We examine the finite-sample properties of the variance ratio test of the random walk hypothesis via Monte Carlo simulations under two null and three alternative hypotheses. These results are compared to the performance of the Dickey-Fuller t and the Box-Pierce Q statistics. Under the null hypothesis of a random walk with independent and identically distributed Gaussian increments, the empirical size of all three tests are comparable. Under the heteroskedastic random walk null, the variance ration test is more reliable than either the Dickey-Fuller or Box-Pierce tests. We compute the power of these three tests against three alternatives of recent empirical interest: a stationary AR(1), the sum of this AR(1) and a random walk, and an integrated AR(1). By choosing the sampling frequency appropriately, the variance ratio test is shown to be as powerful as the Dickey-Fuller and Box-Pierce tests against the stationary alternative and is more powerful than either of the two tests against the two unit root alternatives.

This paper considers the parametric estimation problem for continuous-time stochastic processes described by first-order nonlinear stochastic differential equations of the generalized Ito type (containing both jump and diffusion components). We derive a particular functional partial differential equation which characterizes the exact likelihood function of a discretely sampled Ito process. In addition, we show by a simple counterexample that the common approach of estimating parameters of an Ito process by applying maximum likelihood to a discretization of the stochastic differential equation does not yield consistent estimators.

In this article we test the random walk hypothesis for weekly stock market returns by comparing variance estimators derived from data sampled at difference frequencies. The random walk model is strongly rejected for the entire sample period (1962-1985) and for all subperiods for a variety of aggregate returns indexes and size-sorted portfolios. Although the rejections are due largely to behavior of small stocks, they cannot be attributed completely to the effects of infrequent trading or time-varying volatilities. Moreover, the rejection of the random walk for weekly returns does not support a mean-reverting model of asset prices.

Upper bounds on the expected payoff of call and put options are derived. These bounds depend only on the mean and variance of the terminal stock price and not on its entire distribution, so they are termed semi-parametric. A corollary of this result is a set of upper bounds for option prices obtained by the risk-neutral valuation approach of Cox and Ross. As an example, these bounds are shown to obtain across both lognormal diffusion-jump processes for any given data set. We present an illustrative example that suggests these bounds may be of considerable practical value.

A new methodology for statistically testing contingent-claims asset-pricing models based on asymptotic statistical theory is proposed. It is introduced in the context of the Black-Scholes option-pricing model, for which some illustrative estimation, inference, and simulation results are also presented. The proposed methodology is then extended to arbitrary contingent claims by first considering the estimation problem for general Itô processes and then deriving the asymptotic distribution of a general contingent claim which depends upon such Itô processes.

Two of the most widely used statistical techniques for analyzing discrete economic phenomena are discriminant analysis (DA) and logit analysis. For purposes of parameter estimation, logit has been shown to be more robust than DA. However, under certain distributional assumptions both procedures yield consistent estimates and the DA estimator is asympototically efficient. This suggests a natural Hausman specification test of these distributional assumptions by comparing the two estimators. In this paper, such a test is proposed and an empirical example involving corporate bankruptcies is provided. The finite-sample properties of the test statistic are also explored through some sampling experiments.

A simple large-sample Chow test for stability of coefficients in a linear simultaneous equation is proposed. It is shown that the appropriate test statistic may be formed conveniently from particular sums of squared residuals.