This work proposes novel network analysis techniques for multivariate time series. We define the network of a multivariate time series as a graph where vertices denote the components of the process and edges denote non zero long run partial correlations. We then introduce a two step LASSO procedure, called NETS, to estimate high dimensional sparse Long Run Partial Correlation networks. This approach is based on a VAR approximation of the process and allows to decompose the long run linkages into the contribution of the dynamic and contemporaneous dependence relations of the system. The large sample properties of the estimator are analysed and we establish conditions for consistent selection and estimation of the non zero long run partial correlations. The methodology is illustrated with an application to a panel of U.S. bluechips.
{"title":"NETS: Network Estimation for Time Series","authors":"M. Barigozzi, C. Brownlees","doi":"10.2139/ssrn.2249909","DOIUrl":"https://doi.org/10.2139/ssrn.2249909","url":null,"abstract":"This work proposes novel network analysis techniques for multivariate time series. We define the network of a multivariate time series as a graph where vertices denote the components of the process and edges denote non zero long run partial correlations. We then introduce a two step LASSO procedure, called NETS, to estimate high dimensional sparse Long Run Partial Correlation networks. This approach is based on a VAR approximation of the process and allows to decompose the long run linkages into the contribution of the dynamic and contemporaneous dependence relations of the system. The large sample properties of the estimator are analysed and we establish conditions for consistent selection and estimation of the non zero long run partial correlations. The methodology is illustrated with an application to a panel of U.S. bluechips.","PeriodicalId":299310,"journal":{"name":"Econometrics: Mathematical Methods & Programming eJournal","volume":"85 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124142201","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We propose a novel graph-theoretic method for the detection of circular arbitrage in foreign exchange (FX) markets and discuss and demonstrate runtime improvements of this algorithm over the brute force approach. An application on empirical currency bid/ask price data validates this technique as well as provides an example of increased computational efficiency, especially in the case where a large number of currencies are considered. Using minute level market data for all G10 currency pairs, we demonstrate the efficiency of the algorithm as well as potential returns of higher order circular arbitrage trades. Finally, several potential extensions are discussed.
{"title":"Circular Arbitrage Detection Using Graphs","authors":"Zhenyu Cui, Stephen Michael Taylor","doi":"10.2139/ssrn.3267020","DOIUrl":"https://doi.org/10.2139/ssrn.3267020","url":null,"abstract":"We propose a novel graph-theoretic method for the detection of circular arbitrage in foreign exchange (FX) markets and discuss and demonstrate runtime improvements of this algorithm over the brute force approach. An application on empirical currency bid/ask price data validates this technique as well as provides an example of increased computational efficiency, especially in the case where a large number of currencies are considered. Using minute level market data for all G10 currency pairs, we demonstrate the efficiency of the algorithm as well as potential returns of higher order circular arbitrage trades. Finally, several potential extensions are discussed.","PeriodicalId":299310,"journal":{"name":"Econometrics: Mathematical Methods & Programming eJournal","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133632626","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The classical Uryson-Titze theorem states that every continuous function defined on a closed subset of a normal topological space can be extended to the whole space. However, not every continuous and monotone function defined on a closed subset of a normally preordered space is extendable to the whole space. Nachbin found a necessary and sufficient condition for the existence of such an extension for nonstrictly monotone functions. This paper provides a necessary and sufficient condition for the extendability of the continuous strictly monotone functions defined on closed subsets of a normally preordered space with the separable preorder. Important examples of such spaces are the Euclidean spaces with the strict componentwise order. An application to the extension of strictly monotone preferences in Euclidean spaces is given.
{"title":"Extension of Strictly Monotonic Functions in Order-Separable Spaces","authors":"Farhad Husseinov","doi":"10.2139/ssrn.3260586","DOIUrl":"https://doi.org/10.2139/ssrn.3260586","url":null,"abstract":"The classical Uryson-Titze theorem states that every continuous function defined on a closed subset of a normal topological space can be extended to the whole space. However, not every continuous and monotone function defined on a closed subset of a normally preordered space is extendable to the whole space. Nachbin found a necessary and sufficient condition for the existence of such an extension for nonstrictly monotone functions. This paper provides a necessary and sufficient condition for the extendability of the continuous strictly monotone functions defined on closed subsets of a normally preordered space with the separable preorder. Important examples of such spaces are the Euclidean spaces with the strict componentwise order. An application to the extension of strictly monotone preferences in Euclidean spaces is given.","PeriodicalId":299310,"journal":{"name":"Econometrics: Mathematical Methods & Programming eJournal","volume":"154 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123783425","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper provides a new technique for representing discrete time nonlinear dynamic stochastic time invariant maps. Using this new series representation, the paper augments the usual solution strategy with an additional set of constraints thereby enhancing algorithm reliability. The paper also provides general formulas for evaluating the accuracy of proposed solutions. The technique can readily accommodate models with occasionally binding constraints and regime switching. The algorithm uses Smolyak polynomial function approximation in a way which makes it possible to exploit a high degree of parallelism.
