On the log quantile difference of the temporal aggregation of a stable moving average process

TL;DR

This paper derives a formula for the log quantile difference in the temporal aggregation of stable MA(q) processes, showing its dependence on process parameters but not on quantile levels, with detailed analysis of MA(1) and MA(2).

Contribution

It provides a new formula for analyzing the log quantile difference in stable MA processes and explores its behavior across different process parameters.

Findings

Log quantile difference depends on process parameters, not quantile levels.

Shape of log quantile difference varies with aggregation level and process parameters.

Detailed analysis of invertible stable MA(1) and MA(2) processes.

Abstract

A formula is derived for the log quantile difference of the temporal aggregation of some types of stable moving average processes, MA(q). The shape of the log quantile difference as a function of the aggregation level is examined and shown to be dependent on the parameters of the moving average process but not the quantile levels. The classes of invertible, stable MA(1) and MA(2) processes are examined in more detail.