Tests in functional autoregressive processes via local asymptotic normality condition

Local asymptotic normality (LAN) and uniform local asymptotic normality (ULAN) conditions are obtained for a linear functional autoregressive process of order p, p >= 1, using a martingale central limit theorem. As a consequence of the LAN property, asymptotically efficient tests for determining the order are constructed. An example is discussed as a special cases.

Automated summary

This article obtains the conditions of local asymptotic normality (LAN) and uniform local asymptotic normality (ULAN) for a linear functional autoregressive process using a martingale central limit theorem. As a consequence, asymptotically efficient tests for determining the order are constructed. An example is discussed as a special case.