Maximum Likelihood Estimation for Non-Stationary Location Models with Mixture of Normal Distributions

Francisco Blasques, Janneke van Brummelen, Paolo Gorgi and Siem Jan Koopman

Journal of Econometrics, 2024, vol. 238, issue 1

Abstract: We consider an observation-driven location model where the unobserved location variable is modeled as a random walk process and where the error variable is from a mixture of normal distributions. The time-varying location can be extended with a stationary process to account for cyclical and/or higher order autocorrelation. The mixed normal distribution can accurately approximate many continuous error distributions. We obtain a flexible modeling framework for the robust filtering and forecasting based on time-series models with non-stationary and nonlinear features. We provide sufficient conditions for strong consistency and asymptotic normality of the maximum likelihood estimator of the parameter vector in the specified model. The asymptotic properties are valid under correct model specification and can be generalized to allow for potential misspecification of the model. A simulation study is carried out to monitor the forecast accuracy improvements when extra mixture components are added to the model. In an empirical study we show that our approach is able to outperform alternative observation-driven location models in forecast accuracy for a time-series of electricity spot prices.

Keywords: Time-varying parameters; Asymmetric and heavy-tailed distributions; Robust filter; Invertibility; Consistency; Asymptotic normality (search for similar items in EconPapers)
JEL-codes: C13 C22 (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:238:y:2024:i:1:s0304407623002919

DOI: 10.1016/j.jeconom.2023.105575

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