Abstract

Abstract
The high-order statistics (moments and cumulants of order higher than two) have been widely applied in several fields, specially in problems where it is conjectured a lack of Gaussianity and/or non-linearity. Since the INteger-valued AutoRegressive, INAR, processes are non-Gaussian, the high-order statistics can provide additional information that allows a better characterization of these processes. Thus, an estimation method for the parameters of an INAR process, based on Least Squares for the third-order moments is proposed. The results of a Monte Carlo study to investigate the performance of the estimator are presented and the method is applied to a set of real data.

Abstract
In this work we consider the problem of forecasting integer-valued time series, modelled by the INAR(1) process introduced by McKenzie (1985) and Al-Osh and Alzaid (1987). The theoretical properties and practical applications of INAR and related processes have been discussed extensively in the literature but there is still some discussion on the problem of producing coherent, i.e. integer-valued, predictions. Here Bayesian methodology is used to obtain point predictions as well as confidence intervals for future values of the process. The predictions thus obtained are compared with their classic counterparts. The proposed approaches are illustrated with a simulation study and a real example.

Abstract
The detection of a trend in a time series and the evaluation of its magnitude and statistical significance is an important task in geophysical research. This importance is amplified in climate change contexts, since trends are often used to characterize long-term climate variability and to quantify the magnitude and the statistical significance of changes in climate time series, both at global and local scales. Recent studies have demonstrated that the stochastic behavior of a time series can change the statistical significance of a trend, especially if the time series exhibits long-range dependence. The present study examines the trends in time series of daily average temperature recorded in 26 stations in the Tuscany region (Italy). In this study a new framework for trend detection is proposed. First two parametric statistical tests, the Phillips-Perron test and the Kwiatkowski-Phillips-Schmidt-Shin test, are applied in order to test for trend stationary and difference stationary behavior in the temperature time series. Then long-range dependence is assessed using different approaches, including wavelet analysis, heuristic methods and by fitting fractionally integrated autoregressive moving average models. The trend detection results are further compared with the results obtained using nonparametric trend detection methods: Mann-Kendall, Cox-Stuart and Spearman's rho tests. This study confirms an increase in uncertainty when pronounced stochastic behaviors are present in the data. Nevertheless, for approximately one third of the analyzed records, the stochastic behavior itself cannot explain the long-term features of the time series, and a deterministic positive trend is the most likely explanation.

Abstract
Atmospheric pressure varies within a wide range of scales and thus a multi-scale description of its variability is particularly appealing. In this study, a scale-by-scale analysis of the global sea-level pressure field is carried out from reanalysis data. Wavelet-based analysis of variance is applied in order to describe the variability of the pressure field in terms of patterns representing the contribution of each scale to the overall variance. Signals at the seasonal scales account for the largest fraction of sea-level pressure variance (typically more than 60%) except in the Southern Ocean, in the Equatorial Pacific and in the North Atlantic. In the Southern Ocean and over the North Atlantic, high-frequency signals contribute to a considerable fraction (30-50%) of the overall variance in sea-level pressure. In the Equatorial Pacific, large-scale variability, associated with ENSO, contributes up to 40% of the total variance.

Abstract
Long-term sea-level variability in Chesapeake Bay is examined from long tide gauge records in order to assess the influence of climate factors on sea-level changes in this complex estuarine system. A time series decomposition method based on autoregression is applied to extract flexible seasonal and low-frequency components from the tide gauge records, allowing to analyse long-term sea-level variability not only by estimating linear trends from the records, but also by examining fluctuations in seasonal and long-term patterns. Long-term sea-level variability in Chesapeake Bay shows considerable decadal variability. At the annual scale, variability is mainly determined by atmospheric factors, specifically atmospheric pressure and zonal wind, but no systematic trends are found in the amplitude of the annual cycle. On longer time scales, precipitation rate, a proxy for river discharge, is the main factor influencing decadal sea-level variability. Linear trends in relative sea-level heights range from 2.66 +/- 0.075 mm/year (at Baltimore) to 4.40 +/- 0.086 mm/year (at Hampton Roads) for the 1955-2007 period. Due to the gentle slope of most of the bay margin, a sea-level increase of this magnitude poses a significant threat in terms of wetland loss and consequent environmental impacts.