Distribution-free changepoint detection tests based on the breaking of records

The analysis of record-breaking events is of interest in fields such as climatology, hydrology or anthropology. In connection with the record occurrence, we propose three distribution-free statistics for the changepoint detection problem. They are CUSUM-type statistics based on the upper and/or lower record indicators observed in a series. Using a version of the functional central limit theorem, we show that the CUSUM-type statistics are asymptotically Kolmogorov distributed. The main results under the null hypothesis are based on series of independent and identically distributed random variables, but a statistic to deal with series with seasonal component and serial correlation is also proposed. A Monte Carlo study of size, power and changepoint estimate has been performed. Finally, the methods are illustrated by analyzing the time series of temperatures at Madrid, Spain. The R package RecordTest publicly available on CRAN implements the proposed methods

RecordTest: An R Package to Analyze Non-Stationarity in the Extremes Based on Record-Breaking Events

The study of non-stationary behavior in the extremes is important to analyze data in environmental sciences, climate, finance, or sports. As an alternative to the classical extreme value theory, this analysis can be based on the study of record-breaking events. The R package RecordTest provides a useful framework for non-parametric analysis of non-stationary behavior in the extremes, based on the analysis of records. The underlying idea of all the non-parametric tools implemented in the package is to use the distribution of the record occurrence under series of independent and identically distributed continuous random variables, to analyze if the observed records are compatible with that behavior. Two families of tests are implemented. The first only requires the record times of the series, while the second includes more powerful tests that join the information from different types of records: upper and lower records in the forward and backward series. The package also offers functions that cover all the steps in this type of analysis such as data preparation, identification of the records, exploratory analysis, and complementary graphical tools. The applicability of the package is illustrated with the analysis of the effect of global warming on the extremes of the daily maximum temperature series in Zaragoza, Spain

Record tests to detect non-stationarity in the tails with an application to climate change

The analysis of trends and other non-stationary behaviours at the extremes of a series is an important problem in global warming. This work proposes and compares several statistical tools to analyse that behaviour, using the properties of the occurrence of records in i.i.d. series. The main difficulty of this problem is the scarcity of information in the tails, so it is important to obtain all the possible evidence from the available data. First, different statistics based on upper records are proposed, and the most powerful is selected. Then, using that statistic, several approaches to join the information of four types of records, upper and lower records of forward and backward series, are suggested. It is found that these joint tests are clearly more powerful. The suggested tests are specifically useful in analysing the effect of global warming in the extremes, for example, of daily temperature. They have a high power to detect weak trends and can be widely applied since they are non-parametric. The proposed statistics join the information of M independent series, which is useful given the necessary split of the series to arrange the data. This arrangement solves the usual problems of climate series (seasonality and serial correlation) and provides more series to find evidence. These tools are used to analyse the effect of global warming on the extremes of daily temperature in Madrid

Statistical analysis of extreme and record-breaking daily maximum temperatures in peninsular Spain during 1960–2021

This work analyses the effects of global warming in the upper extremes of daily temperature series over Spain. This objective implies specific analysis, since time evolution of mean temperature is not always parallel to evolution of the extremes. We propose the use of several record tests to study the behavior of the extreme and record-breaking events in different temperature signals, at different time and spatial scales. The underlying idea of the tests is to compare the occurrence of the extreme events in the observed series and the occurrence in a stationary climate. Given that under global warming, an increasing trend, or an increasing variability, can be expected, the alternative is that the probability of the extremes is higher than in a stationary climate. Some of the tests, based on a permutation approach, can be applied to sets of correlated series and this allows the analysis of short periods of time and regional analysis, where series are measured in close days and/or locations. Using these tests, we evaluate and compare the effects of climate change in temperature extreme and record-breaking events using 36 series of daily maximum temperature from 1960 to 2021, all over peninsular Spain. We also compare the behavior in different Spanish regions, in different periods of the year, and in different signals such as the annual maximum temperature. Significant evidences of the effect of an increasing trend in the occurrence of upper extremes are found in most of Spain. The effects are heterogeneous within the year, being autumn the season where the effects are weaker and summer where they are stronger. Concerning the spatial variability, the Mediterranean and the North Atlantic region are the areas where the effects are more and less clear, respectively

Bayesian variable selection in generalized extreme value regression: modeling annual maximum temperature

In many applications, interest focuses on assessing relationships between covariates and the extremes of the distribution of a continuous response. For example, in climate studies, a usual approach to assess climate change has been based on the analysis of annual maximum data. Using the generalized extreme value (GEV) distribution, we can model trends in the annual maximum temperature using the high number of available atmospheric covariates. However, there is typically uncertainty in which of the many candidate covariates should be included. Bayesian methods for variable selection are very useful to identify important covariates. However, such methods are currently very limited for moderately high dimensional variable selection in GEV regression. We propose a Bayesian method for variable selection based on a stochastic search variable selection (SSVS) algorithm proposed for posterior computation. The method is applied to the selection of atmospheric covariates in annual maximum temperature series in three Spanish stations

Modelos bayesianos para representar el efecto de variables atmosféricas en series diarias de temperatura.

