Template-Type: ReDIF-Paper 1.0
Series: Tinbergen Institute Discussion Papers
Creation-Date: 2025-04-17 
Number: 25-027/III
Author-Name: Yicong Lin
Author-Workplace-Name: Vrije Universiteit Amsterdam and Tinbergen Institute
Author-Name: André Lucas
Author-Workplace-Name: Vrije Universiteit Amsterdam and Tinbergen Institute
Title: Functional Location-Scale Models with Robust Observation-Driven Dynamics
Abstract: We introduce a new class of location-scale models for dynamic functional data in arbitrary but fixed dimensions, where the location and scale functional parameters can evolve over time. A key feature of the parameter dynamics in these models is its observation-driven nature, where the one-step-ahead evolution is fully determined conditional on past observations, yet remains stochastic unconditionally. We estimate the model using a likelihood-based approach designed for sparsely observed data and establish the consistency and asymptotic normality of the underlying static parameters that govern the location-scale dynamics. The choice of objective function and the construction of the dynamics together shield the time-varying location and scale parameters from the potentially distorting effects of influential observations. Simulations reveal that our method can recover the unobserved location-scale dynamics from sparse data, even in the presence of model mis-specification and substantial outliers. We apply our framework to examine the intraday volatility dynamics of Pfizer stock returns during the COVID-19 pandemic, and PM2.5 concentrations measured by low-cost sensors across Europe. The proposed model exhibits robust performance in capturing dynamics for both datasets despite the presence of many large shocks.
Classification-JEL: C22, C58, Q56
Keywords: time variation, location-scale, functional score-driven dynamics, sparse data, outlier robustness
File-URL: https://papers.tinbergen.nl/25027.pdf
File-Format: application/pdf
File-Size: 8.939.139 bytes
Handle: RePEc:tin:wpaper:20250027