Diffusion over a network refers to the phenomenon of a change of state of a cross-sectional unit in one period leading to a change of state of its neighbors in the network in the next period. One may estimate or test for diffusion by estimating a cross-sectionally aggregated correlation between neighbors over time from data. However, the estimated diffusion can be misleading if the diffusion is confounded by omitted covariates. This paper focuses on the measure of diffusion proposed by He and Song (2022, Preprint, arXiv:1812.04195v4 [stat.ME]), provides a method of decomposition analysis to measure the role of the covariates on the estimated diffusion, and develops an asymptotic inference procedure for the decomposition analysis in such a situation. This paper also presents results from a Monte Carlo study on the small sample performance of the inference procedure.

This paper studies the properties of predictive regressions for asset returns in economic systems governed by persistent vector autoregressive dynamics. In particular, we allow for the state variables to be fractionally integrated, potentially of different orders, and for the returns to have a latent persistent conditional mean, whose memory is difficult to estimate consistently by standard techniques in finite samples. Moreover, the predictors may be endogenous and “imperfect.” In this setting, we develop a consistent local spectrum (LCM) estimation procedure, that delivers asymptotic Gaussian inference. Furthermore, we provide a new LCM-based estimator of the conditional mean persistence, that leverages biased regression slopes as well as new LCM-based tests for significance of (a subset of) the predictors, which are valid even without estimating the return persistence. Simulations illustrate the theoretical arguments. Finally, an empirical application to monthly S&P 500 return predictions provides evidence for a fractionally integrated conditional mean component. Our new LCM procedure and tools indicate significant predictive power for future returns stemming from key state variables such as the default spread and treasury interest rates.

We propose a new estimator, the quadratic form estimator, of the Kronecker product model for covariance matrices. We show that this estimator has good properties in the large dimensional case (i.e., the cross-sectional dimension n is large relative to the sample size T). In particular, the quadratic form estimator is consistent in a relative Frobenius norm sense provided ${\log }^3n/T\to 0$ . We obtain the limiting distributions of the Lagrange multiplier and Wald tests under both the null and local alternatives concerning the mean vector $\mu $ . Testing linear restrictions of $\mu $ is also investigated. Finally, our methodology is shown to perform well in finite sample situations both when the Kronecker product model is true and when it is not true.