Thibault Vatter, Hau‐Tieng Wu, V. Chavez-Demoulin, Bin Yu
We provide a new framework for modeling trends and periodic patterns in high-frequency financial data. Seeking adaptivity to ever-changing market conditions, we enlarge the Fourier flexible form into a richer functional class: both our smooth trend and the seasonality are non-parametrically time-varying and evolve in real time. We provide the associated estimators and use simulations to show that they behave adequately in the presence of jumps and heteroskedastic and heavy-tailed noise. A study of exchange rate returns sampled from 2010 to 2013 suggests that failing to factor in the seasonality’s dynamic properties may lead to misestimation of the intraday spot volatility.
{"title":"Non-Parametric Estimation of Intraday Spot Volatility: Disentangling Instantaneous Trend and Seasonality","authors":"Thibault Vatter, Hau‐Tieng Wu, V. Chavez-Demoulin, Bin Yu","doi":"10.2139/ssrn.2330159","DOIUrl":"https://doi.org/10.2139/ssrn.2330159","url":null,"abstract":"We provide a new framework for modeling trends and periodic patterns in high-frequency financial data. Seeking adaptivity to ever-changing market conditions, we enlarge the Fourier flexible form into a richer functional class: both our smooth trend and the seasonality are non-parametrically time-varying and evolve in real time. We provide the associated estimators and use simulations to show that they behave adequately in the presence of jumps and heteroskedastic and heavy-tailed noise. A study of exchange rate returns sampled from 2010 to 2013 suggests that failing to factor in the seasonality’s dynamic properties may lead to misestimation of the intraday spot volatility.","PeriodicalId":11744,"journal":{"name":"ERN: Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2015-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83587611","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 consider a firm (e.g., retailer) selling a single nonperishable product over a finite-period planning horizon. Demand in each period is stochastic and price-dependent, and unsatisfied demands are backlogged. At the beginning of each period, the firm determines its selling price and inventory replenishment quantity, but it knows neither the form of demand dependency on selling price nor the distribution of demand uncertainty a priori, hence it has to make pricing and ordering decisions based on historical demand data. We propose a nonparametric data-driven policy that learns about the demand on the fly and, concurrently, applies learned information to determine replenishment and pricing decisions. The policy integrates learning and action in a sense that the firm actively experiments on pricing and inventory levels to collect demand information with the least possible profit loss. Besides convergence of optimal policies, we show that the regret, defined as the average profit loss compared with that of the optimal solution when the firm has complete information about the underlying demand, vanishes at the fastest possible rate as the planning horizon increases.
{"title":"Coordinating Pricing and Inventory Replenishment with Nonparametric Demand Learning","authors":"Boxiao Chen, X. Chao, Hyun-Soo Ahn","doi":"10.2139/ssrn.2694633","DOIUrl":"https://doi.org/10.2139/ssrn.2694633","url":null,"abstract":"We consider a firm (e.g., retailer) selling a single nonperishable product over a finite-period planning horizon. Demand in each period is stochastic and price-dependent, and unsatisfied demands are backlogged. At the beginning of each period, the firm determines its selling price and inventory replenishment quantity, but it knows neither the form of demand dependency on selling price nor the distribution of demand uncertainty a priori, hence it has to make pricing and ordering decisions based on historical demand data. We propose a nonparametric data-driven policy that learns about the demand on the fly and, concurrently, applies learned information to determine replenishment and pricing decisions. The policy integrates learning and action in a sense that the firm actively experiments on pricing and inventory levels to collect demand information with the least possible profit loss. Besides convergence of optimal policies, we show that the regret, defined as the average profit loss compared with that of the optimal solution when the firm has complete information about the underlying demand, vanishes at the fastest possible rate as the planning horizon increases.","PeriodicalId":11744,"journal":{"name":"ERN: Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2015-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74649793","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 present new identification results for a class of nonseparable nonparametric simultaneous equations models introduced by Matzkin (2008). These models combine traditional exclusion restrictions with a requirement that each structural error enter through a “residual index.” Our identification results are constructive and encompass a range of special cases with varying demands on the exogenous variation provided by instruments and the shape of the joint density of the structural errors. The most important of these results demonstrate identification even when instruments have limited variation. A genericity result demonstrates a formal sense in which the associated density conditions may be viewed as mild, even when instruments vary only over a small open ball.
{"title":"Identification of Nonparametric Simultaneous Equations Models with a Residual Index Structure","authors":"Steven T. Berry, Philip A. Haile","doi":"10.2139/ssrn.2898841","DOIUrl":"https://doi.org/10.2139/ssrn.2898841","url":null,"abstract":"We present new identification results for a class of nonseparable nonparametric simultaneous equations models introduced by Matzkin (2008). These models combine traditional exclusion restrictions with a requirement that each structural error enter through a “residual index.” Our identification results are constructive and encompass a range of special cases with varying demands on the exogenous variation provided by instruments and the shape of the joint density of the structural errors. The most important of these results demonstrate identification even when instruments have limited variation. A genericity result demonstrates a formal sense in which the associated density conditions may be viewed as mild, even when instruments vary only over a small open ball.","PeriodicalId":11744,"journal":{"name":"ERN: Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2015-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75371577","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 investigate a nonparametric panel model with heterogeneous regression functions. In a variety of applications, it is natural to impose a group structure on the regression curves. Specifically, we may suppose that the observed individuals can be grouped into a number of classes whose members all share the same regression function. We develop a statistical procedure to estimate the unknown group structure from the observed data. Moreover, we derive the asymptotic properties of the procedure and investigate its finite sample performance by means of a simulation study and a real-data example.
