Testing overidentifying restrictions with many instruments and heteroskedasticity

This paper gives a test of overidentifying restrictions that is robust to many instruments and heteroskedasticity. It is based on a jackknife version of the overidentifying test statistic. Correct asymptotic critical values are derived for this statistic when the number of instruments grows large, at a rate up to the sample size. It is also shown that the test is valid when the number of instruments is fixed and there is homoskedasticity. This test improves on recently proposed tests by allowing for heteroskedasticity and by avoiding assumptions on the instrument projection matrix. This paper finds in Monte Carlo studies that the test is more accurate and less sensitive to the number of instruments than the Hausman–Sargan or GMM tests of overidentifying restrictions.     

Forecasting volatility: A reality check based on option pricing, utility function, value-at-risk, and predictive likelihood

We analyze the predictive performance of various volatility models for stock returns. To compare their performance, we choose loss functions for which volatility estimation is of paramount importance. We deal with two economic loss functions (an option pricing function and an utility function) and two statistical loss functions (a goodness-of-fit measure for a value-at-risk (VaR) calculation and a predictive likelihood function). We implement the tests for superior predictive ability of White [Econometrica 68 (5) (2000) 1097] and Hansen [Hansen, P. R. (2001). An unbiased and powerful test for superior predictive ability. Brown University]. We find that, for option pricing, simple models like the Riskmetrics exponentially weighted moving average (EWMA) or a simple moving average, which do not require estimation, perform as well as other more sophisticated specifications. For a utility-based loss function, an asymmetric quadratic GARCH seems to dominate, and this result is robust to different degrees of risk aversion. For a VaR-based loss function, a stochastic volatility model is preferred. Interestingly, the Riskmetrics EWMA model, proposed to calculate VaR, seems to be the worst performer. For the predictive likelihood-based loss function, modeling the conditional standard deviation instead of the variance seems to be a dominant modeling strategy.     

Optimal prediction under LINLIN loss: Empirical evidence

I compare the forecasts of returns from the mean predictor (optimal under MSE), with the pseudo-optimal and optimal predictor for an asymmetric loss function under the assumption that agents have an asymmetric LINLIN loss function. The results strongly suggest not using the conditional mean predictor under conditions of asymmetry. In general, forecasts can be improved by the use of optimal predictor rather than the pseudo-optimal predictor, suggesting that the loss reduction from using the optimal predictor can actually be important for practitioners as well.     

二元函数微分学两个定理的推广

本文对二元函数可微性及高阶混合偏导数与求导次序无关的充分条件进行了推广并加以证明.     

经济最优化中的动态规划

本文应用动态规划讨论了线性、非线性最优化问题,并提出了递推方程。     

A regularization approach to the many instruments problem

This paper focuses on the estimation of a finite dimensional parameter in a linear model where the number of instruments is very large or infinite. In order to improve the small sample properties of standard instrumental variable (IV) estimators, we propose three modified IV estimators based on three different ways of inverting the covariance matrix of the instruments. These inverses involve a regularization or smoothing parameter. It should be stressed that no restriction on the number of instruments is needed and that all the instruments are used in the estimation. We show that the three estimators are asymptotically normal and attain the semiparametric efficiency bound. Higher-order analysis of the MSE reveals that the bias of the modified estimators does not depend on the number of instruments. Finally, we suggest a data-driven method for selecting the regularization parameter. Interestingly, our regularization techniques lead to a consistent nonparametric estimation of the optimal instrument.     

A SCIENTIFIC CLASSIFICATION OF VOLATILITY MODELS

Abstract.  Modeling volatility, or predictable changes over time and space in a variable, is crucial in the natural and social sciences. Life can be volatile, and anything that matters, and which changes over time and space, involves volatility. Without volatility, many temporal and spatial variables would simply be constants. Our purpose is to propose a scientific classification of the alternative volatility models and approaches that are available in the literature, following the Linnaean taxonomy. This scientific classification is used because the literature has evolved as a living organism, with the birth of numerous new species of models.     

How does inter-industry spillover improve the performance of volatility forecasting?

This study aims to investigate whether introducing inter-industry spillover information into the GARCH-MIDAS model improves out-of-sample forecasting attempts. We explore the transmission of volatility across sectors, as well as the reliance on inter-industry business links. Our findings demonstrate strong cross-industry volatility spillovers that are related to the degree of the industry-to-industry trading linkage. We compare the out-of-sample volatility forecasting performance of the spillovers-information-incorporated GARCH-MIDAS model with that of the traditional GARCH model. The empirical results show that the GARCH-MIDAS model outperforms traditional GARCH models. Notably, we discover that good (bad) news is always transferred from the back end of the production process to the front end, meaning that economic growth (decline) is driven by consumption expansion (shrinkage).