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To capture the dependence in the upper tail of a time series, we develop non‐negative regularly varying time series models that are constructed similarly to classical non‐extreme ARMA models. Rather than fully characterizing tail dependence of the time series, we define the concept of weak tail stationarity which allows us to describe a regularly varying time series via a measure of pairwise extremal dependencies, the tail pairwise dependence function (TPDF). We state consistency requirements among the finite‐dimensional collections of the elements of a regularly varying time series and show that the TPDF's value does not depend on the dimension of the random vector being considered. So that our models take non‐negative values, we use transformed‐linear operations. We show existence and stationarity of these models, and develop their properties such as the model TPDFs. We fit models to hourly windspeed and daily fire weather index data, and we find that the fitted transformed‐linear models produce better estimates of upper tail quantities than a traditional ARMA model, classical linear regularly varying models, a max‐ARMA model, and a Markov model.

 

Wildfire risk is greatest during high winds after sustained periods of dry and hot conditions. This paper is a statistical extreme-event risk attribution study that aims to answer whether extreme wildfire seasons are more likely now than under past climate. This requires modeling temporal dependence at extreme levels. We propose the use of transformed-linear time series models, which are constructed similarly to traditional autoregressive–moving-average (ARMA) models while having a dependence structure that is tied to a widely used framework for extremes (regular variation). We fit the models to the extreme values of the seasonally adjusted fire weather index (FWI) time series to capture the dependence in the upper tail for past and present climate. We simulate 10 000 fire seasons from each fitted model and compare the proportion of simulated high-risk fire seasons to quantify the increase in risk. Our method suggests that the risk of experiencing an extreme wildfire season in Grand Lake, Colorado, under current climate has increased dramatically relative to the risk under the climate of the mid-twentieth century. Our method also finds some evidence of increased risk of extreme wildfire seasons in Quincy, California, but large uncertainties do not allow us to reject a null hypothesis of no change.

 

Farmers in humid states of US, traditionally reliant on rainfall, have more than tripled irrigation since 1978. We examine this trend in Illinois where there has been a nearly threefold increase in center pivot irrigation system (CPIS) installations since 1988. Specifically, we analyze where and when CPIS installations occur and their benefits in terms of crop yield, irrigated acreage, crop selection, and changes to drought-related insurance payouts. To do so, we create a novel data set derived from a deep learning model capable of automatically identifying the location of CPIS during drought years. The results indicate CPIS installations are significantly more common over alluvial aquifers after droughts. Some evidence supports CPIS leads to corn appearing more often in the corn-soy crop rotation. Counties with a higher presence of CPIS do not have higher average crop yields. However, in drought years CPIS presence does have a significant positive effect on corn yield and a significant negative effect on indemnity payments for both soybeans and corn. The results provide insights into an emerging trend of irrigation in humid regions, raising potential policy considerations for crop insurance and signaling a potential need to address water rights as demand increases. 

Abstract We propose a method for analyzing extremal behavior through the lens of a most efficient basis of vectors. The method is analogous to principal component analysis, but is based on methods from extreme value analysis. Specifically, rather than decomposing a covariance or correlation matrix, we obtain our basis vectors by performing an eigendecomposition of a matrix that describes pairwise extremal dependence. We apply the method to precipitation observations over the contiguous United States. We find that the time series of large coefficients associated with the leading eigenvector shows very strong evidence of a positive trend, and there is evidence that large coefficients of other eigenvectors have relationships with El Niño–Southern Oscillation. 

Motivated by the widespread use of large gridded data sets in the atmospheric sciences, we propose a new model for extremes of areal data that is inspired by the simultaneous autoregressive (SAR) model in classical spatial statistics. Our extreme SAR model extends recent work on transformed‐linear operations applied to regularly varying random vectors, and is unique among extremes models in being directly analogous to a classical linear model. An additional appeal is its simplicity; given a proximity matrixW, spatial dependence is described by a single parameter . We develop an estimation method that minimizes the discrepancy between the tail pairwise dependence matrix (TPDM) for the fitted model and the estimated TPDM. Applying this method to simulated data demonstrates that it is able to produce good estimates of extremal spatial dependence even in the case of model misspecification, and additionally produces reasonable estimates of uncertainty. We also apply the method to gridded precipitation observations for a study region over northeast Colorado, and find that a single‐parameter extreme SAR model paired with a neighborhood structure which accounts for longer range dependence effectively models spatial dependence in these data.

 

To assess the compliance of air quality regulations, the Environmental Protection Agency (EPA) must know if a site exceeds a pre-specified level. In the case of ozone, the level for compliance is fixed at 75 parts per billion, which is high, but not extreme at all locations. We present a new space-time model for threshold exceedances based on the skew-t process. Our method incorporates a random partition to permit long-distance asymptotic independence while allowing for sites that are near one another to be asymptotically dependent, and we incorporate thresholding to allow the tails of the data to speak for themselves. We also introduce a transformed AR(1) time-series to allow for temporal dependence. Finally, our model allows for high-dimensional Bayesian inference that is comparable in computation time to traditional geostatistical methods for large data sets. We apply our method to an ozone analysis for July 2005, and find that our model improves over both Gaussian and max-stable methods in terms of predicting exceedances of a high level.