{"title":"Classification of Nonparametric Regression Functions in Heterogeneous Panels","authors":"M. Vogt, O. Linton","doi":"10.2139/ssrn.2567312","DOIUrl":"https://doi.org/10.2139/ssrn.2567312","url":null,"abstract":"We investigate a nonparametric panel model with heterogeneous regression functions. In a variety of applications, it is natural to impose a group structure on the regression curves. Specifically, we may suppose that the observed individuals can be grouped into a number of classes whose members all share the same regression function. We develop a statistical procedure to estimate the unknown group structure from the observed data. Moreover, we derive the asymptotic properties of the procedure and investigate its finite sample performance by means of a simulation study and a real-data example.","PeriodicalId":11744,"journal":{"name":"ERN: Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2015-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76568111","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}
Based on the Lee-Carter (LC) model, the benchmark in population forecasting, a variety of extensions and modifications are proposed in this paper. We investigate one of the extensions, the Hyndman-Ullah (HU) method and apply it to Asian demographic data sets: China, Japan and Taiwan. It combines ideas of functional principal component analysis (fPCA), nonparametric smoothing and time series analysis. Based on this stochastic approach, the demographic characteristics and trends in different Asian regions are calculated and compared. We illustrate that China and Japan exhibited a similar demographic trend in the past decade. We also compared the HU method with the LC model. The HU method can explain more variation of the demographic dynamics when we have data of high quality, however, it also encounters problems and performs similarly as the LC model when we deal with limited and scarce data sets, such as Chinese data sets due to the substandard quality of the data and the population policy.
{"title":"Stochastic Population Analysis: A Functional Data Approach","authors":"Lei Fang, W. Härdle","doi":"10.2139/ssrn.2630301","DOIUrl":"https://doi.org/10.2139/ssrn.2630301","url":null,"abstract":"Based on the Lee-Carter (LC) model, the benchmark in population forecasting, a variety of extensions and modifications are proposed in this paper. We investigate one of the extensions, the Hyndman-Ullah (HU) method and apply it to Asian demographic data sets: China, Japan and Taiwan. It combines ideas of functional principal component analysis (fPCA), nonparametric smoothing and time series analysis. Based on this stochastic approach, the demographic characteristics and trends in different Asian regions are calculated and compared. We illustrate that China and Japan exhibited a similar demographic trend in the past decade. We also compared the HU method with the LC model. The HU method can explain more variation of the demographic dynamics when we have data of high quality, however, it also encounters problems and performs similarly as the LC model when we deal with limited and scarce data sets, such as Chinese data sets due to the substandard quality of the data and the population policy.","PeriodicalId":11744,"journal":{"name":"ERN: Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2015-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80024978","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 impact of scheduled releases of macroeconomic variables on the dynamics of financial markets has always attracted a great deal of academic attention in efforts to quantify market responses in terms of volatility and jumps. We investigate whether the occurrence of market reaction due to macroeconomic announcements has an impact on the probability of a reaction caused by the next release of the same macroeconomic value. We measure this impact by means of both post-event volatility changes and a proposed methodology for jump matching. Our findings show that previous market impact significantly changes the probability of an impact detected for the current release.
{"title":"Persistent Impact of Macroeconomic Announcements in Financial Market Data","authors":"Nicolas Boitout, R. Lupu","doi":"10.2139/ssrn.2556336","DOIUrl":"https://doi.org/10.2139/ssrn.2556336","url":null,"abstract":"The impact of scheduled releases of macroeconomic variables on the dynamics of financial markets has always attracted a great deal of academic attention in efforts to quantify market responses in terms of volatility and jumps. We investigate whether the occurrence of market reaction due to macroeconomic announcements has an impact on the probability of a reaction caused by the next release of the same macroeconomic value. We measure this impact by means of both post-event volatility changes and a proposed methodology for jump matching. Our findings show that previous market impact significantly changes the probability of an impact detected for the current release.","PeriodicalId":11744,"journal":{"name":"ERN: Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2015-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74280494","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 study a multi-period network revenue management (RM) problem where a seller sells multiple products made from multiple resources with finite capacity in an environment where the demand function is unknown a priori. The objective of the seller is to jointly learn the demand and price the products to minimize his expected revenue loss. Both the parametric and the nonparametric cases are considered in this paper. It is widely known in the literature that the revenue loss of any pricing policy under either case is at least k^{1/2} However, there is a considerable gap between this lower bound and the performance bound of the best known heuristic in the literature. To close the gap, we develop several self-adjusting heuristics with strong performance bound. For the general parametric case, our proposed Parametric Self-adjusting Control (PSC) attains a O(k^{1/2}) revenue loss, matching the theoretical lower bound. If the parametric demand function family further satisfies a well-separated condition, by taking advantage of passive learning, our proposed Accelerated Parametric Self-adjusting Control achieves a much sharper revenue loss of O(log^2 k). For the nonparametric case, our proposed Nonparametric Self-adjusting Control (NSC) obtains a revenue loss of O(k^{1/2+系} log k) for any arbitrarily small 系 > 0 if the demand function is sufficiently smooth. Our results suggest that in terms of performance, the nonparametric approach can be as robust as the parametric approach, at least asymptotically. All the proposed heuristics are computationally very efficient and can be used as a baseline for developing more sophisticated heuristics for large-scale problems.
