Principal Component Models for Generating Large GARCH Covariance Matrices

The implementation of multivariate GARCH models in more than a few dimensions is extremely difficult: because the model has many parameters, the likelihood function becomes very flat, and consequently the optimization of the likelihood becomes practicably impossible. There is simply no way that full multivariate GARCH models can be used to estimate directly the very large covariance matrices that are required to net all the risks in a large trading book. This paper begins by describing the principal component GARCH or 'orthogonal GARCH' (O-GARCH) model for generating large GARCH covariance matrices that was first introduced in Alexander and Chibumba (1996) and subsequently developed in Alexander (2000, 2001b). The O-GARCH model is an accurate and efficient method for generating large covariance matrices that only requires the estimation of univariate GARCH models. Hence, it has many practical advantages, for example in value–at–risk models. It works best in highly correlated systems, such as term structures. The purpose of this paper is to show that, if sufficient care is taken with the initial calibration of the model, equities and foreign exchange rates can also be included in one large covariance matrix. Simple conditions for the final covariance matrix to be positive semi-definite are derived.
(J.E.L.: C32, C53, G19, G21, G28).     

Economic benefits of using realized covariance forecasts in risk-based portfolios

This article examines the economic benefit of using the realized covariance matrix forecasts, for constructing the risk-based portfolios. We use the two-scale realized covariance estimator (TSC), the jump robust two-scale realized covariance estimator (RTSC) and the realized bipower covariance estimator (BPC), to forecast the daily realized covariance matrix. Using these covariance matrix forecasts, we implement three risk-based portfolios: the global minimum variance portfolio, the equal risk contribution portfolio and the most diversified portfolio. There is evidence that the portfolio performance improves by using TSC or RTSC estimators as compared to the daily-returns-based estimator. The performance gains are robust to the choice of risk-based portfolio strategy, the degree of investor’s relative risk-aversion, the market conditions and the choice of time intervals.     

Can the Consumption Capital Asset Pricing Model Account for Traders' Expected Currency Returns?

This study uses survey data on traders' exchange rate forecasts to test whether their expected excess returns are related to the covariance between the exchange rate and consumption; as predicted by the consumption capital asset pricing model (CCAPM). The covariance is measured through the novel use of rolling windows of the realized covariance (both forward and backward looking) and testing is conducted with the cointegrated VAR. The model is able to account for expected returns with more plausible degrees of risk aversion, but only when using sufficiently long, backward‐looking measures of the covariance. This suggests that market participants assess risk, in part, based upon the pro‐cyclicality of returns, and infer it from experience in the recent past. There is also evidence that inclusion of the real exchange rate improves the plausibility of the estimates and the model fit.     

Asymptotic confidence bands for the estimated autocovariance and autocorrelation functions of vector autoregressive models

This paper provides closed-form formulae for computing the asymptotic covariance matrices of the estimated autocovariance and autocorrelation functions of stable VAR models by means of the delta method. These covariance matrices can be used to construct asymptotic confidence bands for the estimated autocovariance and autocorrelation functions to assess the underlying estimation uncertainty. The usefulness of the formulae for empirical work is illustrated by an application to inflation and output gap data for the U.S. economy indicating the existence of a significant short-run Phillips-curve tradeoff.First version received: November 2002/Final version received: September 2003     

Measurement Error with Accounting Constraints: Point and Interval Estimation for Latent Data with an Application to U.K. Gross Domestic Product

An econometric methodology is proposed for reconciling inaccurate measures of latent data which are subject to accounting constraints. The method deals with the case in which the measurement errors are serially correlated, generalizing previous contributions. A class of efficient estimators are derived for the latent data. Consistent estimators for the weight matrices applied to the observed information based on a linear regression procedure are obtained together with confidence interval estimators for these weight matrices. Approximate confidence intervals are suggested for the latent data themselves together with specification tests for the assumptions underlying the procedure. An application of the proposed method is made to U.K. Gross Domestic Product in constant prices for 1958Q–1989Q4.     

Forecast of realized covariance matrix based on asymptotic distribution of the LU decomposition with an application for balancing minimum variance portfolio

We derive the asymptotic distribution for the LU decomposition, that is, the Cholesky decomposition, of realized covariance matrix. Distributional properties are combined with an existing generalized heterogeneous autoregressive (GHAR) method for forecasting realized covariance matrix, which will be referred to as a generalized HARQ (GHARQ) method. An out-of-sample forecast comparison of a real data set shows that the proposed GHARQ method outperforms other existing methods in terms of optimizing the variances of portfolios.     

