Several least-squares problems related to the Hodrick–Prescott filtering

The Hodrick–Prescott (HP) filtering is frequently used in macroeconometrics to decompose time series, such as real gross domestic product, into their trend and cyclical components. Because the HP filtering is a basic econometric tool, it is necessary to have a precise understanding of the nature of it. This article contributes to the literature by listing several (penalized) least-squares problems that are related to the HP filtering, three of which are newly introduced in the article, and showing their properties. We also remark on their generalization.     

On the construction of optimal experimental designs: a penalty approach

Tn optimal experimental design theory there are well-known situations, in which additional constraints are implied to the design set. These constraints destroy in general the simplex structure of the set of feasible points of the design set. Thus the available iteration procedures for the unrestricted case are no longer applicable.

In this paper a penalty approach is suggested which transforms the restricted problem to the unrestricted case and allows the application of well-known algorithms such as the Fedorov-Wynn-type or the projected gradient procedure.     

A diagnostic statistic for functional-coefficient autoregressive models

In this paper, functional coefficient autoregressive (FAR) models proposed by Chen and Tsay (1993) are considered. We propose a diagnostic statistic for FAR models constructed by comparing between parametric and nonparametric estimators of the functional form of the FAR models. We show asymptotic properties of our statistic mathematically and it can be applied to the estimation of the delay parameter and the specification of the functional form of FAR models.     

Identifying Latent Structures in Panel Data

This paper provides a novel mechanism for identifying and estimating latent group structures in panel data using penalized techniques. We consider both linear and nonlinear models where the regression coefficients are heterogeneous across groups but homogeneous within a group and the group membership is unknown. Two approaches are considered—penalized profile likelihood (PPL) estimation for the general nonlinear models without endogenous regressors, and penalized GMM (PGMM) estimation for linear models with endogeneity. In both cases, we develop a new variant of Lasso called classifier‐Lasso (C‐Lasso) that serves to shrink individual coefficients to the unknown group‐specific coefficients. C‐Lasso achieves simultaneous classification and consistent estimation in a single step and the classification exhibits the desirable property of uniform consistency. For PPL estimation, C‐Lasso also achieves the oracle property so that group‐specific parameter estimators are asymptotically equivalent to infeasible estimators that use individual group identity information. For PGMM estimation, the oracle property of C‐Lasso is preserved in some special cases. Simulations demonstrate good finite‐sample performance of the approach in both classification and estimation. Empirical applications to both linear and nonlinear models are presented.     

单指标非参数期权定价——改进的非参数定价方法

本文建立一种改进的非参数期权定价模型,称为单指标非参数期权定价模型。相比现有非参数回归期权定价模型是期权价格关于各个因素的多元回归函数,本模型通过变量变换把期权价格多个因素指标转换为一个综合变量——单指标,得到期权价格关于单指标的一元非参数回归方程。改进的模型实现了多元非参数期权定价模型的降维和简化了模型计算;还通过多个期限期权的单指标组合解决了非参数估计的样本数量问题;以及通过期限平滑解决了现有非参数定价模型中的日历效应问题。选取上证50ETF期权数据实证分析表明,无论是样本内的估计结果还是样本外的预测结果都比传统的Black-Scholes模型、半参数Black-Scholes模型和多元非参数回归期权定价模型估计效果有提高。     

The k-factor GARMA Process with Infinite Variance Innovations

In this article, we develop the theory of k-factor Gegenbauer Autoregressive Moving Average (GARMA) process with infinite variance innovations which is a generalization of the stable seasonal fractional Autoregressive Integrated Moving Average (ARIMA) model introduced by Diongue et al. (2008 Diongue, A.K., Guégan, D. (2008). Estimation of k-Factor GIGARCH Process: A Monte Carlo Study. Communications in Statistics-Simulation and Computation 37:2037–2049.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]). Stationarity and invertibility conditions of this new model are derived. Conditional Sum of Squares (CSS) and Markov Chains Monte Carlo (MCMC) Whittle methods are investigated for parameter estimation. Monte Carlo simulations are also used to evaluate the finite sample performance of these estimation techniques. Finally, the usefulness of the model is corroborated with the application to streamflow data for Senegal River at Bakel.     

In-Sample Inference and Forecasting in Misspecified Factor Models

This article considers in-sample prediction and out-of-sample forecasting in regressions with many exogenous predictors. We consider four dimension-reduction devices: principal components, ridge, Landweber Fridman, and partial least squares. We derive rates of convergence for two representative models: an ill-posed model and an approximate factor model. The theory is developed for a large cross-section and a large time-series. As all these methods depend on a tuning parameter to be selected, we also propose data-driven selection methods based on cross-validation and establish their optimality. Monte Carlo simulations and an empirical application to forecasting inflation and output growth in the U.S. show that data-reduction methods outperform conventional methods in several relevant settings, and might effectively guard against instabilities in predictors’ forecasting ability.