Specification testing when the null is nonparametric or semiparametric.

This paper discusses the problem of testing misspecifications in semiparametric regression models for a large family of econometric models under rather general conditions. We focus on two main issues that typically arise in econometrics. First, many econometric models are estimated through maximum likelihood or pseudoML methods like, for example, limited dependent variable or gravity models. Second, often one might not want to fully specify the null hypothesis. Instead, one would rather impose some structure like separability or monotonicity. In order to address these points we introduce an adaptive omnibus test. Special emphasis is given to practical issues like adaptive bandwidth choice, general but simple requirements on the estimates, and finite sample performance, including the resampling approximations.We acknowledge nancial support from FUNCAS, the Spanish Projects MTM2008-03010 and ECO2010-15455, and the DAAD Project 50119348

Nonparametric long term prediction of stock returns with generated bond yields

Recent empirical approaches in forecasting equity returns or premiums found that dynamic interactions among the stock and bond are relevant for long term pension products. Automatic procedures to upgrade or downgrade risk exposure could potentially improve long term performance for such products. The risk and return of bonds is more easy to predict than the risk and return of stocks. This and the well known stock-bond correlation motivates the inclusion of the current bond yield in a model for the prediction of excess stock returns. Here, we take the actuarial long term view using yearly data, and focus on nonlinear relationships between a set of covariates. We employ fully nonparametric models and apply for estimation a local-linear kernel smoother. Since the current bond yield is not known, it is predicted in a prior step. The structure imposed this way in the final estimation process helps to circumvent the curse of dimensionality and reduces bias in the estimation of excess stock returns. Our validated stock prediction results show that predicted bond returns improve stock prediction significantly

Nonparametric Prediction of Stock Returns Based on Yearly Data: The Long-Term View

One of the most studied questions in economics and finance is whether empirical models can be used to predict equity returns or premiums. In this paper, we take the actuarial long-term view and base our prediction on yearly data from 1872 through 2014. While many authors favor the historical mean or other parametric methods, this article focuses on nonlinear relationships between a set of covariates. A bootstrap test on the true functional form of the conditional expected returns confirms that yearly returns on the S&P500 are predictable. The inclusion of prior knowledge in our nonlinear model shows notable improvement in the prediction of excess stock returns compared to a fully nonparametric model. Statistically, a bias and dimension reduction method is proposed to import more structure in the estimation process as an adequate way to circumvent the curse of dimensionality

One Sided Crossvalidation for Density Estimation

We introduce one-sided cross-validation to nonparametric kernel density estimation. The method is more stable than classical cross-validation and it has a better overall performance comparable to what we see in plug-in methods. One-sided cross-validation is a more direct date driven method than plugin methods with weaker assumptions of smoothness since it does not require a smooth pilot with consistent second derivatives. Our conclusions for one-sided kernel density cross-validation are similar to the conclusions obtained by Hart and Li (1998) when they introduced one-sided cross-validation in the regression context. An extensive simulation study conms that our one-sided cross-validation clearly outperforms the simple cross validation. We conclude with real data applications

Semiparametric three step estimation methods in labor supply models

The aim of this paper is to provide an alternative way of specification and estimation of a labor supply model. The proposed estimation procedure can be included in the so called predicted wage methods and its main interest is twofold .. First, under standard assumptions in studies of labor supply, the estimator based on predicted wages is shown to be consistent and asymptotically normal. Moreover, we propose also a consistent estimator of the asymptotic covariance matrix. In the main part of the paper we introduce a semiparametric estimator based on marginal integration techniques that allows for nonlinear relationships between the labor supply variable and its covariates. We show that also the wage equation could be modeled nonparametrically. The asymptotic properties of the estimators are given. Finally, in a detailed application we compare the results empirically against those obtained in standard three step estimators based on predicted wages

Semiparametric estimation of weak and strong separable models

In this paper we introduce a general method for estimating semiparametrically the different components in weak or strong separable models. The family of separable models is quite popular in economic theory and empirical research as this structure offers clear interpretation, has straight forward economic consequences and often is justified by theory. As will be seen in this article they are also of statistical interest since they allow to estimate semiparametrically high dimensional complexity without running in the so called curse of dimensionality. Generalized additive models and generalized partial linear models are special cases in this family of models. The idea of the new method is mainly based on a combination of local likelihood and efficient estimators in non or semiparametric models. Although this imposes some hypothesis on the error distribution this yields a very general usable method with little computational costs and high exactness even for small samples. E. g. it enables us to include models for censored and truncated variables which are quite common in quantitative economics. We give the estimation procedures and provide asymptotic theory for them. Implementation is discussed, simulations and an application demonstrate its feasibility in finite sample behavio

Continuous Chain Ladder: Reformulating and generalizing a classical insurance problem

The single most important number in the accounts of a non-life insurance company is likely to be the estimate of the outlying liabilities. Since non-life insurance is a major part of our financial industry (amounting to up to 5% of BNP in western countries), it is perhaps surprising that mathematical statisticians and experts of operational research (the natural experts of the underlying problem) have left the intellectual work on estimating this number to actuaries. This paper establishes this important problem in a vocabulary accessible to experts of operations research and mathematical statistics and it can be seen as an open invitation to these two important groups of scholars to join this research. The paper introduces a number of new methodologies and approaches to estimating outstanding liabilities in non-life insurance. In particular it reformulates the classical actuarial technique as a histogram type of approach and improves this classical technique by replacing this histogram by a kernel smoother