Continuous Record Asymptotics in Systems of Stochastic Differential Equations

This paper considers estimation based on a set of <italic>T</italic> + 1 discrete observations, <italic>y</italic>(0), <italic>y</italic>(<italic>h</italic>), <italic>y</italic>(2<italic>h</italic>),…, <italic>y</italic>(<italic>Th</italic>) = <italic>y</italic>(<italic>N</italic>), where <italic>h</italic> is the sampling frequency and <italic>N</italic> is the span of the data. In contrast to the standard approach of driving <italic>N</italic> to infinity for a fixed sampling frequency, the current paper follows Phillips [35,36] and Perron [29] and examines the “dual” asymptotics implied by letting <italic>h</italic> tend to zero while the span <italic>N</italic> remains fixed.