Practical Considerations for Fixed-Smoothing Limiting Distributions

Music City Center 

In time series analysis, performing inference on parameters using Wald-type statistics requires adjustments for serial correlation or conditional heteroskedasticity. We use the spectral variance estimator for long-run variance, which makes minimal assumptions about the error term.

We examine two methods for obtaining critical values (CVs): adaptive-smoothing asymptotics, yielding standard chi-square CVs, and fixed-smoothing asymptotics, producing non-standard CVs that need approximation. The fixed-smoothing framework, including lugsail kernels, better captures long-run variance influences on test statistics, especially under strong correlation.

Our contributions include exploring methods for approximating fixed-smoothing CVs and comparing their performance across classical time series models in univariate and multivariate settings. We evaluate estimator corrections, mean squared error, bandwidth selection methods, and testing performance.

These findings extend the work of Kiefer and Vogelsang (2005), Lazarus et al. (2018), Sun (2014), and Kurtz-Garcia and Flegal (2024), offering practical support for researchers using fixed-smoothing frameworks and spectral variance-like estimators in various data contexts, such as spatial and longitudinal data.