Statistical Modelling of the Annual Rainfall Pattern in Guanacaste, Costa Rica

Rainfall in Guanacaste, Costa Rica, has marked wet/dry phases: the rainy season is punctuated by a short midsummer drought, and the dry season frequently has months of no rain. In this region, spring and summer rainfall peaks are important for local rain-fed agriculture and annual total for groundwater recharge and hydroelectricity production. We propose a novel model of rainfall in this region, the double-Gaussian model, which uses monthly total rainfall data collected from 1980 to 2020 from two meteorological observation stations. Our model provides an intuitive way of describing the seasonality of rainfall, the inter-annual variability of the cycle, and variability due to the monthly Oceanic Niño Index, ONI. We also consider two alternative models, a regression model with ARMA errors and a Tweedie model, as a means of assessing the robustness of our conclusions to violations of the assumptions of the double-Gaussian model. We found that the data provide strong evidence of an increase/decrease in rainfall in both temporal maxima during La Niña/El Niño (negative/positive ONI) conditions but no evidence of a decade-scale trend after accounting for ONI effects. Finally, we investigated the problem of forecasting future rainfall based on our three models. We found that when ONI is incorporated as a predictor variable, our models can produce substantial gains in prediction accuracy of spring, summer, and annual totals over naive methods based on monthly sample means or medians

A variance component test for mixed hidden Markov models

The mixed hidden Markov model incorporates covariates and random effects in the hidden Markov model framework. In this paper, we develop a variance component test in the case where there is only one random effect.

Statistical Modelling of the Annual Rainfall Pattern in Guanacaste, Costa Rica

Rainfall in Guanacaste, Costa Rica, has marked wet/dry phases: the rainy season is punctuated by a short midsummer drought, and the dry season frequently has months of no rain. In this region, spring and summer rainfall peaks are important for local rain-fed agriculture and annual total for groundwater recharge and hydroelectricity production. We propose a novel model of rainfall in this region, the double-Gaussian model, which uses monthly total rainfall data collected from 1980 to 2020 from two meteorological observation stations. Our model provides an intuitive way of describing the seasonality of rainfall, the inter-annual variability of the cycle, and variability due to the monthly Oceanic Niño Index, ONI. We also consider two alternative models, a regression model with ARMA errors and a Tweedie model, as a means of assessing the robustness of our conclusions to violations of the assumptions of the double-Gaussian model. We found that the data provide strong evidence of an increase/decrease in rainfall in both temporal maxima during La Niña/El Niño (negative/positive ONI) conditions but no evidence of a decade-scale trend after accounting for ONI effects. Finally, we investigated the problem of forecasting future rainfall based on our three models. We found that when ONI is incorporated as a predictor variable, our models can produce substantial gains in prediction accuracy of spring, summer, and annual totals over naive methods based on monthly sample means or medians