La creciente evidencia del cambio climático, impulsado por el aumento de la concentración de gases de efecto invernadero en la atmósfera, sugiere un aumento generalizado de las temperaturas. Sin embargo, este aumento puede variar significativamente a lo largo del año y entre diferentes regiones geográficas. La identificación precisa de la existencia y magnitud de estas tendencias temporales y espaciales es crucial para formular estrategias de gestión efectivas que mitiguen los impactos adversos del aumento de temperaturas en la salud humana, la agricultura y la economía. Por lo tanto, el objetivo principal de este estudio es desarrollar modelos basados en datos para analizar los efectos del cambio climático en las temperaturas y su variabilidad geográfica en España, utilizando series temporales de temperaturas diarias.La metodología empleada se basa en artículos publicados en el Journal of Agricultural, Biological and Environmental Statistics y en Annals of Applied Statistics por Castillo-Mateo et al. Esos autores utilizaron modelos jerárquicos bayesianos para hacer inferencias sobre la distribución de la temperatura máxima diaria en Aragón. Esos trabajos muestran que la distribución de la temperatura diaria tiene un patrón estacional que afecta tanto al valor medio como a la varianza. De acuerdo con Castillo-Mateo et al., hemos decidido establecer nuestro marco en el enfoque bayesiano debido al hecho de que ofrece un ajuste flexible y una inferencia completa. Nos centramos en 40 estaciones españolas, en el período del 1 de enero de 1955 al 31 de diciembre de 2022, con una amplia variabilidad climática y geográfica. Las series de datos son proporcionadas por la base de datos europea ECA&D. Utilizamos el paquete R bamlss, que proporciona herramientas para la inferencia bayesiana de modelos aditivos flexibles. Este paquete es particularmente adecuado para nuestro análisis ya que buscamos desarrollar un modelo conjunto para la media y la varianza de las temperaturas máximas diarias.Para resumir, el Capítulo 1 trata sobre la introducción, objetivos y fases y procedimientos de este trabajo.El Capítulo 2 contiene una revisión de ideas básicas de modelos lineales, inferencia bayesiana y modelos jerárquicos bayesianos. Las principales ideas y resultados de los trabajos de Castillo-Mateo et al. se resumen para considerar las características que deben ser representadas por modelos estadísticos, como efectos autorregresivos, comportamiento estacional y tendencia temporal. Los resultados de Castillo-Mateo et al. se revisan porque muestran que es necesario modelar la varianza.El Capítulo 3 establecerá el procedimiento para llevar a cabo el análisis exploratorio y posteriormente la inferencia bayesiana. En particular, se propone la estructura del modelo. Se incluye una breve descripción de la función R desarrollada para hacer inferencias.El Capítulo 4 resume los principales resultados obtenidos al aplicar la metodología a series diarias de temperaturas en 40 estaciones meteorológicas españolas. Comenzaremos con un análisis exploratorio de datos, a través de varios procedimientos como el uso de cuantiles móviles de 30 días. Continuaremos con la construcción de modelos lineales para la media y la varianza, y su análisis posterior. A su vez, estudiaremos la distribución espacial de los predictores lineales. Después, desarrollamos un modelo bayesiano local y uno global y los comparamos, además de analizar la distribución posterior de parámetros asociados a la tendencia temporal, es decir, a las señales de cambio climático. Se encuentra que los elementos del modelo son necesarios, tanto la memoria de orden 2 como la tendencia en el valor medio y la varianza. También se descubre que hay una variabilidad geográfica que no se reproduce perfectamente utilizando solo covariables geográficas.Finalmente, en el Capítulo 5, destacamos los principales resultados e implicaciones de este trabajo. Y, concluimos con la propuesta de futuros trabajos y líneas de investigación.<br /

Model-based tools for assessing space and time change in daily maximum temperature: an application to the Ebro basin in Spain

