We describe the fundamental issues that long-horizon event studies face in choosing the proper research methodology, and summarize findings from existing simulation studies about the performance of commonly used methods. We document in detail how to implement a simulation study and report findings from our own study that focuses on large-size samples. The findings have important implications for future research. In our simulation study, we examine the performance of more than twenty different testing procedures, which can be broadly classified into two categories: The buy-and-hold benchmark approach and the calendar-time portfolio approach. The first approach uses a benchmark to measure the abnormal buy-and-hold return for every event firm, and tests the null hypothesis that the average abnormal return is zero. We investigate the performance of five ways of choosing the benchmark and four test statistics including the standard t-test, the Johnson’s skewness-adjusted t-test, the bootstrapped Johnson’s skewness-adjusted t-test, and the Fisher’s sign test. The second approach forms a portfolio in each calendar month consisting of firms that have had an event within a certain time period prior to the month, and tests the null hypothesis that the intercept is zero in the regression of monthly calendar-time portfolio returns against the factors in an asset-pricing model. We implement this approach with both the Fama-French three-factor model and the four-factor model with an additional momentum factor, and with both the ordinary least-squares and weighted least-squares estimation methods. We find that the combination of the sign test and the benchmark with a single most correlated firm provides the best overall performance for various sample sizes and long horizons. Furthermore, the Fama-French three-factor model is a better asset pricing model for monthly returns of calendar-time portfolios than the four-factor model, as the latter leads to serious overrejection of the null hypothesis.
{"title":"Evaluating Long-Horizon Event Study Methodology","authors":"James S. Ang, Shaojun Zhang","doi":"10.2139/ssrn.1865625","DOIUrl":"https://doi.org/10.2139/ssrn.1865625","url":null,"abstract":"We describe the fundamental issues that long-horizon event studies face in choosing the proper research methodology, and summarize findings from existing simulation studies about the performance of commonly used methods. We document in detail how to implement a simulation study and report findings from our own study that focuses on large-size samples. The findings have important implications for future research. In our simulation study, we examine the performance of more than twenty different testing procedures, which can be broadly classified into two categories: The buy-and-hold benchmark approach and the calendar-time portfolio approach. The first approach uses a benchmark to measure the abnormal buy-and-hold return for every event firm, and tests the null hypothesis that the average abnormal return is zero. We investigate the performance of five ways of choosing the benchmark and four test statistics including the standard t-test, the Johnson’s skewness-adjusted t-test, the bootstrapped Johnson’s skewness-adjusted t-test, and the Fisher’s sign test. The second approach forms a portfolio in each calendar month consisting of firms that have had an event within a certain time period prior to the month, and tests the null hypothesis that the intercept is zero in the regression of monthly calendar-time portfolio returns against the factors in an asset-pricing model. We implement this approach with both the Fama-French three-factor model and the four-factor model with an additional momentum factor, and with both the ordinary least-squares and weighted least-squares estimation methods. We find that the combination of the sign test and the benchmark with a single most correlated firm provides the best overall performance for various sample sizes and long horizons. Furthermore, the Fama-French three-factor model is a better asset pricing model for monthly returns of calendar-time portfolios than the four-factor model, as the latter leads to serious overrejection of the null hypothesis.","PeriodicalId":11744,"journal":{"name":"ERN: Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2011-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81880085","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 this selective review, we first provide some empirical examples that motivate the usefulness of semi-nonparametric techniques in modelling economic and financial time series. We describe popular classes of semi-nonparametric dynamic models and some temporal dependence properties. We then present penalized sieve extremum (PSE) estimation as a general method for semi-nonparametric models with cross-sectional, panel, time series, or spatial data. The method is especially powerful in estimating difficult ill-posed inverse problems such as semi-nonparametric mixtures or conditional moment restrictions. We review recent advances on inference and large sample properties of the PSE estimators, which include (1) consistency and convergence rates of the PSE estimator of the nonparametric part; (2) limiting distributions of plug-in PSE estimators of functionals that are either smooth (i.e., root-n estimable) or non-smooth (i.e., slower than root-n estimable); (3) simple criterion-based inference for plug-in PSE estimation of smooth or non-smooth functionals; and (4) root-n asymptotic normality of semiparametric two-step estimators and their consistent variance estimators. Examples from dynamic asset pricing, nonlinear spatial VAR, semiparametric GARCH, and copula-based multivariate financial models are used to illustrate the general results.
