| Abstract: | We consider temporal aggregation of lognormal autoregressive (AR) processes. More specifically, we develop a novel moment‐matching approximation for temporally aggregated lognormal AR processes. In addition, we show that our approximation provides the closest lognormal AR process in terms of Kullback–Leibler divergence. Moreover, we perform a simulation study to compare our proposed approximation with two competing approximations. This study shows that in terms of L1‐ and L2‐norm distances our approximation provides superior results. Our results have an important practical application and one main practical implication. In terms of practical application, our approximation can provide possible candidate solutions for simulation‐based algorithms such as the Metropolis–Hastings algorithm. The practical implication gives support to common practice: when the original fine‐level process follows a lognormal AR process but only aggregated data are available, then instead of assuming a Gaussian process it is better to assume a lognormal AR process at the aggregated level. Finally, we illustrate the utility of our results with two applications. The first example considers a simulated dataset whereas the second example examines the number of yearly sunspots in the period 1700–1984. |
