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

Integer-valued self-exciting periodic threshold autoregressive processes

In this paper, the periodic self-exciting threshold integer-valued autoregressive model of order one with period $T$ driven by a periodic sequence of independent Poisson-distributed random variables is introduced and analyzed in detail. Basic probabilistic and statistical properties of the model are discussed as well as parameter estimation and forecasting

Summarising changes in air temperature over Central Europe by quantile regression and clustering

The analysis of trends in air temperature observations is one of the most common activities in climate change studies. This work examines the changes in daily mean air temperature over Central Europe using quantile regression, which allows the estimation of trends, not only in the mean but in all parts of the data distribution. A bootstrap procedure is applied for assessing uncertainty on the derived slopes and the resulting distributions are summarised via clustering. The results show considerable spatial diversity over the central European region. A distinct behaviour is found for lower (5 %) and upper (95 %) quantiles, with higher trends around 0.15 C decade^{−1} at the 5 % quantile and around 0.20 C decade^{−1} at the 95% quantile, the largest trends (>0.2 C decade^{−1}) occurring in the Alps.grants E-83/09, HP2008-008 and SEJ2007-6450

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

Integer-valued APARCH processes in the analysis of time series of counts

The Asymmetric Power Arch representation for the volatility was introduced by Ding et al.(1993) in order to account for asymmetric responses in the volatility in the analysis of continuous-valued financial time series like, for instance, the log-return series of foreign exchange rates, stock indices or share prices. As reported by Brannas and Quoreshi (2010), asymmetric responses in volatility are also observed in time series of counts such as the number of intra-day transactions in stocks. In this work, an asymmetric power autoregressive conditional Poisson model is introduced for the analysis of time series of counts exhibiting asymmetric overdispersion. Basic probabilistic and statistical properties are summarized and parameter estimation is discussed. A simulation study is presented to illustrate the proposed model. Finally, an empirical application to a set of data concerning the daily number of stock transactions is also presented to attest for its practical applicability in data analysis

A multiplicative thinning-based integer-valued GARCH model

In this paper we introduce a multiplicative integer-valued time series model, which is defined as the product of a unit-mean integer-valued independent and identically distributed (iid) sequence, and an integer-valued dependent process. The latter is defined as a binomial thinning operation of its own past and of the past of the observed process. Furthermore, it combines some features of the integer-valued GARCH (INGARCH), the autoregressive conditional duration (ACD), and the integer autoregression (INAR) processes. The proposed model is semi-parametric and is able to parsimoniously generate very high overdispersion, persistence, and heavy-tailedness. The dynamic probabilistic structure of the model is first analyzed. In addition, parameter estimation is considered by using a two-stage weighted least squares estimate (2SWLSE), consistency and asymptotic normality (CAN) of which are established under mild conditions. Applications of the proposed formulation to simulated and actual count time series data are provided

Association between respiratory hospital admissions and air quality in Portugal: a count time series approach

Although regulatory improvements for air quality in the European Union have been made, air pollution is still a pressing problem and, its impact on health, both mortality and morbidity, is a topic of intense research nowadays. The main goal of this work is to assess the impact of the exposure to air pollutants on the number of daily hospital admissions due to respiratory causes in 58 spatial locations of Portugal mainland, during the period 2005-2017. To this end, INteger Generalised AutoRegressive Conditional Heteroskedastic (INGARCH)-based models are extensively used. This family of models has proven to be very useful in the analysis of serially dependent count data. Such models include information on the past history of the time series, as well as the effect of external covariates. In particular, daily hospitalisation counts, air quality and temperature data are endowed within INGARCH models of optimal orders, where the automatic inclusion of the most significant covariates is carried out through a new block-forward procedure. The INGARCH approach is adequate to model the outcome variable (respiratory hospital admissions) and the covariates, which advocates for the use of count time series approaches in this setting. Results show that the past history of the count process carries very relevant information and that temperature is the most determinant covariate, among the analysed, for daily hospital respiratory admissions. It is important to stress that, despite the small variability explained by air quality, all models include on average, approximately two air pollutants covariates besides temperature. Further analysis shows that the one-step-ahead forecasts distributions are well separated into two clusters: one cluster includes locations exclusively in the Lisbon area (exhibiting higher number of one-step-ahead hospital admissions forecasts), while the other contains the remaining locations. This results highlights that special attention must be given to air quality in Lisbon metropolitan area in order to decrease the number of hospital admissions.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