{"title":"Reliably Computing Nonlinear Dynamic Stochastic Model Solutions: An Algorithm with Error Formulas","authors":"Gary S. Anderson","doi":"10.17016/FEDS.2018.070","DOIUrl":"https://doi.org/10.17016/FEDS.2018.070","url":null,"abstract":"This paper provides a new technique for representing discrete time nonlinear dynamic stochastic time invariant maps. Using this new series representation, the paper augments the usual solution strategy with an additional set of constraints thereby enhancing algorithm reliability. The paper also provides general formulas for evaluating the accuracy of proposed solutions. The technique can readily accommodate models with occasionally binding constraints and regime switching. The algorithm uses Smolyak polynomial function approximation in a way which makes it possible to exploit a high degree of parallelism.","PeriodicalId":299310,"journal":{"name":"Econometrics: Mathematical Methods & Programming eJournal","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125889840","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-09-30DOI: 10.5709/CE.1897-9254.275
W. Brauers
The first systematic research on Location Theory dates back to 1826. Quantitative approaches came much later. On the supply side extensive Input-Output Tables can be mentioned and on the demand side the optimization by Multi-Criteria Decision Making. The advantages of Input-Output Tables for location opportunities on a regional and urban basis have to be emphasized, whereas the link is made between Input-Output and Multi-Criteria Optimization. MOORA, Multi-Objective Optimization by Ratio Analysis, is composed of two methods: Ratio Analysis and Reference Point Theory and responds to the different conditions of robustness needed for optimization. This approach attempts to localize in an optimal way a certain project facing different indicators, criteria or objectives sometimes originating from different groups or individuals. Here however type and importance of objectives and alternatives were only simulated. The real stakeholders to be considered are rather the national and local authorities, the contributing firms and their personnel. In the production sphere consumer sovereignty was only indirectly involved. If consumers, via consumer organizations and trade unions, were directly involved, other claims could emerge. The simulation used was limited in its applications. Clearly if this simulation has no practical consequences, it still provides a learning experience with the use of the MOORA Method in its double composition.
{"title":"Location Theory and Multi-Criteria Decision Making: An Application of the Moora Method","authors":"W. Brauers","doi":"10.5709/CE.1897-9254.275","DOIUrl":"https://doi.org/10.5709/CE.1897-9254.275","url":null,"abstract":"The first systematic research on Location Theory dates back to 1826. Quantitative approaches came much later. On the supply side extensive Input-Output Tables can be mentioned and on the demand side the optimization by Multi-Criteria Decision Making. The advantages of Input-Output Tables for location opportunities on a regional and urban basis have to be emphasized, whereas the link is made between Input-Output and Multi-Criteria Optimization. MOORA, Multi-Objective Optimization by Ratio Analysis, is composed of two methods: Ratio Analysis and Reference Point Theory and responds to the different conditions of robustness needed for optimization. This approach attempts to localize in an optimal way a certain project facing different indicators, criteria or objectives sometimes originating from different groups or individuals. Here however type and importance of objectives and alternatives were only simulated. The real stakeholders to be considered are rather the national and local authorities, the contributing firms and their personnel. In the production sphere consumer sovereignty was only indirectly involved. If consumers, via consumer organizations and trade unions, were directly involved, other claims could emerge. The simulation used was limited in its applications. Clearly if this simulation has no practical consequences, it still provides a learning experience with the use of the MOORA Method in its double composition.","PeriodicalId":299310,"journal":{"name":"Econometrics: Mathematical Methods & Programming eJournal","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133635727","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We describe a numerical method for solving 3-dimensional partial differential equations, which arise in mathematical finance and other applications. The goal of the paper is to introduce a technique based on Wiener-Hopf factorization with application of Laplace transform. We analyze the problem in terms of expectations of random processes. We construct an approximation scheme by using Carr randomization and constructing a Markov chain, and reduce the original problem to a sequence of 1-dimensional integro-differential equations with suitable boundary conditions. The kernels of the equations are defined by Levy processes with constant variance. An analytic solution to each problem can be expressed in terms of Laplace-Carson transform of the corresponding characteristic functions of its supremum and infimum processes. We show that for a class of models it is possible to construct an efficient method for solving these equations which relies upon approximate formulae for the transform, and discuss modifications allowing to reduce the amount of computations.
