Sea Level Rise (SLR) is one of the major challenges the world is facing in times of climate change. Using different approaches in obtaining, studying and modeling SLR data has often resulted in different conclusions for the same data set. This led to a debate between researchers some of whom reported accelerations whereas others advocated decelerations or linear trend. In this project, we model SLR as a linear mean reverting time series, also known as order one autoregressive processes (AR(1)), together with an in-depth study of the innovations associated with the AR process. In this direction, we dene and evaluate moment ratio test to distinguishbetween innovations which come either from a Gaussian distribution, a Gumbel distribution or a mixture of the two. We were motivated by a claim from members of the Actuarial Climate Index (ACI) collaborative regarding the distribution of sea-level rise in the US Atlantic states. They claim that the monthly data, recorded over decades, have no inherent time structure and can be modeled as independent and identically observations from Gumbel distribution. Based on an exploratory data analysis, fitting a stationary, Markovian, mean-revering process to the data was essential, to understand its structure. Since the Ornstein Uhlenbeck process (OU) is the high-frequency liming process for AR(1) processes, and our data has a fixed frequency of observations, we investigated fitting an AR(1) process where the innovations are either Gumbel noise, Gaussian noise, or a mixture of the two distributions. The result of these fittings, based on our moment-ratio tests and other diagnostic checks, demonstrates the preference for an AR(1) process with innovations from a mixture of Gaussian and Gumbel distributions.
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