Testing the exogeneity specification in the complete dynamic simultaneous equation model

It is shown that in the complete dynamic simultaneous equation model exogenous variables cause endogenous variables in the sense of Granger (1969) and satisfy the criterion of econometric exogeneity discussed by Sims (1977a), but that the stationarity assumptions invoked by Granger and Sims are not necessary for this implication. Inference procedures for testing each implication are presented and a new joint test of both implications isderived. Detailed attention is given to estimation and testing when the error vector of the final form of the complete dynamic simultaneous equation model is both singular and serially correlated. The theoretical points of the paper are illustrated by testing the exogeneity specification in a small macroeconometric model.     

基于拟牛顿法频率域全波形反演研究

全波形反演是综合利用地震波场的运动学和动力学参数,通过最小二乘来拟合实际波场和预测波场,从而获得地质结构和岩性资料的方法。本文先简述了频率域地震波正演,之后利用拟牛顿法来推导频率域全波形反演,克服了高斯——牛顿法中海森矩阵可能奇异或者非正定特性,通过图形对比,得到频率域全波形反演局限在于频率的缺失和来自其它地质结构对三维地质模型受到的影响比较大,合理选择频点和频宽进行反演可解决频率缺失的影响,二维地质模型的反演效果理想,而三维地质模型的反演有待提高和改进。     

Jackknife model averaging

We consider the problem of obtaining appropriate weights for averaging M approximate (misspecified) models for improved estimation of an unknown conditional mean in the face of non-nested model uncertainty in heteroskedastic error settings. We propose a “jackknife model averaging” (JMA) estimator which selects the weights by minimizing a cross-validation criterion. This criterion is quadratic in the weights, so computation is a simple application of quadratic programming. We show that our estimator is asymptotically optimal in the sense of achieving the lowest possible expected squared error. Monte Carlo simulations and an illustrative application show that JMA can achieve significant efficiency gains over existing model selection and averaging methods in the presence of heteroskedasticity.     

Simultaneous Parameter Estimation in Exploratory Factor Analysis: An Expository Review

The classical exploratory factor analysis (EFA) finds estimates for the factor loadings matrix and the matrix of unique factor variances which give the best fit to the sample correlation matrix with respect to some goodness-of-fit criterion. Common factor scores can be obtained as a function of these estimates and the data. Alternatively to the classical EFA, the EFA model can be fitted directly to the data which yields factor loadings and common factor scores simultaneously. Recently, new algorithms were introduced for the simultaneous least squares estimation of all EFA model unknowns. The new methods are based on the numerical procedure for singular value decomposition of matrices and work equally well when the number of variables exceeds the number of observations. This paper provides an account that is intended as an expository review of methods for simultaneous parameter estimation in EFA. The methods are illustrated on Harman's five socio-economic variables data and a high-dimensional data set from genome research.     

Linear prediction and estimation methods for regression models with stationary stochastic coefficients

A linear regression model is proposed in which the coefficient vector is a weakly stationary multivariate stochastic process. The model provides a convinient representation of a general class of nonstationary processes. Prediction and estimation methods are proposed that are linear and relatively easy to compute. The proposed procedures are illustrated by estimation of time-varying GNP multipliers of several macro policy instruments over the period 1891-1970. The results are compatible with theoretical priors and suggest that predictability of policy outcomes depends on the mixture of policy instruments.     

Distribution-free and link-free estimation for the sample selection model

The prevalent estimation methods for the sample selection model rely heavily on parametric assumptions and are sensitive to departures from the underlying parametric assumptions [see, e.g., Goldberger (1983)]. We propose an alternative estimation method, the corrected maximum likelihood estimate, which is consistent for the slope vector in the outcome equation up to a multiplicative scalar, even through the parametric model on which the estimate is based might be misspecified. As an important corollary, it follows from our result that Olsen's (1980) corrected ordinary least squares estimate is consistent if the outcome equation is linear, without requiring Olsen's assumptions on the joint error distribution.     

Robust estimation of ARIMA models

The paper discusses methods of estimating univariate ARIMA models with outliers. The approach calls for a state vector representation of a time-series model, on which we can then operate on using the Kalman filter. One of the additional advantages of Kalman filter operating on the state vector representation is that the method and code could easily be adapted to be applicable to the ARIMA model with missing observations. The paper investigates ways to calculate robust initial estimation of the parameters of the ARIMA model. The method proposed is based on the results obtained by R.D. Martin (1980).     

