Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.33392

Fitting time-varying parameter models via partially noncentered parametrizations

Lingjie Wang·Rufeng Liu·Abhinek Shukla·Linda S. L. Tan
View original source ↗Read source document ↗Export metadata ↓

Abstract

Time-varying parameter (TVP) models are widely used to capture evolving relationships but inference is often computationally demanding due to high-dimensional latent states. The efficiency of iterative algorithms depends critically on the choice of latent state augmentation, with centering preferred for genuinely time-varying coefficients and noncentering favored when coefficients are nearly constant. We propose a partially noncentered parametrization that bridges these extremes via dimension-specific working parameters for both location and scale. Optimal working parameters are derived by analyzing EM convergence rates, and an alternating expectation-conditional maximization algorithm is developed to implement the approach. As the convergence rate of mean-field variational Bayes (MFVB) is closely related to EM, we extend the approach to develop partially noncentered MFVB algorithms for the TVP model, placing triple gamma priors on baseline coefficients and process variances to induce shrinkage. Simulations and empirical applications show that the resulting MFVB algorithms yield posterior approximations closer to Markov chain Monte Carlo than conventional centered or noncentered parametrizations. We also develop an efficient solver for the block tridiagonal inverse matrices arising in the proposed algorithms.

Explore related subjects

stat.ME

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Lingjie Wang, Rufeng Liu, Abhinek Shukla, Linda S. L. Tan. 2026-10-24. Fitting time-varying parameter models via partially noncentered parametrizations. https://arxiv.org/abs/2610.33392

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Denoising Data with Measurement Error Using a Reproducing Kernel-Based Diffusion Model

Recent advancements in measurement technologies have facilitated the acquisition of high-resolution data in fields such as engineering, biology, and medicine. However, these observations are frequently corrupted by measurement noise. To address this challenge, we propose a denoising framework that employs diffusion models to recover the underlying error-free data distribution, thereby enabling reliable downstream analysis. Central to our framework is a novel Reproducing Kernel Hilbert Space (RKHS)-based method that trains the diffusion model using only error-contaminated data. This method admits a closed-form solution and achieves a fast convergence rate in terms of estimation error. Theoretically, we validate our approach by deriving an upper bound on the total variation distance between the distributions of the generated denoised data and the true error-free data. Extensive simulations demonstrate the superior empirical performance of our method compared to state-of-the-art baselines. Finally, we illustrate the framework's practical utility in digital health and epidemiology by applying it to Continuous Glucose Monitor (CGM) data and the association analysis between blood lipids and coronary heart disease.

stat.ME↗
arXiv2026

Two-stage least squares with treatment-covariate interactions for treatment effect heterogeneity

Treatment effect heterogeneity with respect to covariates is common in instrumental variable (IV) analyses. An intuitive approach, which we call the interacted two-stage least squares (2sls), is to regress the outcome on the treatment, covariates, and treatment-covariate interactions, using the IV, covariates, and IV-covariate interactions as instruments. We clarify the causal interpretation of the interacted 2sls under the local average treatment effect (LATE) framework when the IV is valid conditional on the covariates. Our main findings are twofold. First, we show that the coefficients on the treatment-covariate interactions from the interacted 2sls identify treatment effect heterogeneity with respect to covariates among compliers for any outcome-generating process if and only if the product of the IV propensity score and the covariates is linear in the covariates, a requirement we call the linear IV-covariate interactions condition. Second, when the covariate vector has dimension K and includes a constant term, we show that the linear IV-covariate interactions condition requires the IV propensity score to take at most K distinct values. The condition holds when (a) the covariates take exactly K distinct values, or (b) the IV is randomly assigned independently of the covariates, but is restrictive beyond these cases. These results underscore the difficulty of interpreting regression coefficients from specifications with treatment-covariate interactions when the covariates are not saturated and the IV is not unconditionally randomized, absent correct specification of the outcome model. We then connect these results to the literature on LATE estimation, and show that under the linear IV-covariate interactions condition, the interacted 2sls with covariates demeaned by their complier means recovers the LATE as a single coefficient.

stat.ME↗
arXiv2026

Sliding-Window Signatures as Features for Time Series Forecasting

The evolution of a time series is often influenced not only by its past values but also by external covariates, giving rise to forecasting with exogenous variables. Nonlinear and delayed effects between covariates and the target series make this task particularly challenging. We propose a forecasting framework based on Ridge regression with sliding-window signature features, combining the computational efficiency of (semi-)parametric models with the flexibility of nonparametric approaches. These features capture complex dependencies between the target and the exogenous variables without relying on prior assumptions about the form of these relationships or the influence of past observations. We establish theoretical guarantees in the discrete-time setting, including universality of approximation and stationarity for the sliding-window transform. To ease implementation, we introduce a novel sequential algorithm that exploits window overlap for efficient signature updates. The method is evaluated on both synthetic and real electricity demand data. Results show that signature features effectively encode temporal and nonlinear dependencies, yielding accurate forecasts competitive with those based on expert knowledge and recent neural network approaches.

stat.ME↗