THE CORRELATION STRUCTURE OF THE LATENT COMPONENTS OF THE TIME SERIES WITH DISCRETE LAPLACE MARGINALS AND ITS IMPACT ON PARAMETER ESTIMATION

Abstract

The main subject of this paper is the proposal of a new method for parameter  estimation, applicable to time series with a discrete Laplace marginal distribution. The proposed estimators are derived from the correlation structure of the latent components of the time series. In this context, the complete correlation structure of the latent components is established and thoroughly analyzed. Based on these results, new estimators are defined, and their key statistical properties, including unbiasedness, consistency, and asymptotic behavior, are rigorously examined. Owing to their fast convergence properties, the proposed estimators are particularly advantageous in low-data regimes, enabling, for example, more effective training of machine learning models on limited datasets. A comparison with existing estimators is also provided, highlighting several important improvements in efficiency and applicability. Finally, all theoretical findings are supported and validated through simulation studies and real-life data applications.