Strong consistency estimators of the Brennan‐Schwartz diffusion process based on martingales approach. Issue 1 (8th December 2022)

• Record Type: Journal Article
• Authors: El Ansari, Youness; Chaayra, Toufik; El Bouanani, Faissal; Omari, Lahcen; Amrouch, Mustapha
• Is Part Of: Stat. Volume 11:Issue 1(2022)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2022-12-08
• Subjects: diffusion process -- Euler‐Maruyama scheme -- martingales -- maximum‐likelihood estimator -- real interest rate -- stochastic differential equation -- strong consistency -- strong law of large numbers; Statistics -- Periodicals; 519.2
• DOI: 10.1002/sta4.499
• Languages: English
• ISSNs: 2049-1573

Abstract

Abstract : In this paper, the strong consistency of the Brennan‐Schwartz diffusion process (BSDP) Euler‐maximum likelihood (EML) parameter estimators is investigated. The Euler‐Maruyama scheme is first utilized to produce a discretized solution process, and then, the EML estimation technique is employed to construct explicit forms of the parameter estimators. Following that, using martingale theory (specifically, conditional expectancy, the strong law of large numbers for martingales and some inequalities), we show that, under certain reasonable conditions, the estimators α ^ and β ^ converge almost surely to their true values, implying strong consistency, and the estimator σ ^ 2 converges in L 2 to its true value. We have demonstrated that the interest rates (IRs) of Morocco and France may be represented using the BSDP, taking into consideration the possible convergence requirements of the estimators and some numerical simulation. This model helps us to anticipate how these IRs will evolve in the future years.