This paper describes a simple method of calculating a heteroskedasticity and autocorrelation consistent covariance matrix that is positive semi-definite by construction. It also establishes consistency of the estimated covariance matrix under fairly general conditions.

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A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix

SUMMARY This paper proposes new tests for detecting the presence of a unit root in quite general time series models. Our approach is nonparametric with respect to nuisance parameters and thereby allows for a very wide class of weakly dependent and possibly heterogeneously distributed data. The tests accommodate models with a fitted drift and a time trend so that they may be used to discriminate between unit root nonstationarity and stationarity about a deterministic trend. The limiting distributions of the statistics are obtained under both the unit root null and a sequence of local alternatives. The latter noncentral distribution theory yields local asymptotic power functions for the tests and facilitates comparisons with alternative procedures due to Dickey & Fuller. Simulations are reported on the performance of the new tests in finite samples.

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Testing for a Unit Root in Time Series Regression

Factor analysis, path analysis, structural equation modeling, and related multivariate statistical methods are based on maximum likelihood or generalized least squares estimation developed for covariance structure models. Large-sample theory provides a chi-square goodness-of-fit test for comparing a model against a general alternative model based on correlated variables. This model comparison is insufficient for model evaluation: In large samples virtually any model tends to be rejected as inadequate, and in small samples various competing models, if evaluated, might be equally acceptable. A general null model based on modified independence among variables is proposed to provide an additional reference point for the statistical and scientific evaluation of covariance structure models. Use of the null model in the context of a procedure that sequentially evaluates the statistical necessity of various sets of parameters places statistical methods in covariance structure analysis into a more complete framework. The concepts of ideal models and pseudo chi-square tests are introduced, and their roles in hypothesis testing are developed. The importance of supplementing statistical evaluation with incremental fit indices associated with the comparison of hierarchical models is also emphasized. Normed and nonnormed fit indices are developed and illustrated.

Significance tests and goodness of fit in the analysis of covariance structures

Large sample properties of generalized method of moments estimators

Several issues relating to goodness of fit in structural equations are examined. The convergence and differentiation criteria, as applied by Bagozzi, are shown not to stand up under mathematical or...

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Structural Equation Models with Unobservable Variables and Measurement Error: Algebra and Statistics:

This article presents convenient reduced-form models of the valuation of contingent claims subject to default risk, focusing on applications to the term structure of interest rates for corporate or sovereign bonds. Examples include the valuation of a credit-spread option. This article presents a new approach to modeling term structures of bonds and other contingent claims that are subject to default risk. As in previous “reduced-form” models, we treat default as an unpredictable event governed by a hazard-rate process. 1 Our approach is distinguished by the parameterization of losses at default in terms of the fractional reduction in market value that occurs at default. Specifically, we fix some contingent claim that, in the event of no default, pays X at time T . We take as given an arbitrage-free setting in which all securities are priced in terms of some short-rate process r and equivalent martingale measure Q [see Harrison and Kreps (1979) and Harrison and Pliska (1981)]. Under this “risk-neutral” probability measure, we letht denote the hazard rate for default at time t and let Lt denote the expected fractional loss in market value if default were to occur at time t , conditional

Modeling Term Structures of Defaultable Bonds

Generalized Instrumental Variables Estimation of Nonlinear Rational Expectations Models

In the setting of ‘‘affine’’ jump-diffusion state processes, this paper provides an analytical treatment of a class of transforms, including various Laplace and Fourier transforms as special cases, that allow an analytical treatment of a range of valuation and econometric problems. Example applications include fixed-income pricing models, with a role for intensity-based models of default, as well as a wide range of option-pricing applications. An illustrative example examines the implications of stochastic volatility and jumps for option valuation. This example highlights the impact on option ‘smirks’ of the joint distribution of jumps in volatility and jumps in the underlying asset price, through both jump amplitude as well as jump timing.

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Transform analysis and asset pricing for affine jump-diffusions

This paper studies the time-series behavior of asset returns and aggregate consumption. Using a representative consumer model and imposing restrictions on preferences and the joint distribution of consumption and returns, we deduce a restricted log-linear time-series representation. Preference parameters for the representative agent are estimated and the implied restrictions are tested using postwar data.

Stochastic Consumption, Risk Aversion, and the Temporal Behavior of Asset Returns

In this paper, we explore the features of affine term structure models that are empirically important for explaining the joint distribution of yields on short and long-term interest rate swaps. We begin by showing that the family of N-factor affine models can be classified into N+1 non-nested sub-families of models. For each sub-family, we derive a maximal model with the property that every admissible member of this family is equivalent to or a nested special case of our maximal model. Second, using our classification scheme and maximal models, we show that many of the three-factor models in the literature impose potentially strong over-identifying restrictions on the joint distribution of short- and long-term rates. Third, we compute simulated method-of-moments estimates for several members of one of the four branches of three-factor models, and test the over-identifying restrictions implied by these models. We conclude that many of the extant affine models in the literature fail to describe important features of the distribution of long- and short- term rates. The source of the model misspecification is shown to be overly strong restrictions on the correlations among the state variables. Relaxing these restrictions leads to a model that passes several goodness-of-fit tests over our sample period.

Kenneth J. Singleton

Papers

Modeling Term Structures of Defaultable Bonds

Generalized Instrumental Variables Estimation of Nonlinear Rational Expectations Models

Transform analysis and asset pricing for affine jump-diffusions

Stochastic Consumption, Risk Aversion, and the Temporal Behavior of Asset Returns

Specification Analysis of Affine Term Structure Models