Strong Uniform Consistency of the Frequency Polygon Density Estimator for Stable Non-Anticipative Stochastic Processes

TL;DR

This paper proves the strong uniform consistency of the frequency polygon density estimator for certain stable non-anticipative stationary stochastic processes, providing a new mathematical expression and relevant examples.

Contribution

It introduces a new mathematical expression for the frequency polygon and establishes its strong uniform consistency for stable non-anticipative stationary processes.

Findings

Proves strong uniform consistency of the frequency polygon estimator.

Provides examples of applicable time series models.

Introduces a new mathematical expression for the frequency polygon.

Abstract

The author establishes a new mathematical expression for the Frequency Polygon. He uses it to prove the strong uniform consistency of the Frequency Polygon marginal density estimator for non-anticipative stationary stochastic processes which are stable in the sense of Wu. He gives examples of several times series models for which this result is relevant.