{"title":"A Numercal Realization of the Wiener-Hopf Method For the Backward Kolmogorov Equation","authors":"O. Kudryavtsev, V. Rodochenko","doi":"10.2139/ssrn.3285443","DOIUrl":"https://doi.org/10.2139/ssrn.3285443","url":null,"abstract":"We describe a numerical method for solving 3-dimensional partial differential equations, which arise in mathematical finance and other applications. The goal of the paper is to introduce a technique based on Wiener-Hopf factorization with application of Laplace transform. We analyze the problem in terms of expectations of random processes. We construct an approximation scheme by using Carr randomization and constructing a Markov chain, and reduce the original problem to a sequence of 1-dimensional integro-differential equations with suitable boundary conditions. The kernels of the equations are defined by Levy processes with constant variance. An analytic solution to each problem can be expressed in terms of Laplace-Carson transform of the corresponding characteristic functions of its supremum and infimum processes. We show that for a class of models it is possible to construct an efficient method for solving these equations which relies upon approximate formulae for the transform, and discuss modifications allowing to reduce the amount of computations.","PeriodicalId":299310,"journal":{"name":"Econometrics: Mathematical Methods & Programming eJournal","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134007227","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Longxiao Zhao, Deepayan Chakrabarti, K. Muthuraman
We address the problem of poor portfolio performance when a minimum-variance portfolio is constructed using the sample estimates. Estimation errors are mostly blamed for the poor portfolio performa...
{"title":"Portfolio Construction by Mitigating Error Amplification: The Bounded-Noise Portfolio","authors":"Longxiao Zhao, Deepayan Chakrabarti, K. Muthuraman","doi":"10.2139/ssrn.2999407","DOIUrl":"https://doi.org/10.2139/ssrn.2999407","url":null,"abstract":"We address the problem of poor portfolio performance when a minimum-variance portfolio is constructed using the sample estimates. Estimation errors are mostly blamed for the poor portfolio performa...","PeriodicalId":299310,"journal":{"name":"Econometrics: Mathematical Methods & Programming eJournal","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127427058","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Problem definition: The theoretical investigation of the effectiveness of limited flexibility has mainly focused on a performance metric that is based on the maximum sales in units. However, this could lead to substantial profit losses when the maximum sales metric is used to guide flexibility designs while the products have considerably large profit margin differences. Academic/practical relevance: We address this issue by introducing margin differentials into the analysis of process flexibility designs, and our results can provide useful guidelines for the evaluation and design of flexibility configurations when the products have heterogeneous margins. Methodology: We adopt a robust optimization framework and study process flexibility designs from the worst-case perspective by introducing the dual margin group index (DMGI). Results and managerial implications: We show that a general class of worst-case performance measures can be expressed as functions of a design’s DMGIs and the given uncertainty set. Moreover, the DMGIs lead to a partial ordering that enables us to compare the worst-case performance of different designs. Applying these results, we prove that under the so-called partwise independently symmetric uncertainty sets and a broad class of worst-case performance measures, the alternate long-chain design is optimal among all long-chain designs with equal numbers of high-profit products and low-profit products. Finally, we develop a heuristic based on the DMGIs to generate effective flexibility designs when products exhibit margin differentials.
问题定义:对有限灵活性有效性的理论研究主要集中在基于单位最大销售额的绩效指标上。然而，当最大销售指标用于指导灵活性设计，而产品有相当大的利润率差异时，这可能导致大量的利润损失。学术/实践相关性:我们通过在过程灵活性设计的分析中引入边际差异来解决这个问题，当产品具有异质边际时，我们的结果可以为灵活性配置的评估和设计提供有用的指导。方法:采用稳健优化框架，引入双边际群指数(dual margin group index, DMGI)，从最坏情况的角度研究过程灵活性设计。结果和管理意义:我们表明，一般的最坏情况性能度量可以表示为设计的dmgi和给定的不确定性集的函数。此外，dmgi导致部分排序，使我们能够比较不同设计的最坏情况性能。应用这些结果，我们证明了在所谓的部分独立对称不确定性集和一类广泛的最坏情况性能度量下，在高利润产品和低利润产品数量相等的所有长链设计中，备选长链设计是最优的。最后，我们开发了一种基于dmgi的启发式方法，以在产品表现出边际差异时产生有效的灵活性设计。
{"title":"Robust Optimization Approach to Process Flexibility Designs with Contribution Margin Differentials","authors":"Shixin Wang, Xuan Wang, Jiawei Zhang","doi":"10.2139/ssrn.3233721","DOIUrl":"https://doi.org/10.2139/ssrn.3233721","url":null,"abstract":"Problem definition: The theoretical investigation of the effectiveness of limited flexibility has mainly focused on a performance metric that is based on the maximum sales in units. However, this could lead to substantial profit losses when the maximum sales metric is used to guide flexibility designs while the products have considerably large profit margin differences. Academic/practical relevance: We address this issue by introducing margin differentials into the analysis of process flexibility designs, and our results can provide useful guidelines for the evaluation and design of flexibility configurations when the products