Mean square error tests for restrictions in singular linear models

Weak and strong mean square error tests of restrictions presented in Wallace (1972) are generalized to apply to singular linear models. The singularity necessitates a slight change in the strong m.s.e. criterion and the requirement that the restrictions be estimable, but otherwise the tests are applied in a fashion analogous to the non-singular case. Use of those tests implies that the solution for the linear model parameter vector is contingent on a test result. The risk behavior of these contingent solutions is discussed.     

Constrained Kalman Filtering: Additional Results

This paper deals with linear state space modelling subject to general linear constraints on the state vector. The discussion concentrates on four topics: the constrained Kalman filtering versus the recursive restricted least squares estimator; a new proof of the constrained Kalman filtering under a conditional expectation framework; linear constraints under a reduced state space modelling; and state vector prediction under linear constraints. The techniques proposed are illustrated in two real problems. The first problem is related to investment analysis under a dynamic factor model, whereas the second is about making constrained predictions within a GDP benchmarking estimation.     

基于声波信号小波包奇异谱熵和支持向量机的断路器故障诊断研究

在断路器投切时伴随着较强的声波信号,它包含了大量断路器状态信息,通过分析声波信号能够特征提取方法,能够为后续故障诊断提供依据。断路器声波信号易受环境因素影响,且包含非线性、非平稳成份,文中利用小波包奇异谱熵的信号特征提取方法对其进行处理,同时使用支持向量机进行故障识别判断。     

The method of elimination and substitution in the GMM estimation of mixed regressive,spatial autoregressive models

This paper proposes a computationally simple GMM for the estimation of mixed regressive spatial autoregressive models. The proposed method explores the advantage of the method of elimination and substitution in linear algebra. The modified GMM approach reduces the joint (nonlinear) estimation of a complete vector of parameters into estimation of separate components. For the mixed regressive spatial autoregressive model, the nonlinear estimation is reduced to the estimation of the (single) spatial effect parameter. We identify situations under which the resulting estimator can be efficient relative to the joint GMM estimator where all the parameters are jointly estimated.     

FIML estimation of the dynamic simultaneous equations model with ARMA disturbances

A method is presented for the estimation of the parameters in the dynamic simultaneous equations model with vector autoregressive moving average disturbances. The estimation procedure is derived from the full information maximum likelihood approach and is based on Newton-Raphson techniques applied to the likelihood equations. The resulting two-step Newton-Raphson procedure involves only generalized instrumental variables estimation in the second step. This procedure also serves as the basis for an iterative scheme to solve the normal equations and obtain the maximum likelihood estimates of the conditional likelihood function. A nine-equation variant of the quarterly forecasting model of the US economy developed by Fair is then used as a realistic example to illustrate the estimation procedure described in the paper.     

Testing for two-regime threshold cointegration in vector error-correction models

This paper examines a two-regime vector error-correction model with a single cointegrating vector and a threshold effect in the error-correction term. We propose a relatively simple algorithm to obtain maximum likelihood estimation of the complete threshold cointegration model for the bivariate case. We propose a SupLM test for the presence of a threshold. We derive the null asymptotic distribution, show how to simulate asymptotic critical values, and present a bootstrap approximation. We investigate the performance of the test using Monte Carlo simulation, and find that the test works quite well. Applying our methods to the term structure model of interest rates, we find strong evidence for a threshold effect.     

Estimation of the scale matrix of a multivariate t-model under entropy loss

This paper deals with the estimation of the scale matrix of a multivariatet-model with unknown location vector and scale matrix to improve upon the usual estimators based on the sample sum of product matrix. The well-known results of the estimation of the scale matrix of the multivariate normal model under the assumption of entropy loss function have been generalized to that of a multivariatet-model. The paper is based on the first author’s unpublished Ph.D. dissertation ‘Estimation of the Scale Matrix of a Multivariate T-model’, University of Western Ontario, Canada. Present address: School of Mathematics and Statistics, The University of Sydney, NSW 2006, Australia.     

