Multivariate integer-valued time series with flexible autocovariances and their application to major hurricane counts

Abstract

This paper examines a bivariate count time series with some curious statistical features: Saffir–Simpson Category 3 and stronger annual hurricane counts in the North Atlantic and eastern Pacific Ocean Basins. As land and ocean temperatures on our planet warm, an intense climatological debate has arisen over whether hurricanes are becoming more numerous, or whether the strengths of the individual storms are increasing. Recent literature concludes that an increase in hurricane counts occurred in the Atlantic Basin circa 1994. This increase persisted through 2012; moreover, the 1994–2012 period was one of relative inactivity in the eastern Pacific Basin. When Atlantic activity eased in 2013, heavy activity in the eastern Pacific Basin commenced. When examined statistically, a Poisson white noise model for the annual severe hurricane counts is difficult to resoundingly reject. Yet, decadal cycles (longer term dependence) in the hurricane counts is plausible. This paper takes a statistical look at the issue, developing a stationary multivariate count time series model with Poisson marginal distributions and a flexible autocovariance structure. Our auto- and cross-correlations can be negative and have long-range dependence; features that most previous count models cannot achieve in tandem. Our model is new in the literature and is based on categorizing and super-positioning multivariate Gaussian time series. We derive the autocovariance function of the model and propose a method to estimate model parameters. In the end, we conclude that severe hurricane counts are indeed negatively correlated across the two ocean basins. Some evidence for long-range dependence is also presented; however, with only a 49-year record, this issue cannot be definitively judged without additional data.