We propose a new nonparametric test for detecting the presence of jumps in asset prices using discretely observed data. Compared with the test in Ait-Sahalia and Jacod (2009), our new test enjoys the same asymptotic properties but has smaller variance. These results are justified both theoretically and numerically. We also propose a new procedure to locate the jumps. The jump identification problem reduces to a multiple comparison problem. We employ the false discovery rate approach to control the probability of type I error. Numerical studies further demonstrate the power of our new method.
{"title":"Testing and Detecting Jumps Based on a Discretely Observed Process","authors":"Yingying Fan, Jianqing Fan","doi":"10.2139/ssrn.1184442","DOIUrl":"https://doi.org/10.2139/ssrn.1184442","url":null,"abstract":"We propose a new nonparametric test for detecting the presence of jumps in asset prices using discretely observed data. Compared with the test in Ait-Sahalia and Jacod (2009), our new test enjoys the same asymptotic properties but has smaller variance. These results are justified both theoretically and numerically. We also propose a new procedure to locate the jumps. The jump identification problem reduces to a multiple comparison problem. We employ the false discovery rate approach to control the probability of type I error. Numerical studies further demonstrate the power of our new method.","PeriodicalId":11744,"journal":{"name":"ERN: Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2008-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87617399","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 asymptotic validity of tests is usually established by making appropriate primitive assumptions, which imply the weak convergence of a specific function of the data, and an appeal to the continuous mapping theorem. This paper, instead, takes the weak convergence of some function of the data to a limiting random element as the starting point and studies efficiency in the class of tests that remain asymptotically valid for all models that induce the same weak limit. It is found that efficient tests in this class are simply given by efficient tests in the limiting problem—that is, with the limiting random element assumed observed—evaluated at sample analogues. Efficient tests in the limiting problem are usually straightforward to derive, even in nonstandard testing problems. What is more, their evaluation at sample analogues typically yields tests that coincide with suitably robustified versions of optimal tests in canonical parametric versions of the model. This paper thus establishes an alternative and broader sense of asymptotic efficiency for many previously derived tests in econometrics, such as tests for unit roots, parameter stability tests, and tests about regression coefficients under weak instruments.
{"title":"Efficient Tests under a Weak Convergence Assumption","authors":"Ulrich K. Müller","doi":"10.2139/ssrn.1105731","DOIUrl":"https://doi.org/10.2139/ssrn.1105731","url":null,"abstract":"The asymptotic validity of tests is usually established by making appropriate primitive assumptions, which imply the weak convergence of a specific function of the data, and an appeal to the continuous mapping theorem. This paper, instead, takes the weak convergence of some function of the data to a limiting random element as the starting point and studies efficiency in the class of tests that remain asymptotically valid for all models that induce the same weak limit. It is found that efficient tests in this class are simply given by efficient tests in the limiting problem—that is, with the limiting random element assumed observed—evaluated at sample analogues. Efficient tests in the limiting problem are usually straightforward to derive, even in nonstandard testing problems. What is more, their evaluation at sample analogues typically yields tests that coincide with suitably robustified versions of optimal tests in canonical parametric versions of the model. This paper thus establishes an alternative and broader sense of asymptotic efficiency for many previously derived tests in econometrics, such as tests for unit roots, parameter stability tests, and tests about regression coefficients under weak instruments.","PeriodicalId":11744,"journal":{"name":"ERN: Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2008-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90530403","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}
In nonparametric multivariate regression analysis, one usually seeks methods to reduce the dimensionality of the regression function to bypass the difficulty caused by the curse of dimensionality. We study nonparametric estimation of multivariate conditional distribution and quantile regression via local univariate quadratic estimation of partial derivatives of bivariate copulas. Without restricting the form of underlying regression function or using dimensional reduction, we show that a d-dimensional multivariate conditional distribution and quantile regression could be estimated by d(d 1)/2 times of univariate smoothers. The asymptotic bias and variance as well as smoothing parameter selection method are derived. Simulations show that the method works quite well. The techniques are illustrated by application to exchange rate data.