{"title":"Adaptive Parametric and Nonparametric Multi-Product Pricing via Self-Adjusting Controls","authors":"Qi (George) Chen, Stefanus Jasin, Izak Duenyas","doi":"10.2139/SSRN.2533468","DOIUrl":"https://doi.org/10.2139/SSRN.2533468","url":null,"abstract":"We study a multi-period network revenue management (RM) problem where a seller sells multiple products made from multiple resources with finite capacity in an environment where the demand function is unknown a priori. The objective of the seller is to jointly learn the demand and price the products to minimize his expected revenue loss. Both the parametric and the nonparametric cases are considered in this paper. It is widely known in the literature that the revenue loss of any pricing policy under either case is at least k^{1/2} However, there is a considerable gap between this lower bound and the performance bound of the best known heuristic in the literature. To close the gap, we develop several self-adjusting heuristics with strong performance bound. For the general parametric case, our proposed Parametric Self-adjusting Control (PSC) attains a O(k^{1/2}) revenue loss, matching the theoretical lower bound. If the parametric demand function family further satisfies a well-separated condition, by taking advantage of passive learning, our proposed Accelerated Parametric Self-adjusting Control achieves a much sharper revenue loss of O(log^2 k). For the nonparametric case, our proposed Nonparametric Self-adjusting Control (NSC) obtains a revenue loss of O(k^{1/2+系} log k) for any arbitrarily small 系 > 0 if the demand function is sufficiently smooth. Our results suggest that in terms of performance, the nonparametric approach can be as robust as the parametric approach, at least asymptotically. All the proposed heuristics are computationally very efficient and can be used as a baseline for developing more sophisticated heuristics for large-scale problems.","PeriodicalId":11744,"journal":{"name":"ERN: Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89742085","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}
Methods for estimating equivalence scales usually rely on rather strong identifying assumptions. This paper considers a partially identified estimator for equivalence scales derived from the potential outcomes framework and using nonparametric methods for estimation, which requires only mild assumptions. Instead of point estimates, the method yields only lower and upper bounds of equivalence scales. Results of an analysis using German expenditure data show that the range implied by these bounds is rather wide, but can be reduced using additional covariates.
{"title":"A Nonparametric Partially Identified Estimator for Equivalence Scales","authors":"C. Dudel","doi":"10.2139/ssrn.2566241","DOIUrl":"https://doi.org/10.2139/ssrn.2566241","url":null,"abstract":"Methods for estimating equivalence scales usually rely on rather strong identifying assumptions. This paper considers a partially identified estimator for equivalence scales derived from the potential outcomes framework and using nonparametric methods for estimation, which requires only mild assumptions. Instead of point estimates, the method yields only lower and upper bounds of equivalence scales. Results of an analysis using German expenditure data show that the range implied by these bounds is rather wide, but can be reduced using additional covariates.","PeriodicalId":11744,"journal":{"name":"ERN: Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79123835","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 study the validity of the pairs bootstrap for lasso estimators in linear regression models with random covariates and heteroscedastic error terms. We show that the naive pairs bootstrap does not provide a valid method for approximating the distribution of the lasso estimator. To overcome this deficiency, we introduce a modified pairs bootstrap procedure and prove its consistency. Finally, we consider the adaptive lasso and show that the modified pairs bootstrap consistently estimates the distribution of the adaptive lasso estimator.
{"title":"On the Validity of the Pairs Bootstrap for Lasso Estimators","authors":"Lorenzo Camponovo","doi":"10.2139/ssrn.2443728","DOIUrl":"https://doi.org/10.2139/ssrn.2443728","url":null,"abstract":"We study the validity of the pairs bootstrap for lasso estimators in linear regression models with random covariates and heteroscedastic error terms. We show that the naive pairs bootstrap does not provide a valid method for approximating the distribution of the lasso estimator. To overcome this deficiency, we introduce a modified pairs bootstrap procedure and prove its consistency. Finally, we consider the adaptive lasso and show that the modified pairs bootstrap consistently estimates the distribution of the adaptive lasso estimator.","PeriodicalId":11744,"journal":{"name":"ERN: Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75453029","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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