CORRELATIONS BETWEEN OIL AND STOCK MARKETS: A WAVELET-BASED APPROACH

In a global economy, shocks occurring in one market can spill over to other markets. This paper investigates the impact of oil shocks and stock markets crashes on correlations between stock and oil markets. We test changes in correlations at different scales with non-overlapping confidence intervals based on estimated wavelet correlations. Contrary to other approaches, this method does not need adjustment for heteroskedasticity biases on the correlation coefficients. Our results show that oil shocks affect the correlation between both markets. The evidence on the change of correlation between stock markets after an oil shock is weaker; except in some specific cases during the Kuwait war and the OPEC cutback period. Conversely, we only find weak evidence that stock market crashes change the correlation between oil and stock markets. Overall, the evidence gives support to including oil as an asset class in asset allocation strategies.he authors acknowledge financial support from Financial Research Center–UNIDE and from the Spanish Ministry of Education and Science, research projects MTM2010-17323, ECO2011-25706, ECO2012-32401 and MTM2012-36163-C06-03

Binarized support vector machines

The widely used Support Vector Machine (SVM) method has shown to yield very good results in Supervised Classification problems. Other methods such as Classification Trees have become more popular among practitioners than SVM thanks to their interpretability, which is an important issue in Data Mining. In this work, we propose an SVM-based method that automatically detects the most important predictor variables, and the role they play in the classifier. In particular, the proposed method is able to detect those values and intervals which are critical for the classification. The method involves the optimization of a Linear Programming problem, with a large number of decision variables. The numerical experience reported shows that a rather direct use of the standard Column-Generation strategy leads to a classification method which, in terms of classification ability, is competitive against the standard linear SVM and Classification Trees. Moreover, the proposed method is robust, i.e., it is stable in the presence of outliers and invariant to change of scale or measurement units of the predictor variables. When the complexity of the classifier is an important issue, a wrapper feature selection method is applied, yielding simpler, still competitive, classifiers

Computing (R, S) policies with correlated demand

This paper considers the single-item single-stocking non-stationary stochastic lot-sizing problem under correlated demand. By operating under a nonstationary (R, S) policy, in which R denote the reorder period and S the associated order-up-to-level, we introduce a mixed integer linear programming (MILP) model which can be easily implemented by using off-theshelf optimisation software. Our modelling strategy can tackle a wide range of time-seriesbased demand processes, such as autoregressive (AR), moving average(MA), autoregressive moving average(ARMA), and autoregressive with autoregressive conditional heteroskedasticity process(AR-ARCH). In an extensive computational study, we compare the performance of our model against the optimal policy obtained via stochastic dynamic programming. Our results demonstrate that the optimality gap of our approach averages 2.28% and that computational performance is good

Detecting outliers in multivariate volatility models:A wavelet procedure

It is well known that outliers can affect both the estimation of parameters and volatilities when fitting a univariate GARCH-type model. Similar biases and impacts are expected to be found on correlation dynamics in the context of multivariate time series. We study the impact of outliers on the estimation of correlations when fitting multivariate GARCH models and propose a general detection algorithm based on wavelets, that can be applied to a large class of multivariate volatility models. Its effectiveness is evaluated through a Monte Carlo study before it is applied to real data. The method is both effective and reliable, since it detects very few false outliers

Interpretable support vector machines for functional data

Support Vector Machines (SVMs) is known to be a powerful nonparametric classification technique even for high-dimensional data. Although predictive ability is important, obtaining an easy-to-interpret classifier is also crucial in many applications. Linear SVM provides a classifier based on a linear score. In the case of functional data, the coefficient function that defines such linear score usually has many irregular oscillations, making it difficult to interpret. This paper presents a new method, called Interpretable Support Vector Machines for Functional Data, that provides an interpretable classifier with high predictive power. Interpretability might be understood in different ways. The proposed method is flexible enough to cope with different notions of interpretability chosen by the user, thus the obtained coefficient function can be sparse, linear-wise, smooth, etc. The usefulness of the proposed method is shown in real applications getting interpretable classifiers with comparable, sometimes better, predictive ability versus classical SVM.The authors thank the anonymous referees and the associate editor for their helpful comments to improve the article. This work has been partially supported by projects MTM2009-14039, ECO2011-25706 of Ministerio de Ciencia e Innovación and FQM-329 of Junta de Andalucía, Spain

Computing non-stationary (s,S) policies using mixed integer linear programming

This paper addresses the single-item single-stocking location stochastic lot sizing problem under the $(s, S)$ policy. We first present a mixed integer non-linear programming (MINLP) formulation for determining near-optimal $(s, S)$ policy parameters. To tackle larger instances, we then combine the previously introduced MINLP model and a binary search approach. These models can be reformulated as mixed integer linear programming (MILP) models which can be easily implemented and solved by using off-the-shelf optimisation software. Computational experiments demonstrate that optimality gaps of these models are around $0.3\%$ of the optimal policy cost and computational times are reasonable