The aim of this paper is to illustrate how the stability of a stochastic dynamic system is measured using the Lyapunov exponents. Specifically, we use a feedforward neural network to estimate these exponents as well as asymptotic results for this estimator to test for unstable (chaotic)...

This article tests the linearity assumption underlying the popular heterogeneous autoregressive model for realized volatility (HAR-RV). We implement a consistent model specification test that is robust to both distributional and model misspecification. We find that, using a nonparametric HAR-RV...

This paper describes a simple yet powerful methodology to decompose asset returns sampled at high frequency into their base components (continuous, small jumps, large jumps), determine the relative magnitude of the components, and analyze the finer characteristics of these components such as the...

We develop a nonparametric test to check whether a process can be represented by a stochastic differential equation driven only by a Brownian motion. Our testing procedure utilizes the infinitesimal operator-based martingale characterization combined with a generalized spectral approach. Such a...

We propose a rank-test of the null hypothesis of short memory stationarity possibly after linear detrending.

In this paper, we develop two cointegration tests for two varying coefficient cointegration regression models, respectively. Our test statistics are residual based. We derive the asymptotic distributions of test statistics under the null hypothesis of cointegration and show that they are...

We propose non-nested hypothesis tests for conditional moment restriction models based on the method of generalized empirical likelihood (GEL). By utilizing the implied GEL probabilities from a sequence of unconditional moment restrictions that contains equivalent information of the conditional...

We construct two classes of smoothed empirical likelihood ratio tests for the conditional independence hypothesis by writing the null hypothesis as an infinite collection of conditional moment restrictions indexed by a nuisance parameter. One class is based on the CDF; another is based on smoother...

This paper shows how revealed preference relations, observed under general budget sets, can be extended using closure operators which impose certain assumptions on preferences. Common extensions are based on the assumption that preferences are convex and/or monotonic, but we also consider...

This paper considers the problem of testing a finite number of moment inequalities. We propose a two-step approach. In the first step, a confidence region for the moments is constructed. In the second step, this set is used to provide information about which moments are "negative." A...