cases, sequential and group sequential tests are recommended. Unlike a sequential test, a group of sequential test provides substantial savings in sample and enables us to make decisions as early as possible. This intends paper to combine the benefits of group sequential test and Buckleys approach using α-cuts. It attempts to show that using α-cuts can be used within the group sequential tests. To illustrate the test more explicitly a numerical example is also given.

The comparison of robust partial least squares regression with robust principal component regression on a real

One of the problems encountered in Multiple Linear Regression (MLR) is multicollinearity, which causes the overestimation of the regression parameters and increase of the variance of these parameters. Hence, in case of multicollinearity presents, biased estimation procedures such as classical Principal Component Regression (CPCR) and Partial Least Squares Regression (PLSR) are then performed. SIMPLS algorithm is the leading PLSR algorithm because of its speed, efficiency and results are easier to interpret. However, both of the CPCR and SIMPLS yield very unreliable results when the data set contains outlying observations. Therefore, Hubert and Vanden Branden (2003) have been presented a robust PCR (RPCR) method and a robust PLSR (RPLSR) method called RSIMPLS. In RPCR, firstly, a robust Principal Component Analysis (PCA) method for high-dimensional data on the independent variables is applied, then, the dependent variables are regressed on the scores using a robust regression method. RSIMPLS has been const...

Least Median of Squares Solution of Multiple Linear Regression Models Through the Origin

Barreto and Maharry (2006) showed that PROGRESS algorithm fails to find a correct minimum “Least Median of Squares/LMS” estimate for bivariate regression models which have no intercept. Kayhan and Gunay (2008) presented a different approach for the regression models through the origin which includes at most two unknown parameters. However, LMS estimate for multiple linear regression models still remains an open issue. The aim of this study is to show that finding true LMS estimate for zero intercept multiple linear regression models can be treated as a convex optimization problem and to provide a more general algorithm for any dimensional linear regression models.