{"title":"Nonparametric Multivariate Conditional Distribution and Quantile Regression","authors":"Keming Yu, Xiaochen (Michael) Sun, G. Mitra","doi":"10.2139/ssrn.1264946","DOIUrl":"https://doi.org/10.2139/ssrn.1264946","url":null,"abstract":"In nonparametric multivariate regression analysis, one usually seeks methods to reduce the dimensionality of the regression function to bypass the difficulty caused by the curse of dimensionality. We study nonparametric estimation of multivariate conditional distribution and quantile regression via local univariate quadratic estimation of partial derivatives of bivariate copulas. Without restricting the form of underlying regression function or using dimensional reduction, we show that a d-dimensional multivariate conditional distribution and quantile regression could be estimated by d(d 1)/2 times of univariate smoothers. The asymptotic bias and variance as well as smoothing parameter selection method are derived. Simulations show that the method works quite well. The techniques are illustrated by application to exchange rate data.","PeriodicalId":11744,"journal":{"name":"ERN: Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2008-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86766447","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 considers allocation rules. First, we demonstrate that costs allocated by the Aumann-Shapley and the Friedman-Moulin cost allocation rules are easy to determine in practice using convex envelopment of registered cost data and parametric programming. Second, from the linear programming problems involved it becomes clear that the allocation rules, technically speaking, allocate the non-zero value of the dual variable for a convexity constraint on to the output vector. Hence, the allocation rules can also be used to allocate inefficiencies in non-parametric efficiency measurement models such as Data Envelopment Analysis (DEA). The convexity constraint of the BCC model introduces a non-zero slack in the objective function of the multiplier problem and we show that the cost allocation rules discussed in this paper can be used as candidates to allocate this slack value on to the input (or output) variables and hence enable a full allocation of the inefficiency on to the input (or output) variables as in the CCR model.
{"title":"Cost Allocation and Convex Data Envelopment","authors":"J. Hougaard, J. Tind","doi":"10.2139/ssrn.1135262","DOIUrl":"https://doi.org/10.2139/ssrn.1135262","url":null,"abstract":"This paper considers allocation rules. First, we demonstrate that costs allocated by the Aumann-Shapley and the Friedman-Moulin cost allocation rules are easy to determine in practice using convex envelopment of registered cost data and parametric programming. Second, from the linear programming problems involved it becomes clear that the allocation rules, technically speaking, allocate the non-zero value of the dual variable for a convexity constraint on to the output vector. Hence, the allocation rules can also be used to allocate inefficiencies in non-parametric efficiency measurement models such as Data Envelopment Analysis (DEA). The convexity constraint of the BCC model introduces a non-zero slack in the objective function of the multiplier problem and we show that the cost allocation rules discussed in this paper can be used as candidates to allocate this slack value on to the input (or output) variables and hence enable a full allocation of the inefficiency on to the input (or output) variables as in the CCR model.","PeriodicalId":11744,"journal":{"name":"ERN: Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2008-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77861897","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 three residual-based tests for conditional asymmetry. The distribution is assumed to fall into the class of skewed distributions of Fernandez and Steel (1998). In this class, asymmetry is measured by the ratio between the probabilities of being larger and smaller than the mode. Estimation is performed under the null hypothesis of constant asymmetry of the innovations and, in a second step, tests for conditional asymmetry are performed on generalized residuals through parametric and nonparametric methods. We derive the asymptotic distribution of the tests that incorporates the uncertainty of the estimated parameters in the first step. A Monte Carlo study shows that neglecting this uncertainty severely biases the tests and an empirical application on a basket of daily returns reveals that financial data often present dynamics in the conditional skewness.