Asymptotic Variance–Covariance Matrices of Two-Stage Estimators in the Presence of Continuous and Binary Dependent Variables with an Empirical Application

Journal of Quantitative Economics - We develop a general procedure to derive the asymptotic variance–covariance matrices of several two-stage estimators that can be used to estimate...     

Excess Volatility of Realized Excess Profit from Currency Speculation in a Two-Country General Equilibrium Model

This paper examines whether the Lucas model can explain stylized facts in foreign exchange markets, by employing Monte Carlo studies. It is assumed that changes in the logarithms of endowments and of money supplies follow a multivariate Markov switching process. From the results of the Monte Carlo studies, with plausible values of the preference parameters, the excess volatility of the realized excess profit from currency speculation, the strong autocorrelation of the forward premium in the sample can be found in the model for four exchange rates. However, the implied covariance between the forward premium and depreciation rates is positive.     

Forecasting stock market volatility and information content of implied volatility index

This study investigates the incremental information content of implied volatility index relative to the GARCH family models in forecasting volatility of the three Asia-Pacific stock markets, namely India, Australia and Hong Kong. To examine the in-sample information content, the conditional variance equations of GARCH family models are augmented by incorporating implied volatility index as an explanatory variable. The return-based realized variance and the range-based realized variance constructed from 5-min data are used as proxy for latent volatility. To assess the out-of-sample forecast performance, we generate one-day-ahead rolling forecasts and employ the Mincer–Zarnowitz regression and encompassing regression. We find that the inclusion of implied volatility index in the conditional variance equation of GARCH family model reduces volatility persistence and improves model fitness. The significant and positive coefficient of implied volatility index in the augmented GARCH family models suggests that it contains relevant information in describing the volatility process. The study finds that volatility index is a biased forecast but possesses relevant information in explaining future realized volatility. The results of encompassing regression suggest that implied volatility index contains additional information relevant for forecasting stock market volatility beyond the information contained in the GARCH family model forecasts.     

集群企业资源获取、吸收能力与技术创新绩效——珠三角传统产业集群中的企业研究

以珠三角传统产业集群中的企业为研究对象,从资源依赖理论出发,探索集群企业技术创新的影响因素和路径。构建了资源获取、吸收能力与技术创新绩效的概念模型,编制问卷,并使用结构方程模型对其进行检验。结果表明,企业的"软资源的获取"(信息、技术、人才)能够积极提高企业的潜在吸收能力,进而促进企业的模仿创新和率先创新。企业的"硬资源的获取"(资金)虽然可以提高企业的现实吸收能力,但对两种技术创新的作用都不显著。根据所得结论,从企业、政府、行业协会3个方面提出要构建良好的外部网络和发展环境,促进其资源获取从而提高企业的技术创新绩效。     

Estimating SUR system with random coefficients: the unbalanced panel data case

A system of regression equations for analyzing panel data with random heterogeneity in intercepts and coefficients, and unbalanced panel data is considered. A maximum likelihood (ML) procedure for joint estimation of all parameters is described. Since its implementation for numerical computation is complicated, simplified procedures are presented. The simplifications essentially concern the estimation of the covariance matrices of the random coefficients. The application and ‘anatomy’ of the proposed algorithm for modified ML estimation are illustrated by using panel data for output, inputs and costs for 111 manufacturing firms observed up to 22 years.     

A model selection approach for multiple indicators multiple causes model

This study proposes a model selection approach for determining the inclusion or exclusion of a latent variable when two exogenous and two endogenous variables are provided. The models compared are the multivariate regression model without latent variables (MR model) and the multiple indicators multiple causes model (MIMIC model). The inclusion of a latent variable in the MR model yields the MIMIC model. In the proposed approach, an information criterion is used to select the best model of the two. The efficacy of the proposed approach is examined through two types of simulation studies and empirical analyses of the shadow economy and the fiscal illusion.     

