Ayşe Özmen

The new robust conic GPLM method with an application to finance: prediction of credit default

This paper contributes to classification and identification in modern finance through advanced optimization. In the last few decades, financial misalignments and, thereby, financial crises have been increasing in numbers due to the rearrangement of the financial world. In this study, as one of the most remarkable of these, countries’ debt crises, which result from illiquidity, are tried to predict with some macroeconomic variables. The methodology consists of a combination of two predictive regression models, logistic regression and robust conic multivariate adaptive regression splines (RCMARS), as linear and nonlinear parts of a generalized partial linear model. RCMARS has an advantage of coping with the noise in both input and output data and of obtaining more consistent optimization results than CMARS. An advanced version of conic generalized partial linear model which includes robustification of the data set is introduced: robust conic generalized partial linear model (RCGPLM). This new model is applied on a data set that belongs to 45 emerging markets with 1,019 observations between the years 1980 and 2005.

Precipitation Modeling by Polyhedral RCMARS and Comparison with MARS and CMARS

Climate change is becoming an ever important issue due to the possibility that it may result in extreme weather events such as floods or droughts. Consequently, precipitation forecasting has similarly gained in significance as it is a useful tool in meeting the increasing need for the efficient management of water resources as well as in preventing disasters before they happen. In the literature, there are various statistical and computational methods used for this purpose, including linear and nonlinear regression, kriging, time series models, neural networks, and multivariate adaptive regression splines (MARS). Among them, MARS stands out as the better performing precipitation modeling method. In this article, we used a recently developed method called robust conic mars (RCMARS), based on MARS (also on CMARS), to forecast precipitation owing to its ability to model complex uncertain data. In CMARS, which was developed as a powerful alternative to MARS, the model complexity is penalized in the form of Tikhonov regularization and studied as a conic quadratic programming. In RCMARS, on the other hand, CMARS is refined further by including the existence of uncertainty in the future scenarios and robustifying it with a robust optimization technique. To evaluate the performance of the RCMARS method, it was applied to build a precipitation model constructed as an early warning system for the continental Central Anatolia Region of Turkey, where drought has been a recurrent phenomenon for the last few decades. Furthermore, the performance of the RCMARS precipitation model was also compared to that of MARS and CMARS. The results indicated that RCMARS builds more accurate, precise, and stable precipitation models compared to those of MARS and CMARS. In addition to these advantageous features of the RCMARS precipitation model, it also provided a good fit to the data. As a result, we propose its use in precipitation forecasting for the region studied.

Electricity Price Modelling for Turkey

This paper presents customized models to predict next-day’s electricity price in short-term periods for Turkey’s electricity market. Turkey’s electricity market is evolving from a centralized approach to a competitive market. Fluctuations in the electricity consumption show that there are three periods; day, peak, and night. The approach proposed here is based on robust and continuous optimization techniques, which ensures achieving the optimum electricity price to minimize error in periodic price prediction. Commonly, next-day’s electricity prices are forecasted by using time series models, specifically dynamic regression model. Therefore electricity price prediction performance was compared with dynamic regression. Numerical results show that CMARS and RCMARS predicts the prices with 30% less error compared to dynamic regression.

Robust conic generalized partial linear models using RCMARS method - A robustification of CGPLM

GPLM is a combination of two different regression models each of which is used to apply on different parts of the data set. It is also adequate to high dimensional, non-normal and nonlinear data sets having the flexibility to reflect all anomalies effectively. In our previous study, Conic GPLM (CGPLM) was introduced using CMARS and Logistic Regression. According to a comparison with CMARS, CGPLM gives better results. In this study, we include the existence of uncertainty in the future scenarios into CMARS and linear/logit regression part in CGPLM and robustify it with robust optimization which is dealt with data uncertainty. Moreover, we apply RCGPLM on a small data set as a numerical experience from the financial sector.

Inversion of top of atmospheric reflectance values by conic multivariate adaptive regression splines

Spatial technologies offer high flexibility to handle substantial amount of spatial data and wide range of modelling capabilities. Remotely sensed data are the most significant data source used in spatial technologies. However, it is often associated with uncertainties due to atmospheric effects (i.e. absorption and scattering by atmospheric gases and aerosols). Methods based on rigorous treatment of radiative transfer models still have some drawbacks in the inversion of top of atmospheric reflectance values to surface reflectance values on large numbers of satellite images. In this paper, our aim is to represent a more flexible (adaptive) approach for the regional atmospheric correction by employing nonparametric regression splines within the frame of inverse problems and modern techniques of continuous optimization. To achieve this objective, atmospheric correction models obtained through conic multivariate adaptive regression splines, which is an alternative method to multivariate adaptive regression splines by constructing a penalized residual sum of squares as a Tikhonov regularization problem, are applied on a set of satellite images in order to convert the top of atmospheric reflectance values into surface reflectance values. The results are compared with the ones obtained by both multivariate adaptive regression splines and a radiative transfer-based method.