{"title":"Penalized Sieve Estimation and Inference of Semi-Nonparametric Dynamic Models: A Selective Review","authors":"Xiaohong Chen","doi":"10.2139/ssrn.1850615","DOIUrl":"https://doi.org/10.2139/ssrn.1850615","url":null,"abstract":"In this selective review, we first provide some empirical examples that motivate the usefulness of semi-nonparametric techniques in modelling economic and financial time series. We describe popular classes of semi-nonparametric dynamic models and some temporal dependence properties. We then present penalized sieve extremum (PSE) estimation as a general method for semi-nonparametric models with cross-sectional, panel, time series, or spatial data. The method is especially powerful in estimating difficult ill-posed inverse problems such as semi-nonparametric mixtures or conditional moment restrictions. We review recent advances on inference and large sample properties of the PSE estimators, which include (1) consistency and convergence rates of the PSE estimator of the nonparametric part; (2) limiting distributions of plug-in PSE estimators of functionals that are either smooth (i.e., root-n estimable) or non-smooth (i.e., slower than root-n estimable); (3) simple criterion-based inference for plug-in PSE estimation of smooth or non-smooth functionals; and (4) root-n asymptotic normality of semiparametric two-step estimators and their consistent variance estimators. Examples from dynamic asset pricing, nonlinear spatial VAR, semiparametric GARCH, and copula-based multivariate financial models are used to illustrate the general results.","PeriodicalId":11744,"journal":{"name":"ERN: Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2011-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84455278","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}
Asset prices depend on two elements: the dynamics of the state variables and the pricing kernel. Traditional term structure models differ in factor dynamics. However, most of them imply a log-linear pricing kernel. We investigate empirically the role of factor dynamics and pricing kernel in pricing interest rate derivatives using a nonparametric approach. We find that interest rate cap prices are very sensitive to the specification of factor dynamics, especially when they are close to expiration. In addition, nonlinear log-pricing kernels improve the pricing of long-maturity caps, although significant pricing errors remain. Recent research document models that fit LIBOR and swap rates but do not price derivatives well, leading to the so called "unspanned stochastic volatility puzzle". Additional volatility factors seem to be needed to explain cap prices. However, the relative mispricing between interest rate caps and underlying LIBOR and swap rates could also potentially be due to mis-specifications of the parametric models used. Our paper provides evidence for unspanned stochastic volatility from a nonparametric perspective.
{"title":"Nonparametric Interest Rate Cap Pricing: Implications for the 'Unspanned Stochastic Volatility'","authors":"Tao Wu","doi":"10.2139/ssrn.1746450","DOIUrl":"https://doi.org/10.2139/ssrn.1746450","url":null,"abstract":"Asset prices depend on two elements: the dynamics of the state variables and the pricing kernel. Traditional term structure models differ in factor dynamics. However, most of them imply a log-linear pricing kernel. We investigate empirically the role of factor dynamics and pricing kernel in pricing interest rate derivatives using a nonparametric approach. We find that interest rate cap prices are very sensitive to the specification of factor dynamics, especially when they are close to expiration. In addition, nonlinear log-pricing kernels improve the pricing of long-maturity caps, although significant pricing errors remain. Recent research document models that fit LIBOR and swap rates but do not price derivatives well, leading to the so called \"unspanned stochastic volatility puzzle\". Additional volatility factors seem to be needed to explain cap prices. However, the relative mispricing between interest rate caps and underlying LIBOR and swap rates could also potentially be due to mis-specifications of the parametric models used. Our paper provides evidence for unspanned stochastic volatility from a nonparametric perspective.","PeriodicalId":11744,"journal":{"name":"ERN: Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2011-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89202120","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}
When the endogenous variable enters the structural equation non-parametrically the linear Instrumental Variable (IV) estimator is no longer consistent. Non-parametric IV (NPIV) can be used but it requires one to impose restrictions during estimation to make the problem well-posed. The non-parametric control function estimator of Newey, Powell, and Vella (1999) (NPV-CF) is an alternative approach that uses the residuals from the conditional mean decomposition of the endogenous variable as controls in the structural equation. While computationally simple identification relies upon independence between the instruments and the expected value of the structural error conditional on the controls, which is hard to motivate in many economic settings including estimation of returns to education, production functions, and demand or supply elasticities. We develop an estimator for non-linear and non-parametric regressions that maintains the simplicity of the NPV-CF estimator but allows the conditional expectation of the structural error to depend on both the control variables and the instruments. Our approach combines the conditional moment restrictions (CMRs) from NPIV with the controls from NPV-CF setting. We show that the CMRs place shape restrictions on the conditional expectation of the error given instruments and controls that are sufficient for identification. When sieves are used to approximate both the structural function and the control function our estimator reduces to a series of Least Squares regressions. Our monte carlos are based on the economic settings suggested above and illustrate that our new estimator performs well when the NPV-CF estimator is biased. Our empirical example replicates NPV-CF and we reject the maintained assumption of the independence of the instruments and the expected value of the structural error conditional on the controls in their setting.
