# Joint Time Series and Cross-Section Limit Theory under Mixingale Assumptions

## TL;DR

This paper extends joint time series and cross-section limit theory to include serial correlation, providing new limiting distributions under strict stationarity and independence assumptions, relevant for models with aggregate uncertainty.

## Contribution

It introduces a framework allowing serial correlation in joint limit theory, expanding the applicability of previous results to more realistic data scenarios.

## Key findings

- Derived limiting distributions with long run variances for serially correlated data
- Established conditions for stationarity and independence in joint convergence
- Applicable to estimators combining time series and cross-section data

## Abstract

In this paper we complement joint time series and cross-section convergence results of Hahn, Kuersteiner and Mazzocco (2016) by allowing for serial correlation in the time series sample. The implications of our analysis are limiting distributions that have a well known form of long run variances for the time series limit. We obtain these results at the cost of imposing strict stationarity for the time series model and conditional independence between the time series and cross-section samples. Our results can be applied to estimators that combine time series and cross-section data in the presence of aggregate uncertainty in models with rationally forward looking agents.