{"title":"Testing Conditional Asymmetry: A Residual-Based Approach","authors":"S. Laurent, P. Lambert, David Veredas","doi":"10.2139/ssrn.1029645","DOIUrl":"https://doi.org/10.2139/ssrn.1029645","url":null,"abstract":"We propose three residual-based tests for conditional asymmetry. The distribution is assumed to fall into the class of skewed distributions of Fernandez and Steel (1998). In this class, asymmetry is measured by the ratio between the probabilities of being larger and smaller than the mode. Estimation is performed under the null hypothesis of constant asymmetry of the innovations and, in a second step, tests for conditional asymmetry are performed on generalized residuals through parametric and nonparametric methods. We derive the asymptotic distribution of the tests that incorporates the uncertainty of the estimated parameters in the first step. A Monte Carlo study shows that neglecting this uncertainty severely biases the tests and an empirical application on a basket of daily returns reveals that financial data often present dynamics in the conditional skewness.","PeriodicalId":11744,"journal":{"name":"ERN: Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2007-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73080770","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 extend the nonparametric 'revealed preference' methodology for analyzing collective consumption behavior (with consumption externalities and public consumption), to ren- der it useful for empirical applications that deal with welfare-related questions. First, we provide a nonparametric necessary and su¢ cient condition for collectively rational group behavior that incorporates the possibility of assignable quantity information. This charac- terizes collective rationality in terms of feasible personalized prices, personalized quantities and income shares (representing the underlying sharing rule). Subsequently, we present nonparametric testing tools for data consistency with special cases of the collective model, which impose specific structure on the preferences of the group members (in terms of con- sumption externalities and public consumption); and we show that these testing tools in turn allow for nonparametrically recovering (bounds on) feasible personalized prices, per- sonalized quantities and income shares that underlie observed (collectively rational) group behavior. In addition, we present formally similar testing and recovery tools for the general collective consumption model, which imposes minimal a priori structure. Interestingly, the proposed testing and recovery methodology can be implemented through integer program- ming (IP and MILP), which is attractive for practical applications. Finally, while we argue that assignable quantity information generally entails more powerful recovery results, we also demonstrate that precise nonparametric recovery (i.e. tight bounds) can be obtained even if no assignable quantity information is available.
{"title":"The Revealed Preference Approach to Collective Consumption Behavior: Testing, Recovery, and Welfare Analysis","authors":"L. Cherchye, B. Rock, Frederic Vermeulen","doi":"10.2139/ssrn.1016653","DOIUrl":"https://doi.org/10.2139/ssrn.1016653","url":null,"abstract":"We extend the nonparametric 'revealed preference' methodology for analyzing collective consumption behavior (with consumption externalities and public consumption), to ren- der it useful for empirical applications that deal with welfare-related questions. First, we provide a nonparametric necessary and su¢ cient condition for collectively rational group behavior that incorporates the possibility of assignable quantity information. This charac- terizes collective rationality in terms of feasible personalized prices, personalized quantities and income shares (representing the underlying sharing rule). Subsequently, we present nonparametric testing tools for data consistency with special cases of the collective model, which impose specific structure on the preferences of the group members (in terms of con- sumption externalities and public consumption); and we show that these testing tools in turn allow for nonparametrically recovering (bounds on) feasible personalized prices, per- sonalized quantities and income shares that underlie observed (collectively rational) group behavior. In addition, we present formally similar testing and recovery tools for the general collective consumption model, which imposes minimal a priori structure. Interestingly, the proposed testing and recovery methodology can be implemented through integer program- ming (IP and MILP), which is attractive for practical applications. Finally, while we argue that assignable quantity information generally entails more powerful recovery results, we also demonstrate that precise nonparametric recovery (i.e. tight bounds) can be obtained even if no assignable quantity information is available.","PeriodicalId":11744,"journal":{"name":"ERN: Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2007-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91510672","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 : 2006-12-01DOI: 10.21648/ARTHAVIJ/2006/V48/I4/115444
Shahid Ahmed
The present study examines the Day-of-the-Week effect anomaly in the Indian equity market during the period of July 1997 to March 2006 using daily data of NSE Nifty and BSE Sensex. The Day-of-the-Week effect implies that the stocks return is not independent of the Day-of-the-Week in which they are generated. If such an anomaly exists, market participants can take advantage of the same and adjust their buying and selling strategies accordingly to increase their returns. Both parametric and non-parametric approaches are applied to detect the Day-of- the-Week effect in both mean and volatility of returns. The results indicate that BSE starts upwards, declines in middle of the week and end downwards while NSE starts downward, upward in middle of the week and end downwards. The study reveals U-shaped intra-day pattern in price volatility in both the markets. The results also indicate differential pattern of movements in mean and variance of trading and non-trading returns across the weekdays. It is also observed that there is an improvement in the Day-of-the-Week anomaly during the period of January 2002 to March 2006.