{"title":"A New Control Function Approach for Non-Parametric Regressions with Endogenous Variables","authors":"K. Kim, Amil Petrin","doi":"10.3386/W16679","DOIUrl":"https://doi.org/10.3386/W16679","url":null,"abstract":"When the endogenous variable enters the structural equation non-parametrically the linear Instrumental Variable (IV) estimator is no longer consistent. Non-parametric IV (NPIV) can be used but it requires one to impose restrictions during estimation to make the problem well-posed. The non-parametric control function estimator of Newey, Powell, and Vella (1999) (NPV-CF) is an alternative approach that uses the residuals from the conditional mean decomposition of the endogenous variable as controls in the structural equation. While computationally simple identification relies upon independence between the instruments and the expected value of the structural error conditional on the controls, which is hard to motivate in many economic settings including estimation of returns to education, production functions, and demand or supply elasticities. We develop an estimator for non-linear and non-parametric regressions that maintains the simplicity of the NPV-CF estimator but allows the conditional expectation of the structural error to depend on both the control variables and the instruments. Our approach combines the conditional moment restrictions (CMRs) from NPIV with the controls from NPV-CF setting. We show that the CMRs place shape restrictions on the conditional expectation of the error given instruments and controls that are sufficient for identification. When sieves are used to approximate both the structural function and the control function our estimator reduces to a series of Least Squares regressions. Our monte carlos are based on the economic settings suggested above and illustrate that our new estimator performs well when the NPV-CF estimator is biased. Our empirical example replicates NPV-CF and we reject the maintained assumption of the independence of the instruments and the expected value of the structural error conditional on the controls in their setting.","PeriodicalId":11744,"journal":{"name":"ERN: Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2011-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86822274","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 : 2011-01-01DOI: 10.7208/9780226988061-005
R. Goodhue, C. Russo
This paper examines interactions between market power and agricultural policy in the U.S. wheat flour milling industry using a non-parametric approach. The analysis focuses on marketing loan and pre-1986 deficiency payment programs; farmers' payments from these programs are dependent on whether or not the market price exceeds a "policy" price. It assesses if the payments trigger a change in the underlying economic behavior of the milling industry, and any resulting change in the flour-wheat price margin. The analysis compares the outcomes of using constrained and unconstrained sliced inverse regressions in order to identify the significant factors affecting millers' pricing behavior. In both cases, the link functions are then estimated using a non-parametric regression of prices on these factors. Constraining the factors in the sliced inverse regression in order to generate coefficients that are easily interpreted using economic theory does not affect the results. Based on the SIR factors, millers were able to extract an additional $0.24/cwt. of flour by increasing their marketing margins in years farmers received program payments. Based on the CIR factors, the increase in the marketing margin was $0.23/cwt. In both cases the increase was approximately 10 percent of the estimated marketing margin in years farmers received program payments.
