Local generalised method of moments: an application to point process-based rainfall models.

Area of Science:

• Environmental science
• Hydrology
• Statistical modeling

Background:

• Clustered point process models are used for rainfall simulation but are limited by stationarity.
• Existing models are unsuitable for climate impact studies due to their inability to capture non-stationary rainfall patterns.

Purpose of the Study:

• To develop a new methodology to address the stationarity limitation in rainfall models.
• To extend current fitting approaches by incorporating continuous covariates related to rainfall characteristics.

Main Methods:

• Replaced discrete calendar month covariates with continuous covariates in point process models.
• Estimated covariate-dependent model parameters using a kernel-based nonparametric approach.
• Employed a generalized method-of-moments framework for parameter estimation.

Main Results:

• Demonstrated the new methodology using a time series of 5-min rainfall data.
• Considered both local mean and local linear approaches for parameter estimation.
• Addressed practical issues such as weighting matrix selection, parameter uncertainty, bandwidth selection, and model selection.

Conclusions:

• The developed methodology provides a usable approach for creating non-stationary rainfall models.
• This advancement is crucial for improving the accuracy of climate impact studies.
• The new method enhances the simulation of rainfall patterns by moving beyond static models.