S-values and Bayesian weighted all-subsets regressions

This paper compares and contrasts Bayesian variable-exclusion methods proposed by Eduardo Ley and coauthors with methods proposed by Raftery and Sala-i-Martin et al. and with the s-values proposed by myself. A distinction is drawn between estimation uncertainty which is the focus of Ley׳s research and model ambiguity which arises in Ley׳s work and is the focus of my own recent proposal. The discussion is organized around the prior covariance matrix, which needs to be diagonal to support all-subsets regressions. The basic question addressed here is: what aspects of the prior covariance matrix can be taken as known, what aspects can be estimated and what aspects require a sensitivity analysis because they are neither known nor estimable. When diagonality is in doubt, we are more-or-less forced into a model ambiguity sensitivity mode because the data are never rich enough credibly to estimate the full prior covariance matrix. When diagonality is assumed, the data evidence, though very limited, can help to estimate the diagonal elements, but this literature has not yet produced a compelling conventional treatment which will necessarily include both estimation uncertainty and model ambiguity as they relate both to the diagonal values and to the rest of the prior covariance matrix. But there has been a lot of progress.     

基于截集的加权可能性均值-方差模型

本文以模糊数的截集为切入点,给出随机变量取值为模糊数时基于截集的加权可能性均值、加权可能性方差和加权可能性协方差的定义,研究了基于截集的加权可能性均值、加权可能性方差和加权可能性协方差的性质,给出三角模糊数的基于截集的加权可能性均值、加权可能性方差和加权可能性协方差的具体形式.并以基于截集的加权可能性均值作为证券组合投资收益率为模糊数时投资未来收益的度量,以基于截集的加权可能性方差作为证券组合投资收益率为模糊数时投资风险的度量,以基于截集的加权可能性协方差作为不同资产之间相关程度的度量,以不同的权重表示不同投资者的对投资收益的风险偏好程度,构建基于模糊数截集的加权可能性均值-方差组合投资模型,给出模型的求解方法.最后将基于截集的加权可能性均值-方差模型与传统的均值-方差模型进行了比较分析,并结合我国证券交易市场的具体实例说明该模型的应用价值.     

A Tobit-type estimator for the censored Poisson regression model

The Poisson counterpart to the Tobit model is presented. Formulae for the gradient and Hessian of the relevant log-likelihood function are given and incorporated into a Newton-Raphson optimization algorithm. The asymptotic covariance matrix of the estimator is detailed. As an illustration, the NR algorithm is applied to a model of individual shopping behavior.     

Latent Consideration Sets and Continuous Demand Systems

This paper develops a theoretically consistent continuous demand system model that incorporates latent, probabilistic consideration sets. In contrast to existing discrete choice consideration models, the proposed model is econometrically tractable with consumption data for many goods. The model’s empirical properties are illustrated with an 89-site recreation data set from the 1994 National Survey of Recreation and the Environment (NSRE). Parameter and welfare estimates suggest that the latent consideration set models fit the data better and may imply a bias-variance tradeoff relative to traditional models.      

CONSISTENT ESTIMATION OF A LIMITING COVARIANCE MATRIX

This paper provides a consistent and positive semi-definite estimator of the limiting covariance matrix of a nonlinear instrumental variable estimator for a nonlinear simultaneous equation model with selectivity studied in Sapra (1989).     

潜在变量、宏观变量与动态利率期限结构——基于DRA模型的实证分析

本文从金融-宏观经济学视角出发,运用DRA模型研究了潜在变量、宏观变量与利率期限结构之间的动态关系。通过脉冲响应函数分析了潜在变量与宏观变量之间的相互冲击效应的大小,以及潜在变量、宏观变量对收益率曲线冲击的影响,借助于方差分解量化了潜在变量、宏观变量冲击对收益率曲线预测误差的贡献率,并利用似然比检验,发现中国的收益率曲线与宏观变量之间存在双向的互动关系,但收益率曲线对未来宏观变量的影响更强。     

Step-by-step computation of corrected asymptotic variance-covariance matrices of two-stage estimators in a simultaneous equations model with a mixture of four continuous and binary dependent variables

The current study presents easily computable formulas for asymptotic variance-covariance matrices of the two-stage estimators in a simultaneous equation model with a mixture of four continuous and binary dependent variables. For the sake of econometrics practitioners, the study uses an illustrative example from the current literature and demonstrates step-by-step computation of these variance-covariance matrices by using the matrix routine of a popular econometric software.