{"title":"Modeling Processor Market Power and the Incidence of Agricultural Policy: A Non-Parametric Approach","authors":"R. Goodhue, C. Russo","doi":"10.7208/9780226988061-005","DOIUrl":"https://doi.org/10.7208/9780226988061-005","url":null,"abstract":"This paper examines interactions between market power and agricultural policy in the U.S. wheat flour milling industry using a non-parametric approach. The analysis focuses on marketing loan and pre-1986 deficiency payment programs; farmers' payments from these programs are dependent on whether or not the market price exceeds a \"policy\" price. It assesses if the payments trigger a change in the underlying economic behavior of the milling industry, and any resulting change in the flour-wheat price margin. The analysis compares the outcomes of using constrained and unconstrained sliced inverse regressions in order to identify the significant factors affecting millers' pricing behavior. In both cases, the link functions are then estimated using a non-parametric regression of prices on these factors. Constraining the factors in the sliced inverse regression in order to generate coefficients that are easily interpreted using economic theory does not affect the results. Based on the SIR factors, millers were able to extract an additional $0.24/cwt. of flour by increasing their marketing margins in years farmers received program payments. Based on the CIR factors, the increase in the marketing margin was $0.23/cwt. In both cases the increase was approximately 10 percent of the estimated marketing margin in years farmers received program payments.","PeriodicalId":11744,"journal":{"name":"ERN: Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2011-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90146983","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 new test of market timing, based on the randomisation of the dynamic risk structures of hedge funds. This test enables us to assess the capacity of managers to time the market (positive market timing) or to assess the costs inherent to some negative externalities, such as the exposure to liquidity risk, sensitivity to risk aversion or the mismanagement of leverage (negative market timing). By applying this test to more than 6,700 individual hedge funds, we show that the performance attribution of various investment styles cannot be restricted to the two usual components, i.e. alpha and beta. Our results show that market timing is a major performance driver for Managed Futures, CTAs and certain Global Macro funds. Conversely, leverage needed to capture alpha and increased risk aversion sensitivity in relative value and arbitrage strategies induces a cost in terms of performance, formalised by negative market timing. We also show that within the different hedge fund styles, good market timers tend to deliver lower alpha.
{"title":"A Non-Parametric Test of Market Timing for Hedge Funds: Beyond Alpha and Beta","authors":"Guillaume Monarcha","doi":"10.2139/ssrn.1687018","DOIUrl":"https://doi.org/10.2139/ssrn.1687018","url":null,"abstract":"We propose a new test of market timing, based on the randomisation of the dynamic risk structures of hedge funds. This test enables us to assess the capacity of managers to time the market (positive market timing) or to assess the costs inherent to some negative externalities, such as the exposure to liquidity risk, sensitivity to risk aversion or the mismanagement of leverage (negative market timing). By applying this test to more than 6,700 individual hedge funds, we show that the performance attribution of various investment styles cannot be restricted to the two usual components, i.e. alpha and beta. Our results show that market timing is a major performance driver for Managed Futures, CTAs and certain Global Macro funds. Conversely, leverage needed to capture alpha and increased risk aversion sensitivity in relative value and arbitrage strategies induces a cost in terms of performance, formalised by negative market timing. We also show that within the different hedge fund styles, good market timers tend to deliver lower alpha.","PeriodicalId":11744,"journal":{"name":"ERN: Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2010-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91124407","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 nonparametric estimation of the volatility function of a diffusion process from discrete data, when the data are blurred by additional noise. This noise can be white or correlated, and serves as a model for microstructure effects in financial modeling, when the data are given on an intra-day scale. By developing pre-averaging techniques combined with wavelet thresholding, we construct adaptive estimators that achieve a nearly optimal rate within a large scale of smoothness constraints of Besov type. Since the underlying signal (the volatility) is genuinely random, we propose a new criterion to assess the quality of estimation; we retrieve the usual minimax theory when this approach is restricted to deterministic volatility.
