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 describt tbe 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: 1) positive correlation between conditional volatility and volume, 2) large price movements are followed by high volume, 3) conditioning on lagged volume substantially attenuates the "leverage " effect, and 4) after conditioning on lagged volume, there is a positive risk/return relation.

This paper develops a nonparametric approach to examine how portfolio and consumption choice depends on variables that forecast time-varying investment opportunities. I estimate single-period and multiperiod portfolio and consumption rules of an investor with constant relative risk aversion and a one-month to 20year horizon. The investor allocates wealth to the NYSE index and a 30-day Treasury bill. I find that the portfolio choice varies significantly with the dividend yield, default premium, term premium, and lagged excess return. Furthermore, the optimal decisions depend on the investor’s horizon and rebalancing frequency.

A number of recent papers have used nonparametric density estimation or nonparametric regression to study the instantaneous spot interest rate, and to test term structure models. However, little is known about the performance of these methods when applied to persistent time-series, such as U.S. interest rates. This paper uses the Vasicek [1977] model to study the performance of kernel density estimates of the ergodic distribution of the instantaneous spot rate. The model's tractability allows me to analyze the MISE of the kernel estimate as a function of persistence, variance of the ergodic distribution, span of the data, sampling frequency, and kernel bandwidth. Our principle result is that persistence has an important impact on optimal bandwidth selection and on nite sample performance. We also nd that sampling the data more frequently has little e ect on estimator quality. We also examine one of Ait-Sahalia's [1996a] new nonparametric tests of parametric continuous-time Markov models of the instantaneous spot interest rate. The test is based on the distance between parametric and nonparametric (kernel) estimates of the ergodic distribution of the interest rate process. Our principal result is that the test rejects too often when using asymptotic critical values and 22 years of data. The reason for the high rejection rate is probably because the asymptotic distribution of the test does not depend on persistence, but the nite sample performance of the estimator does. After critical values are adjusted for size, the test has low power in distinguishing between the Vasicek and Cox-Ingersoll-Ross models when compared with a conditional moment based speci cation test.

Ait-Sahalia (1996) and Stanton (1997) use nonparametric estimators applied to short term interest rate data to conclude that the drift function contains important nonlinearities. We study the finite-sample properties of their estimators by applying them to simulated sample paths of a square-root diffusion. Although the drift function is linear, both estimators suggest nonlinearities of the type and magnitude reported in Ait-Sahalia (1996) and Stanton (1997). Combined with the results of a weighted least squares estimator, this evidence implies that nonlinearity of the short rate drift is not a robust stylized fact.

Abstract not found

Local high-order polynomial fitting is employed for the estimation of the multivariate regression function m (x 1 , . . . , x d ) = E [y (Y d ) | X 1 = x 1 , . . . , X d = x d ], and of its partial derivatives, for stationary random processes {Y i , X i }. The function y may be selected to yield estimates of the conditional mean, conditional moments and conditional distributions. Uniform strong consistency over compact subsets of R d , along with rates, are established for the regression function and its partial derivatives for strongly mixing processes. Short Title: Multivariate Regression Estimation. Key Words: Multivariate regression estimation, local polynomial fitting, mixing processes, uniform strong consistency, rates of convergence. AMS (1991) Subject Classification: 62G07, 62H12, 62M09. ################## This work was supported by the Office of Naval Research under Grant N00014-90-J-1175. - 2 - 1. Introduction Let {Y i , X i } i =- be jointly stationary processes on...

this paper was written while the author was visiting the Graduate School of Business at the University of Chicago. This paper incorporates some results previously circulated in Is the Expected Compensation for Market Volatility Constant Through Time? and On the Linearity of Conditionally Expected Returns. I have bene tted from the comments of Daniel Beneish, Marshall Blume, Doug Breeden, Wayne Ferson, Doug Foster, Mike Giarla, Mike Hemler, Ravi Jagannathan, Dan Nelson, Adrian Pagan, Tom Smith, Rob Stambaugh, S

We consider a vector conditional heteroskedastic autoregressive nonlinear (CHARN) model in which both the conditional mean and the conditional variance (volatility) matrix are unknown functions of the past. Nonparametric estimators of these functions are constructed based on local polynomial fitting. We examine the rates of convergence of these estimators and give a result on their asymptotic normality. These results are applied to estimation of volatility matrices in foreign exchange markets. Estimation of the conditional covariance surface for the DEM/USD and DEM/GBP daily returns show negative correlation when the two series have opposite lagged values and positive correlation elsewhere. 1 Nonparametric Vector Autoregression Multivariate time series occur in many scientific disciplines. Their analysis helps in modelling dynamics over time as well as explaining interdependence among variables. A common model in this context is vector autoregression where the dynamics over time is mo...

We consider the problem of one-step-ahead prediction of a real-valued, stationary, strongly mixing random process fX i g i=01 . The best mean-square predictor of X0 is its conditional mean given the entire infinite past fX i g i=01 . Given a sequence of observations X1 X2 111 XN, we propose estimators for the conditional mean based on sequences of parametric models of increasing memory and of increasing dimension, for example, neural networks and Legendre polynomials. The proposed estimators select both the model memory and the model dimension, in a data-driven fashion, by minimizing certain complexity regularized least squares criteria. When the underlying predictor function has a finite memory, we establish that the proposed estimators are memory-universal: the proposed estimators, which do not know the true memory, deliver the same statistical performance (rates of integrated mean-squared error) as that delivered by estimators that know the true memory. Furthermore, when the underlying predictor function does not have a finite memory, we establish that the estimator based on Legendre polynomials is consistent.

For over a decade, nonparametric modelling has been successfully applied to studying nonlinear structures in nancial time series. It is well known that the usual nonparametric models often have less than satisfactory performance when dealing with more than one lag. When the mean has an additive structure, however, better estimation methods are available which fully exploit such a structure. Although in the past such nonparametric applications had been focused more on the estimation of the conditional mean, it is equally if not more important to measure the future risk of the series along with the mean. For the volatility function, i.e. the conditional variance given the past, a multiplicative structure is more appropriate than an additive structure, as the volatility is a positive scale function and a multiplicative model provides a better interpretation of each lagged value's inuence on such a function. In this paper we consider the joint estimation of both the additive mean and the multiplicative volatility. The technique used is marginally integrated local polynomial estimation. The procedure is applied to the deutschmark/US dollar daily exchange returns.