Likelihood-Based Inference and Model Selection for Record Series

We investigate the statistical properties of upper records observed in a time series $\{X_t\}_{t\geq1}$ under four widely studied record models: the Classical Record, the Yang-Nevzorov, the Linear Drift, and the Discrete-Time Random Walk Model. Our study focuses on the likelihood function constructed from the pairs of record values and their occurrence indicators, denoted as $\{R_n, L_n\}$. Using this likelihood function, we derive estimators for the key parameters governing these models. Furthermore, we explore statistical inference techniques for model selection, enabling the identification of the most suitable record model for a given series. To validate our theoretical findings, we conduct a comprehensive simulation study, illustrating the behavior of the estimators and their performance under different model settings.