A0892
Title: Testing weak dependence and stationarity by universal inference
Authors: Arnab Bhattacharjee - Heriot-Watt University (United Kingdom) [presenting]
Joseph Paul - Heriot-Watt University (United Kingdom)
Mark Schaffer - Heriot-Watt University (United Kingdom)
Abstract: A sequential universal inference (UI) test is presented for detecting strong spatial dependence and non-stationarity in dynamic panel data with expanding dimensions $N$ and $T$. Starting from a general spatial autoregressive (SAR) model with both contemporaneous and lagged spatial effects, an incremental likelihood-ratio is computed between an unrestricted quasi-MLE and the null of zero contemporaneous and lagged spatial coefficients. The cumulative product of these ratios forms a non-negative martingale with unit mean under the null, so Villes' inequality results in an any-time, finite-sample level-$\alpha$ test as the time dimension $T$ grows, without relying on large-$T$ or large-$N$ approximations. The roles of the two dimensions are interchangeable, hence the argument works in both the cross-section and time dimensions. Inverting the same statistic delivers finite-sample confidence sets for the spatial-autoregressive parameters that remain valid in finite samples. Monte-Carlo evidence shows strong size and power performance relative to the Pesaran CD test, a prior study, and conventional asymptotic LR tests, especially when spatial coefficients lie near the unit-root boundary. Robust extensions are outlined for heavy-tailed and heteroskedastic disturbances, and an asymptotic refinement that results in an exact asymptotically level-$\alpha$ test is derived.