{"title":"Day-of-the-Week Effect on Trading and Non-Trading Stock Market Returns in India: A Parametric and Non-Parametric Testing","authors":"Shahid Ahmed","doi":"10.21648/ARTHAVIJ/2006/V48/I4/115444","DOIUrl":"https://doi.org/10.21648/ARTHAVIJ/2006/V48/I4/115444","url":null,"abstract":"The present study examines the Day-of-the-Week effect anomaly in the Indian equity market during the period of July 1997 to March 2006 using daily data of NSE Nifty and BSE Sensex. The Day-of-the-Week effect implies that the stocks return is not independent of the Day-of-the-Week in which they are generated. If such an anomaly exists, market participants can take advantage of the same and adjust their buying and selling strategies accordingly to increase their returns. Both parametric and non-parametric approaches are applied to detect the Day-of- the-Week effect in both mean and volatility of returns. The results indicate that BSE starts upwards, declines in middle of the week and end downwards while NSE starts downward, upward in middle of the week and end downwards. The study reveals U-shaped intra-day pattern in price volatility in both the markets. The results also indicate differential pattern of movements in mean and variance of trading and non-trading returns across the weekdays. It is also observed that there is an improvement in the Day-of-the-Week anomaly during the period of January 2002 to March 2006.","PeriodicalId":11744,"journal":{"name":"ERN: Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87463641","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 shows that the Fed reacts to change in spreads between corporate bond yields and government bond yields over and beyond their information content on future inflation and future activity. This result, obtained in a GMM framework, is confirmed by simulation methods. Moreover, when credit spreads are on the rise, the probability that the Fed will make a large error in forecasting output and inflation increases. In this sense, the Fed's preemptive easings - despite their short-term costs, as monetary policy may become too accommodative - are a way to take into account the downside risks to the baseline forecasts and insure the economy against increasing uncertainty and the likelihood of a very costly extreme event.
{"title":"The Fed and the Question of Financial Stability: An Empirical Investigation","authors":"Thierry Grunspan","doi":"10.2139/ssrn.1703444","DOIUrl":"https://doi.org/10.2139/ssrn.1703444","url":null,"abstract":"This paper shows that the Fed reacts to change in spreads between corporate bond yields and government bond yields over and beyond their information content on future inflation and future activity. This result, obtained in a GMM framework, is confirmed by simulation methods. Moreover, when credit spreads are on the rise, the probability that the Fed will make a large error in forecasting output and inflation increases. In this sense, the Fed's preemptive easings - despite their short-term costs, as monetary policy may become too accommodative - are a way to take into account the downside risks to the baseline forecasts and insure the economy against increasing uncertainty and the likelihood of a very costly extreme event.","PeriodicalId":11744,"journal":{"name":"ERN: Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2005-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84915981","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 presents a new method of testing for IID. The test is suggested as an alternative to the nonparametric BDS test, which requires a proximity parameter (and an embedding dimension m to be chosen arbitrarily. A limited statistical theory exists to determine the right choice of these parameters. The presented method aims to eliminate such indecisiveness by integration over the correlation integral. The Monte Carlo simulation is used to tabulate critical values of the new statistic. In a comparative analysis the presented test is able to find nonlinear dependencies in cases where the BDS test does not find them. The test becomes more critical to the question whether the data is true white noise.
{"title":"A Test for Iid Residuals Based on Integrating Over the Correlation Integral","authors":"E. Kočenda","doi":"10.2139/ssrn.1543758","DOIUrl":"https://doi.org/10.2139/ssrn.1543758","url":null,"abstract":"This paper presents a new method of testing for IID. The test is suggested as an alternative to the nonparametric BDS test, which requires a proximity parameter (and an embedding dimension m to be chosen arbitrarily. A limited statistical theory exists to determine the right choice of these parameters. The presented method aims to eliminate such indecisiveness by integration over the correlation integral. The Monte Carlo simulation is used to tabulate critical values of the new statistic. In a comparative analysis the presented test is able to find nonlinear dependencies in cases where the BDS test does not find them. The test becomes more critical to the question whether the data is true white noise.","PeriodicalId":11744,"journal":{"name":"ERN: Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1996-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86841226","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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