have heterogeneous margins. Methodology: We adopt a robust optimization framework and study process flexibility designs from the worst-case perspective by introducing the dual margin group index (DMGI). Results and managerial implications: We show that a general class of worst-case performance measures can be expressed as functions of a design’s DMGIs and the given uncertainty set. Moreover, the DMGIs lead to a partial ordering that enables us to compare the worst-case performance of different designs. Applying these results, we prove that under the so-called partwise independently symmetric uncertainty sets and a broad class of worst-case performance measures, the alternate long-chain design is optimal among all long-chain designs with equal numbers of high-profit products and low-profit products. Finally, we develop a heuristic based on the DMGIs to generate effective flexibility designs when products exhibit margin differentials.","PeriodicalId":299310,"journal":{"name":"Econometrics: Mathematical Methods & Programming eJournal","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115547651","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We estimate models of consumption growth that allow for long-run risks and disasters using data for a series of countries over a time span of 200 years. Our estimates indicate that a model with small and frequent disasters that arrive at a mean-reverting rate best fits international consumption data. The implied posterior disaster intensity in such a model predicts equity returns without compromising the unpredictability of consumption growth. It also generates time-varying excess stock volatility, empirically validating key economic mechanisms often assumed in consumption-based asset pricing models.
{"title":"Estimating the Dynamics of Consumption Growth","authors":"G. Schwenkler","doi":"10.2139/ssrn.3140044","DOIUrl":"https://doi.org/10.2139/ssrn.3140044","url":null,"abstract":"We estimate models of consumption growth that allow for long-run risks and disasters using data for a series of countries over a time span of 200 years. Our estimates indicate that a model with small and frequent disasters that arrive at a mean-reverting rate best fits international consumption data. The implied posterior disaster intensity in such a model predicts equity returns without compromising the unpredictability of consumption growth. It also generates time-varying excess stock volatility, empirically validating key economic mechanisms often assumed in consumption-based asset pricing models.","PeriodicalId":299310,"journal":{"name":"Econometrics: Mathematical Methods & Programming eJournal","volume":"117 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124169138","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We reconsider the theory of Thompson aggregators proposed by Marinacci and Montrucchio [34]. We prove a variant of their Recovery Theorem establishing the existence of extremal solutions to the Koopmans equation. We apply the constructive Tarski-Kantorovich Fixed Point Theorem rather than the nonconstructive Tarski Theorem employed in [34]. We also obtain additional properties of the extremal solutions. The Koopmans operator possesses two distinct order continuity properties. Each is sufficient for the application of the Tarski-Kantorovich Theorem. One version builds on the order properties of the underlying vector spaces for utility functions and commodities. The second form is topological. The Koopmans operator is continuous in Scott's [40] induced topology. The least fixed point is constructed with either continuity hypothesis by the partial sum method. This solution is a concave function whenever the Thompson aggregator is concave and also norm continuous on the interior of its effective domain.
{"title":"Recursive Utility and Thompson Aggregators I: Constructive Existence Theory for the Koopmans Equation","authors":"R. Becker, J. P. Rincón-Zapatero","doi":"10.2139/ssrn.3228079","DOIUrl":"https://doi.org/10.2139/ssrn.3228079","url":null,"abstract":"We reconsider the theory of Thompson aggregators proposed by Marinacci and Montrucchio [34]. We prove a variant of their Recovery Theorem establishing the existence of extremal solutions to the Koopmans equation. We apply the constructive Tarski-Kantorovich Fixed Point Theorem rather than the nonconstructive Tarski Theorem employed in [34]. We also obtain additional properties of the extremal solutions. The Koopmans operator possesses two distinct order continuity properties. Each is sufficient for the application of the Tarski-Kantorovich Theorem. One version builds on the order properties of the underlying vector spaces for utility functions and commodities. The second form is topological. The Koopmans operator is continuous in Scott's [40] induced topology. The least fixed point is constructed with either continuity hypothesis by the partial sum method. This solution is a concave function whenever the Thompson aggregator is concave and also norm continuous on the interior of its effective domain.","PeriodicalId":299310,"journal":{"name":"Econometrics: Mathematical Methods & Programming eJournal","volume":"163 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126593902","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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