On the extremes of randomly sub-sampled time series

In this paper, we investigate the extremal properties of randomly sub-sampled stationary sequences. Motivation comes from the need to account for the effect of missing values on the analysis of time series and the comparison of schemes for monitoring systems with breakdowns or systems with automatic replacement of devices in case of failures

Dynamic fator Models for bivariate Count Data: an application to fire activity

The study of forest re activity, in its several aspects, is essencial to understand the phenomenon and to prevent environmental public catastrophes. In this context the analysis of monthly number of res along several years is one aspect to have into account in order to better comprehend this tematic. The goal of this work is to analyze the monthly number of forest res in the neighboring districts of Aveiro and Coimbra, Portugal, through dynamic factor models for bivariate count series. We use a bayesian approach, through MCMC methods, to estimate the model parameters as well as to estimate the common latent factor to both series

Bivariate models for time series of counts: a comparison study between PBINAR models and dynamic factor models

The aim of this work is to assess the modeling performance of two bivariate models for time series of counts, within the context of a forest fires analysis in two counties of Portugal. The first model is a periodic bivariate integer-valued autoregressive (PBINAR), easily interpreted due to the PINAR description of each component. The alternative model is a bivariate dynamic factor (BDF) that has a flexible structure, with the dynamics described through the mean value of each component that is a function of latent factors. The results reveal that BDF model exhibits a better ability to capture the dependence structure.publishe

The max-BARMA models for counts with bounded support

In this note, we introduce a discrete counterpart of the conventional max-autoregressive moving-average process of Davis & Resnick (1989), based on the binomial thinning operator and driven by a sequence of i. i. d. nonnegative integer-valued random variables with a finite range of counts. Basic probabilistic and statistical properties of this new class of models are discussed in detail, namely the existence of a stationary distribution, and how observations’ and innovations’ distributions are related to each other. Furthermore, parameter estimation is also addressed.publishe

Bivariate binomial autoregressive models

This paper introduces new classes of bivariate time series models being useful to fit count data time series with a finite range of counts. Motivation comes mainly from the comparison of schemes for monitoring tourism demand, stock data, production and environmental processes. All models are based on the bivariate binomial distribution of Type II. First, a new family of bivariate integer-valued GARCH models is proposed. Then, a new bivariate thinning operation is introduced and explained in detail. The new thinning operation has a number of advantages including the fact that marginally it behaves as the usual binomial thinning operation and also that allows for both positive and negative cross-correlations. Based upon this new thinning operation, a bivariate extension of the binomial autoregressive model of order one is introduced. Basic probabilistic and statistical properties of the model are discussed. Parameter estimation and forecasting are also covered. The performance of these models is illustrated through an empirical application to a set of rainy days time series collected from 2000 up to 2010 in the German cities of Bremen and Cuxhaven.publishe

Integer-valued self-exciting threshold autoregressive processes

In this article, we introduce a class of self-exciting threshold integer-valued autoregressive models driven by independent Poisson-distributed random variables. Basic probabilistic and statistical properties of this class of models are discussed. Moreover, parameter estimation is also addressed. Specifically, the methods of estimation under analysis are the least squares-type and likelihood-based ones. Their performance is compared through a simulation study. Copyright © 2012 Taylor and Francis Group, LLC

Extreme value and cluster analysis of European daily temperature series

Time series of daily mean temperature obtained from the European Climate Assessment data set is analyzed with respect to their extremal properties. A time-series clustering approach which combines Bayesian methodology, extreme value theory and classification techniques is adopted for the analysis of the regional variability of temperature extremes. The daily mean temperature records are clustered on the basis of their corresponding predictive distributions for 25-, 50- and 100-year return values. The results of the cluster analysis showa clear distinction between the highest altitude stations, for which the return values are lowest, and the remaining stations. Furthermore, a clear distinction is also found between the northernmost stations in Scandinavia and the stations in central and southern Europe. This spatial structure of the return period distributions for 25-, 50- and 100-years seems to be consistent with projected changes in the variability of temperature extremes over Europe pointing to a different behavior in central Europe than in northern Europe and the Mediterranean area, possibly related to the effect of soil moisture and land-atmosphere coupling.‘Acções Integradas Luso-Espanholas’ under the grants E-83/09 and HP2008- 008

The Structure of Climate Variability Across Scales

One of the most intriguing facets of the climate system is that it exhibits variability across all temporal and spatial scales; pronounced examples are temperature and precipitation. The structure of this variability, however, is not arbitrary. Over certain spatial and temporal ranges it can be described by scaling relationships in the form of power‐laws in probability density distributions and autocorrelation functions. These scaling relationships can be quantified by scaling exponents which measure how the variability changes across scales and how the intensity changes with frequency of occurrence. Scaling determines the relative magnitudes and persistence of natural climate fluctuations. Here, we review various scaling mechanisms and their relevance for the climate system. We show observational evidence of scaling and discuss the application of scaling properties and methods in trend detection, climate sensitivity analyses, and climate predictio

Changes in extreme sea-levels in the Baltic Sea

In a climate change context, changes in extreme sea-levels rather than changes in the mean are of particular interest from the coastal protection point of view. In this work, extreme sea-levels in the Baltic Sea are investigated based on daily tide gauge records for the period 1916–2005 using the annual block maxima approach. Extreme events are analysed based on the generalised extreme value distribution considering both stationary and time-varying models. The likelihood ratio test is applied to select between stationary and non-stationary models for the maxima and return values are estimated from the final model. As an independent and complementary approach, quantile regression is applied for comparison with the results from the extreme value approach. The rates of change in the uppermost quantiles are in general consistent and most pronounced for the northernmost stations

Self-exciting threshold binomial autoregressive processes

We introduce a new class of integer-valued self-exciting threshold models, which is based on the binomial autoregressive model of order one as introduced by McKenzie (Water Resour Bull 21:645–650, 1985. doi:10.1111/j.1752-1688.1985. tb05379.x). Basic probabilistic and statistical properties of this class of models are discussed. Moreover, parameter estimation and forecasting are addressed. Finally, the performance of these models is illustrated through a simulation study and an empirical application to a set of measle cases in Germany