Predicting default probabilities in emerging markets by new conic generalized partial linear models and their optimization

Nowadays, the importance of financial crises and defaults of countries are becoming clear due to the globalization in the economic area and investments. Generalized partial linear model (GPLM) is a combination of two different regression models connecting with the mean of the dependent variable with the help of a link function. It is adequate to high-dimensional, non-normal data sets having the flexibility to reflect all anomalies effectively. The nonlinear patterns are also easily explained by the nonparametric component of the model. In this study, we introduce a newly developed conic GPLM (CGPLM) to predict default probabilities of 45 emerging markets using the contribution of a continuous model CMARS and a discrete model logistic regression. We present its application results on a data set with 13 macroeconomic variables in 25 years’ time. To predict debt crises, CGPLM gives better results than a single CMARS and a single logistic regression. In fact, we have 91.81% and 89.31% accuracy rates, computed according to the correctness of the model output, for training and validation sample, respectively. This improvement in prediction of crises can contribute to new prospects and developments in financial mathematics to make more accurate previsions for investments and to take measures due to coming risks.

Spline regression models for complex multi-modal regulatory networks

Complex regulatory networks often have to be further expanded and improved with regard to the unknown effects of additional parameters and factors that can emit a disturbing influence on the key variables under consideration. The concept of target-environment (TE) networks provides a holistic framework for the analysis of such parameter-dependent multi-modal systems. In this study, we consider time-discrete TE regulatory systems with spline entries. We introduce a new regression model for these particular two-modal systems that allows us to determine the unknown system parameters by applying the multivariate adaptive regression spline (MARS) technique and the newly developed conic multivariate adaptive regression spline (CMARS) method. We obtain a relaxation by means of continuous optimization, especially, conic quadratic programming (CQP) that could be conducted by interior point methods. Finally, a numerical example demonstrates the efficiency of the spline-based approach.

Modern Applied Mathematics for Alternative Modeling of the Atmospheric Effects on Satellite Images

Nonparametric regression and classification techniques are mostly the key data mining tools in explaining real life problems and natural phenomena where many effects often exhibit nonlinear behavior. The remotely sensed earth data collected by earth-observing satellites is degraded due to the absorption and scattering of solar radiation by atmospheric gases and aerosols. In order to use these data for information extraction, they must first be corrected for the atmospheric effects. Recent methods based on radiative transfer modelling still have many challenges including achieving high accuracy and developing real-time processing capability of large numbers of satellite images acquired with high temporal resolution and Large Field of View instruments. In this chapter, two state-of-the-art nonparametric tools, Multivariate Adaptive Regression Splines (MARS) and its successor Conic Multivariate Adaptive Regression Splines (CMARS), are reviewed within the frame of an earth science example. Both methods are utilized for the atmospheric correction of five sets of MODIS images taken over European Alps. The Simplified Method for Atmospheric Correction (SMAC), a simplified version of 6S radiative transfer model, is also applied on the image data sets for the removal of atmospheric effects. The performance of the models was evaluated by comparing their results with the MODIS atmospherically corrected surface reflectance product in terms of RMSE. Although MARS and CMARS approaches produce similar results on the data sets, they both outperform SMAC.

Robust optimization in spline regression models for multi-model regulatory networks under polyhedral uncertainty

Abstract In our study, we integrate the data uncertainty of real-world models into our regulatory systems and robustify them. We newly introduce and analyse robust time-discrete target–environment regulatory systems under polyhedral uncertainty through robust optimization. Robust optimization has reached a great importance as a modelling framework for immunizing against parametric uncertainties and the integration of uncertain data is of considerable importance for the model’s reliability of a highly interconnected system. Then, we present a numerical example to demonstrate the efficiency of our new robust regression method for regulatory networks. The results indicate that our approach can successfully approximate the target–environment interaction, based on the expression values of all targets and environmental factors.

Stability advances in robust portfolio optimization under parallelepiped uncertainty

In financial markets with high uncertainties, the trade-off between maximizing expected return and minimizing the risk is one of the main challenges in modeling and decision making. Since investors mostly shape their invested amounts towards certain assets and their risk aversion level according to their returns, scientists and practitioners have done studies on that subject since the beginning of the stock markets’ establishment. In this study, we model a Robust Optimization problem based on data. We found a robust optimal solution to our portfolio optimization problem. This approach includes the use of Robust Conditional Value-at-Risk under Parallelepiped Uncertainty, an evaluation and a numerical finding of the robust optimal portfolio allocation. Then, we trace back our robust linear programming model to the Standard Form of a Linear Programming model; consequently, we solve it by a well-chosen algorithm and software package. Uncertainty in parameters, based on uncertainty in the prices, and a risk-return analysis are crucial parts of this study. A numerical experiment and a comparison (back testing) application are presented, containing real-world data from stock markets as well as a simulation study. Our approach increases the stability of portfolio allocation and reduces the portfolio risk.