There is continuing interest in the investigation of change in temperature over space and time. We offer a set of tools to illuminate such change temporally, at desired temporal resolution, and spatially, according to region of interest, using data generated from suitable space-time models. These tools include predictive spatial probability surfaces and spatial extents for an event. Working with exceedance events around the center of the temperature distribution, the probability surfaces capture the spatial variation in the risk of an exceedance event, while the spatial extents capture the expected proportion of incidence of a given exceedance event for a region of interest. Importantly, the proposed tools can be used with the output from any suitable model fitted to any set of spatially referenced time series data. As an illustration, we employ a dataset from 1956 to 2015 collected at 18 stations over Arag\'{o}n in Spain, and a collection of daily maximum temperature series obtained from posterior predictive simulation of a Bayesian hierarchical daily temperature model. The results for the summer period show that although there is an increasing risk in all the events used to quantify the effects of climate change, it is not spatially homogeneous, with the largest increase arising in the center of Ebro valley and Eastern Pyrenees area. The risk of an increase of the average temperature between 1966-1975 and 2006-2015 higher than $1^\circ$C is higher than 0.5 all over the region, and close to 1 in the previous areas. The extent of daily temperature higher than the reference mean has increased 3.5% per decade. The mean of the extent indicates that 95% of the area under study has suffered a positive increment of the average temperature, and almost 70% higher than $1^{\circ}$C.Comment: 23 pages main manuscript and 7 pages supplemen

Spatial quantile autoregression for season within year daily maximum temperature data

Regression is the most widely used modeling tool in statistics. Quantile regression offers a strategy for enhancing the regression picture beyond customary mean regression. With time-series data, we move to quantile autoregression and, finally, with spatially referenced time series, we move to space-time quantile regression. Here, we are concerned with the spatiotemporal evolution of daily maximum temperature, particularly with regard to extreme heat. Our motivating data set is 60 years of daily summer maximum temperature data over Aragón in Spain. Hence, we work with time on two scales—days within summer season across years—collected at geocoded station locations. For a specified quantile, we fit a very flexible, mixed-effects autoregressive model, introducing four spatial processes. We work with asymmetric Laplace errors to take advantage of the available conditional Gaussian representation for these distributions. Further, while the autoregressive model yields conditional quantiles, we demonstrate how to extract marginal quantiles with the asymmetric Laplace specification. Thus, we are able to interpolate quantiles for any days within years across our study region

Assessing space and time changes in daily maximum temperature in the Ebro basin (Spain) using model-based statistical tools

There is continuing interest in the investigation of change in temperature over space and time. For this analysis, we offer statistical tools to illuminate changes temporally, at desired temporal resolution, and spatially, using data generated from suitable space–time models. The proposed tools can be used with the output from any suitable model fitted to any set of spatially referenced time series data. The tools to assess space and time changes include spatial surfaces of probabilities and spatial extents for events defined by exceeding a threshold. The spatial surfaces capture the spatial variation in the probability or risk of an exceedance event, while the spatial extents capture the expected proportion of incidence of an event for a region of interest. This approach is used analyse the changes in daily maximum temperature in an inland Mediterranean region (NE of Spain) in the period 1956–2015. The area is very heterogeneous in orography and climate, including the central Ebro valley and part of the Pyrenees. We use a collection of daily temperature series obtained from simulation under a Bayesian daily temperature model fitted to 18 stations in that area. The results for the summer period show that, although there is an increasing risk in all the events used to quantify the effects of climate change, it is not spatially homogeneous, with the largest increase arising in the centre of the Ebro valley and the Eastern Pyrenees area. The risk of an increase in the average daily maximum temperature from 1966–1975 to 2006–2015 higher than 1°C is higher than 0.5 over all of the region, and close to 1 in the previous areas. The extent of daily maximum temperature higher than the reference mean has increased 3.5% per decade. The mean of the extent indicates that 95% of the area under study has suffered a positive increment of the average temperature, and almost 70% an increment higher than 1°C

Bayesian joint quantile autoregression

Quantile regression continues to increase in usage, providing a useful alternative to customary mean regression. Primary implementation takes the form of so-called multiple quantile regression, creating a separate regression for each quantile of interest. However, recently, advances have been made in joint quantile regression, supplying a quantile function which avoids crossing of the regression across quantiles. Here, we turn to quantile autoregression (QAR), offering a fully Bayesian version. We extend the initial quantile regression work of Koenker and Xiao (2006) in the spirit of Tokdar and Kadane (2012). We offer a directly interpretable parametric model specification for QAR. Further, we offer a p-th order QAR(p) version, a multivariate QAR(1) version, and a spatial QAR(1) version. We illustrate with simulation as well as a temperature dataset collected in Arag\'on, Spain.Comment: 21 pages (+18 pages supplement), 8 figures (+15 figures supplement), 1 table (+6 tables supplement