{"title":"Nonparametric Estimation of the Volatility Under Microstructure Noise: Wavelet Adaptation","authors":"M. Hoffmann, A. Munk, J. Schmidt-Hieber","doi":"10.2139/ssrn.1661906","DOIUrl":"https://doi.org/10.2139/ssrn.1661906","url":null,"abstract":"We study nonparametric estimation of the volatility function of a diffusion process from discrete data, when the data are blurred by additional noise. This noise can be white or correlated, and serves as a model for microstructure effects in financial modeling, when the data are given on an intra-day scale. By developing pre-averaging techniques combined with wavelet thresholding, we construct adaptive estimators that achieve a nearly optimal rate within a large scale of smoothness constraints of Besov type. Since the underlying signal (the volatility) is genuinely random, we propose a new criterion to assess the quality of estimation; we retrieve the usual minimax theory when this approach is restricted to deterministic volatility.","PeriodicalId":11744,"journal":{"name":"ERN: Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2010-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88138367","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}
Product offerings in many consumer packaged goods (CPG) categories come in a variety of complex branding structures built around some discernable branding hierarchy. We develop a nonparametric statistical method in the context of a market response model to estimate the residual equity of each hierarchical level in a typical CPG branding structure, consistent with certain economic restrictions on the equity values. Our proposed model uses readily accessible aggregate sales and product data and exploits structure inherent in the set of brand and product relations to estimate its effects on market response. We propose that established brands in mature categories must be value-enhancing and that this translates into bounds on the domain of possible brand equity values. Our model, based on a set of independent Dirichlet process priors, avoids the drawbacks inherent in alternative approaches such as fixed effects, parametric random effects and finite mixtures of continuous densities. We examine the value contribution at different levels of the branding structure and derive insights therein. We demonstrate a brand valuation procedure using a dollar metric transformation of the residual equity estimates obtained. Finally, we validate our brand valuation results with those from independent, external sources. We test our model using AC Nielsen data on aggregate beer sales in US grocery stores. We find substantial heterogeneity in residual equity at different hierarchical levels in the branding structure, substantial differences between residual equity and more aggregate notions of brand equity and external validation of our residual equity estimates in terms of agreement with intuition, theory and previous financial data based brand equity valuations.
{"title":"Estimation of Residual Equity in Hierarchical Branding Structures: A Nonparametric Approach on Aggregate Beer Category Data","authors":"Sudhir Voleti, Paul Nelson, Pulak Ghosh","doi":"10.2139/ssrn.1633230","DOIUrl":"https://doi.org/10.2139/ssrn.1633230","url":null,"abstract":"Product offerings in many consumer packaged goods (CPG) categories come in a variety of complex branding structures built around some discernable branding hierarchy. We develop a nonparametric statistical method in the context of a market response model to estimate the residual equity of each hierarchical level in a typical CPG branding structure, consistent with certain economic restrictions on the equity values. Our proposed model uses readily accessible aggregate sales and product data and exploits structure inherent in the set of brand and product relations to estimate its effects on market response. We propose that established brands in mature categories must be value-enhancing and that this translates into bounds on the domain of possible brand equity values. Our model, based on a set of independent Dirichlet process priors, avoids the drawbacks inherent in alternative approaches such as fixed effects, parametric random effects and finite mixtures of continuous densities. We examine the value contribution at different levels of the branding structure and derive insights therein. We demonstrate a brand valuation procedure using a dollar metric transformation of the residual equity estimates obtained. Finally, we validate our brand valuation results with those from independent, external sources. We test our model using AC Nielsen data on aggregate beer sales in US grocery stores. We find substantial heterogeneity in residual equity at different hierarchical levels in the branding structure, substantial differences between residual equity and more aggregate notions of brand equity and external validation of our residual equity estimates in terms of agreement with intuition, theory and previous financial data based brand equity valuations.","PeriodicalId":11744,"journal":{"name":"ERN: Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2010-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78151314","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}
For manifest variables with additive noise and for a given number of latent variables with an assumed distribution, we propose to nonparametrically estimate the association between latent and manifest variables. Our estimation is a two step procedure: first it employs standard factor analysis to estimate the latent variables as theoretical quantiles of the assumed distribution; second, it employs the additive models’ backfitting procedure to estimate the monotone nonlinear associations between latent and manifest variables. The estimated fit may suggest a different latent distribution or point to nonlinear associations. We show on simulated data how, based on mean squared errors, the nonparametric estimation improves on factor analysis. We then employ the new estimator on real data to illustrate its use for exploratory data analysis.
