Statistical modelling of tropical cyclone tracks: modelling the autocorrelation in track shape

TL;DR

This paper develops a statistical model for hurricane tracks focusing on autocorrelation in fluctuations, using AR(1) models, and evaluates its effectiveness through various diagnostic methods.

Contribution

It introduces a method to model autocorrelations in hurricane track fluctuations using AR(1) models, advancing previous models of mean and variance.

Findings

The AR(1) model captures key behaviors of hurricane tracks.

The model shows systematic errors in detailed predictions.

Goodness-of-fit assessments demonstrate reasonable performance.

Abstract

We describe results from the third stage of a project to build a statistical model for hurricane tracks. In the first stage we modelled the unconditional mean track. In the second stage we modelled the unconditional variance of fluctuations around the mean. Now we address the question of how to model the autocorrelations in the standardised fluctuations. We perform a thorough diagnostic analysis of these fluctuations, and fit a type of AR(1) model. We then assess the goodness of fit of this model in a number of ways, including an out-of-sample comparison with a simpler model, an in-sample residual analysis, and a comparison of simulated tracks from the model with the observed tracks. Broadly speaking, the model captures the behaviour of observed hurricane tracks. In detail, however, there are a number of systematic errors.