We present an extreme-value analysis of the classical law of the iterated logarithm (LIL) for Brownian motion. Our result can be viewed as a new improvement to the LIL.

Large fires are a major disturbance in Canadian forests and exert significant effects on both the climate system and ecosystems. During the last century, extremely large fires accounted for the majority of Canadian burned area. By making an instaneous change over a vast area of ecosystems, extreme fires often have significant social, economic, and ecological consequences. Since extreme values o...

Extreme value theory for the maximum of a time series of daily precipitation amount is described. A chain-dependent process is assumed as a stochastic model for daily precipitation, with the intensity distribution being the gamma. To examine how the e€ective return period for extreme high precipitation amounts would change as the parameters of the chain-dependent process change (i.e., probabili...

In this paper, we describe a new version (≥ 2.0) of the R (R Core Team 2013) package extRemes (Gilleland and Katz 2011), which is a major redesign from previous versions. Weather and climate applications are the intended focus of the package, although the functions could be used in other applications. The new version of the package is a command-line package for implementing various methods from...

Abstract: We develop Bayesian nonparametric modeling and inference methods for the analysis of extremes of stochastic processes. We use a point process approach under which the pairwise observations, comprising the time of excesses and the exceedances over a high threshold, are assumed to arise from a non-homogeneous Poisson process. To understand and capture the behavior of rare events, we pro...

The debate over the Phillips Curve as the relation between level of unemployment rate and inflation rate in historical economics is shortly reviewed. By using the analysis in the Extreme Value Theory, i.e.: the rank order statistics the unemployment and inflation data over countries from various regions are observed. The calculations brought us to conjecture that there exists the general patter...

The least-squares (or Lomb-Scargle) periodogram is a powerful tool which is used routinely in many branches of astronomy to search for periodicities in observational data. The problem of assessing statistical significance of candidate periodicities for different periodograms is considered. Based on results in extreme value theory, improved analytic estimations of false alarm probabilities are g...

The objectives of a robust statistical analysis and of an extreme value analysis apparently are contradictory. Where the extreme data are downweighted in robust statistics, these observations receive most attention in an extreme value approach. The most prominent extreme value methods however are constructed on maximum likelihood estimates based on specific parametric models which are fitted to...

Crude oil markets are highly volatile and risky. Extreme value theory (EVT), an approach to modelling and measuring risks under rare events, has seen a more prominent role in risk management in recent years. This paper presents an application of EVT to the daily returns of crude oil prices in the Canadian spot market between 1998 and 2006. We focus on the peak over threshold method by analyzing...