{"title":"Generalized Monotone Additive Latent Variable Models","authors":"S. Sardy, Maria-Pia Victoria-Feser","doi":"10.2139/ssrn.1762653","DOIUrl":"https://doi.org/10.2139/ssrn.1762653","url":null,"abstract":"For manifest variables with additive noise and for a given number of latent variables with an assumed distribution, we propose to nonparametrically estimate the association between latent and manifest variables. Our estimation is a two step procedure: first it employs standard factor analysis to estimate the latent variables as theoretical quantiles of the assumed distribution; second, it employs the additive models’ backfitting procedure to estimate the monotone nonlinear associations between latent and manifest variables. The estimated fit may suggest a different latent distribution or point to nonlinear associations. We show on simulated data how, based on mean squared errors, the nonparametric estimation improves on factor analysis. We then employ the new estimator on real data to illustrate its use for exploratory data analysis.","PeriodicalId":11744,"journal":{"name":"ERN: Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2010-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73090106","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}
It has increasingly become standard practice to supplement point macroeconomic forecasts with an appraisal of the degree of uncertainty and the prevailing direction of risks. Several alternative approaches have been proposed in the literature to compute the probability distribution of macroeconomic forecasts; all of them rely on combining the predictive density of model-based forecasts with subjective judgment about the direction and intensity of prevailing risks. We propose a non-parametric, model-based simulation approach, which does not require specific assumptions to be made regarding the probability distribution of the sources of risk. The probability distribution of macroeconomic forecasts is computed as the result of model-based stochastic simulations which rely on re-sampling from the historical distribution of risk factors and are designed to deliver the desired degree of skewness. By contrast, other approaches typically make a specific, parametric assumption about the distribution of risk factors. The approach is illustrated using the Bank of Italyi?½s Quarterly Macroeconometric Model. The results suggest that the distribution of macroeconomic forecasts quickly tends to become symmetric, even if all risk factors are assumed to be asymmetrically distributed.
用对不确定程度和风险的主要方向的评估来补充点宏观经济预测，已日益成为标准做法。文献中提出了几种替代方法来计算宏观经济预测的概率分布;所有这些都依赖于将基于模型的预测密度与对当前风险的方向和强度的主观判断相结合。我们提出了一种非参数的、基于模型的模拟方法，它不需要对风险源的概率分布做出特定的假设。宏观经济预测的概率分布是基于模型的随机模拟的结果，它依赖于从风险因素的历史分布中重新抽样，并旨在提供所需的偏度。相比之下，其他方法通常对风险因素的分布做出具体的参数假设。意大利央行(Bank of italy ?3.5季度宏观计量经济模型。结果表明，即使假设所有风险因素都是非对称分布，宏观经济预测的分布也会迅速趋于对称。
{"title":"A Non-Parametric Model-Based Approach to Uncertainty and Risk Analysis of Macroeconomic Forecast","authors":"C. Miani, S. Siviero","doi":"10.2139/ssrn.1670566","DOIUrl":"https://doi.org/10.2139/ssrn.1670566","url":null,"abstract":"It has increasingly become standard practice to supplement point macroeconomic forecasts with an appraisal of the degree of uncertainty and the prevailing direction of risks. Several alternative approaches have been proposed in the literature to compute the probability distribution of macroeconomic forecasts; all of them rely on combining the predictive density of model-based forecasts with subjective judgment about the direction and intensity of prevailing risks. We propose a non-parametric, model-based simulation approach, which does not require specific assumptions to be made regarding the probability distribution of the sources of risk. The probability distribution of macroeconomic forecasts is computed as the result of model-based stochastic simulations which rely on re-sampling from the historical distribution of risk factors and are designed to deliver the desired degree of skewness. By contrast, other approaches typically make a specific, parametric assumption about the distribution of risk factors. The approach is illustrated using the Bank of Italyi?½s Quarterly Macroeconometric Model. The results suggest that the distribution of macroeconomic forecasts quickly tends to become symmetric, even if all risk factors are assumed to be asymmetrically distributed.","PeriodicalId":11744,"journal":{"name":"ERN: Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2010-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73101544","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：