# Oscillating Gaussian Processes

## TL;DR

This paper introduces oscillating Gaussian processes constructed from stationary or self-similar Gaussian processes, analyzes their properties, and develops parameter estimation methods with proven convergence and asymptotic normality.

## Contribution

It defines a new class of oscillating Gaussian processes and provides theoretical results on their properties and parameter estimation techniques.

## Key findings

- Moment estimators converge in L^p
- Estimators are asymptotically normal when normalized
- Basic properties of oscillating Gaussian processes are characterized

## Abstract

In this article we introduce and study oscillating Gaussian processes defined by $X_t = \alpha_+ Y_t {\bf 1}_{Y_t >0} + \alpha_- Y_t{\bf 1}_{Y_t<0}$, where $\alpha_+,\alpha_->0$ are free parameters and $Y$ is either stationary or self-similar Gaussian process. We study the basic properties of $X$ and we consider estimation of the model parameters. In particular, we show that the moment estimators converge in $L^p$ and are, when suitably normalised, asymptotically normal.