[We undertake a comprehensive investigation of price and volume co-movement using daily New York Stock Exchange data from 1928 to 1987. We adjust the data to take into account well-known calendar effects and long-run trends. To describe the process, we use a seminonparametric estimate of the joint density of current price change and volume conditional on past price changes and volume. Four empirical regularities are found: (i) positive correlation between conditional volatility and volume; (ii) large price movements are followed by high volume; (iii) conditioning on lagged volume substantially attenuates the "leverage" effect; and (iv) after conditioning on lagged volume, there is a positive risk-return relation.]

This article theoretically explores the characteristics underpinning quadratic term structure models (QTSMs), which designate the yield on a bond as a quadratic function of underlying state variables. We develop a comprehensive QTSM, which is maximally flexible and thus encompasses the features of several diverse models including the double square-root model of Longstaff (1989), the univariate quadratic model of Beaglehole and Tenney (1992), and the squared-autoregressive-independent-variable nominal term structure (SAINTS) model of Constantinides (1992). We document a complete classification of admissibility and empirical identification for the QTSM, and demonstrate that the QTSM can overcome limitations inherent in affine term structure models (ATSMs). Using the efficient method of moments of Gallant and Tauchen (1996), we test the empirical performance of the model in determining bond prices and compare the performance to the ATSMs. The results of the goodness-of-fit tests suggest that the QTSMs outperform the ATSMs in explaining historical bond price behavior in the United States.

The SNP density estimator is a truncation (or sieve) estimator based upon a Hermite series expansion. Other nonparametric estimators based on orthogonal series expansions have been proposed.

A. Ronald Gallant, George Tauchen, Seminonparametric Estimation of Conditionally Constrained Heterogeneous Processes: Asset Pricing Applications, Econometrica, Vol. 57, No. 5 (Sep., 1989), pp. 1091-1120

A. Ronald Gallant, Alberto Holly, Statistical Inference in an Implicit, Nonlinear, Simultaneous Equation Model in the Context of Maximum Likelihood Estimation, Econometrica, Vol. 49, No. 2 (Mar., 1981), p. 554

A. Ronald Gallant, Alberto Holly, Statistical Inference in an Implicit, Nonlinear, Simultaneous Equation Mode in the Context of Maximum Likelihood Estimation, Econometrica, Vol. 48, No. 3 (Apr., 1980), pp. 697-720

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We consider an open question in applied price theory: Without a priori knowledge of a firm's cost function or a consumer's indirect utility function, is it possible to estimate price and substitution elasticities consistently by observing a demand system? As the work of White [30], Guilkey, Lovell, and Sickles [19], and others has shown, ordinary flexible functional forms such as the translog cannot achieve this objective. We find that if one is prepared to assume that elasticities of substitution cannot oscillate wildly over the region of interest then consistent estimation is possible using the Fourier flexible form provided the number of fitted parameters increases as the number of observations increases. This result obtains with any of the commonly used statistical methods as, for example, multivariate least squares, maximum likelihood, and three-stage least squares. It obtains if the number of fitted parameters is chosen adaptively by observing the data or chosen deterministically according to some fixed rule. We approach the problem along the classical lines of estimability considerations as used in the study of less than full rank linear statistical models and thereby discover that the problem has a fascinating structure which we explore in detail.

We undertake a comprehensive investigation of price and volume co-movement using daily New York Stock Exchange data from 1928 to 1987. We adjust the data to take into account well-known calendar effects and long-run trends. To describe the process, we use a seminonparametric estimate of the joint density of current price change and volume conditional on past price changes and volume. Four empirical regularities are found: (i) positive correlation between conditional volatility and volume; (ii) large price movements are followed by high volume; (iii) conditioning on lagged volume substantially attenuates the “leverage” effect; and (iv) after conditioning on lagged volume, there is a positive risk-return relation.

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