An information-theoretic approach for forecasting interval-valued SP500 daily returns

We develop an iterative and efficient information-theoretic estimator for forecasting interval-valued data, and use our estimator to forecast the SP500 returns up to five days ahead using moving windows. Our forecasts are based on 13 years of data. We show that our estimator is superior to its competitors under all of the common criteria that are used to evaluate forecasts of interval data. Our approach differs from other methods that are used to forecast interval data in two major ways. First, rather than applying the more traditional methods that use only certain moments of the intervals in the estimation process, our estimator uses the complete sample information. Second, our method simultaneously selects the model (or models) and infers the model’s parameters. It is an iterative approach that imposes minimal structure and statistical assumptions.     

Estimation of the location parameter under LINEX loss function: multivariate case

The Baysian estimation of the mean vector θ of a p-variate normal distribution under linear exponential (LINEX) loss function is studied when as a special restricted model, it is suspected that for a p × r known matrix Z the hypothesis θ = Zβ, ${\beta\in\Re^r}The Baysian estimation of the mean vector θ of a p-variate normal distribution under linear exponential (LINEX) loss function is studied when as a special restricted model, it is suspected that for a p × r known matrix Z the hypothesis θ = Zβ, b ? ?^r{\beta\in\Re^r} may hold. In this area we show that the Bayes and empirical Bayes estimators dominate the unrestricted estimator (when nothing is known about the mean vector θ).     

The estimation of a state space model by estimating functions with an application

Conventionally the parameters of a linear state space model are estimated by maximizing a Gaussian likelihood function, even when the input errors are not Gaussian. In this paper we propose estimation by estimating functions fulfilling Godambe's optimality criterion. We discuss the issue of an unknown starting state vector, and we also develop recursive relations for the third- and fourth-order moments of the state predictors required for the calculations. We conclude with a simulation study demonstrating the proposed procedure on the estimation of the stochastic volatility model. The results suggest that the new estimators outperform the Gaussian likelihood.     

The importance of common cyclical features in VAR analysis: a Monte-Carlo study

Despite the commonly held belief that aggregate data display short-run comovement, there has been little discussion about the econometric consequences of this feature of the data. We use exhaustive Monte-Carlo simulations to investigate the importance of restrictions implied by common-cyclical features for estimates and forecasts based on vector autoregressive models. First, we show that the “best” empirical model developed without common cycle restrictions need not nest the “best” model developed with those restrictions. This is due to possible differences in the lag-lengths chosen by model selection criteria for the two alternative models. Second, we show that the costs of ignoring common cyclical features in vector autoregressive modelling can be high, both in terms of forecast accuracy and efficient estimation of variance decomposition coefficients. Third, we find that the Hannan–Quinn criterion performs best among model selection criteria in simultaneously selecting the lag-length and rank of vector autoregressions.     

Priors,posteriors and bayes factors for a Bayesian analysis of cointegration

Cointegration occurs when the long-run multiplier matrix of a vector autoregressive model exhibits rank reduction. Using a singular value decomposition of the unrestricted long-run multiplier matrix, we construct a parameter that reflects the presence of rank reduction. Priors and posteriors of the parameters of the cointegration model follow from conditional priors and posteriors of the unrestricted long-run multiplier matrix given that the parameter that reflects rank reduction is equal to zero. This idea leads to a complete Bayesian framework for cointegration analysis. It includes prior specification, simulation schemes for obtaining posterior distributions and determination of the cointegration rank via Bayes factors. We apply the proposed Bayesian cointegration analysis to the Danish data of Johansen and Juselius (Oxford Bull. Econom. Stat. 52 (1990) 169).     

Order-invariant tests for proper calibration of multivariate density forecasts

Established tests for proper calibration of multivariate density forecasts based on Rosenblatt probability integral transforms can be manipulated by changing the order of variables in the forecasting model. We derive order-invariant tests. The new tests are applicable to densities of arbitrary dimensions and can deal with parameter estimation uncertainty and dynamic misspecification. Monte Carlo simulations show that they often have superior power relative to established approaches. We use the tests to evaluate generalized autoregressive conditional heteroskedasticity-based multivariate density forecasts for a vector of stock market returns and macroeconomic forecasts from a Bayesian vector autoregression with time-varying parameters.