Numerical convergence of the Block-Maxima approach to the generalized extreme value distribution

In this paper we perform an analytical and numerical study of Extreme Value distributions in discrete dynamical systems. In this setting, recent works have shown how to get a statistics of extremes in agreement with the classical Extreme Value Theory. We pursue these investigations by giving analytical expressions of Extreme Value distribution parameters for maps that have an absolutely continuous invariant measure. We compare these analytical results with numerical experiments in which we study the convergence to limiting distributions using the so called block-maxima approach, pointing out in which cases we obtain robust estimation of parameters. In regular maps for which mixing properties do not hold, we show that the fitting procedure to the classical Extreme Value Distribution fails, as expected. However, we obtain an empirical distribution that can be explained starting from a different observable function for which Nicolis et al. (Phys. Rev. Lett. 97(21): 210602, 2006) have found analytical results.

Extreme value distribution for singular measures

In this paper we perform an analytical and numerical study of Extreme Value distributions in discrete dynamical systems that have a singular measure. Using the block maxima approach described in Faranda et al. [2011] we show that, numerically, the Extreme Value distribution for these maps can be associated to the Generalised Extreme Value family where the parameters scale with the information dimension. The numerical analysis are performed on a few low dimensional maps. For the middle third Cantor set and the Sierpinskij triangle obtained using Iterated Function Systems, experimental parameters show a very good agreement with the theoretical values. For strange attractors like Lozi and H\`enon maps a slower convergence to the Generalised Extreme Value distribution is observed. Even in presence of large statistics the observed convergence is slower if compared with the maps which have an absolute continuous invariant measure. Nevertheless and within the uncertainty computed range, the results are in good agreement with the theoretical estimates.

Modelling European winter wind storm losses in current and future climate

Severe wind storms are one of the major natural hazards in the extratropics and inflict substantial economic damages and even casualties. Insured storm-related losses depend on (i) the frequency, nature and dynamics of storms, (ii) the vulnerability of the values at risk, (iii) the geographical distribution of these values, and (iv) the particular conditions of the risk transfer. It is thus of great importance to assess the impact of climate change on future storm losses. To this end, the current study employs—to our knowledge for the first time—a coupled approach, using output from high-resolution regional climate model scenarios for the European sector to drive an operational insurance loss model. An ensemble of coupled climate-damage scenarios is used to provide an estimate of the inherent uncertainties. Output of two state-of-the-art global climate models (HadAM3, ECHAM5) is used for present (1961–1990) and future climates (2071–2100, SRES A2 scenario). These serve as boundary data for two nested regional climate models with a sophisticated gust parametrizations (CLM, CHRM). For validation and calibration purposes, an additional simulation is undertaken with the CHRM driven by the ERA40 reanalysis. The operational insurance model (Swiss Re) uses a European-wide damage function, an average vulnerability curve for all risk types, and contains the actual value distribution of a complete European market portfolio. The coupling between climate and damage models is based on daily maxima of 10 m gust winds, and the strategy adopted consists of three main steps: (i) development and application of a pragmatic selection criterion to retrieve significant storm events, (ii) generation of a probabilistic event set using a Monte-Carlo approach in the hazard module of the insurance model, and (iii) calibration of the simulated annual expected losses with a historic loss data base. The climate models considered agree regarding an increase in the intensity of extreme storms in a band across central Europe (stretching from southern UK and northern France to Denmark, northern Germany into eastern Europe). This effect increases with event strength, and rare storms show the largest climate change sensitivity, but are also beset with the largest uncertainties. Wind gusts decrease over northern Scandinavia and Southern Europe. Highest intra-ensemble variability is simulated for Ireland, the UK, the Mediterranean, and parts of Eastern Europe. The resulting changes on European-wide losses over the 110-year period are positive for all layers and all model runs considered and amount to 44% (annual expected loss), 23% (10 years loss), 50% (30 years loss), and 104% (100 years loss). There is a disproportionate increase in losses for rare high-impact events. The changes result from increases in both severity and frequency of wind gusts. Considerable geographical variability of the expected losses exists, with Denmark and Germany experiencing the largest loss increases (116% and 114%, respectively). All countries considered except for Ireland (−22%) experience some loss increases. Some ramifications of these results for the socio-economic sector are discussed, and future avenues for research are highlighted. The technique introduced in this study and its application to realistic market portfolios offer exciting prospects for future research on the impact of climate change that is relevant for policy makers, scientists and economists.

Modelling economic returns to plant variety protection in the UK

This paper attempts an empirical assessment of the incentive effects of plant variety protection regimes in the generation of crop variety innovations. A duration model of plant variety protection certificates is used to infer the private appropriability of returns from agricultural crop variety innovations in the UK over the period 1965-2000. The results suggest that plant variety protection provides only modest appropriability of returns to innovators of agricultural crop varieties. The value distribution of plant variety protection certificates is highly skewed with a large proportion of innovations providing virtually no returns to innovators. Increasing competition from newer varieties appears to have accelerated the turnover of varieties reducing appropriability further. Plant variety protection emerges as a relatively weak instrument of protection.

Identification and ranking of extraordinary rainfall events over northwest Italy: the role of Atlantic moisture

An objective identification and ranking of extraordinary rainfall events for Northwest Italy is established using time series of annual precipitation maxima for 1938–2002 at over 200 stations. Rainfall annual maxima are considered for five reference durations (1, 3, 6, 12, and 24 h). In a first step, a day is classified as an extraordinary rainfall day when a regional threshold calculated on the basis of a two-components extreme value distribution is exceeded for at least one of the stations. Second, a clustering procedure taking into account the different rainfall durations is applied to the identified 163 events. Third, a division into six clusters is chosen using Ward's distance criteria. It is found that two of these clusters include the seven strongest events as quantified from a newly developed measure of intensity which combines rainfall intensities and spatial extension. Two other clusters include the weakest 72% historical events. The obtained clusters are analyzed in terms of typical synoptic characteristics. The two top clusters are characterized by strong and persistent upper air troughs inducing not only moisture advection from the North Atlantic into the Western Mediterranean but also strong northward flow towards the southern Alpine ranges. Humidity transports from the North Atlantic are less important for the weaker clusters. We conclude that moisture advection from the North Atlantic plays a relevant role in the magnitude of the extraordinary events over Northwest Italy.

Loss potentials associated with European windstorms under future climate conditions

Possible changes in the frequency and intensity of windstorms under future climate conditions during the 21st century are investigated based on an ECHAM5 GCM multi-scenario ensemble. The intensity of a storm is quantified by the associated estimated loss derived with using an empirical model. The geographical focus is ‘Core Europe’, which comprises countries of Western Europe. Possible changes of losses are analysed by comparing ECHAM5 GCM data for recent (20C, 1960 to 2000) and future climate conditions (B1, A1B, A2; 2060 to 2100), each with 3 ensemble members. Changes are quantified using both rank statistics and return periods (RP) estimated by fitting an extreme value distribution using the peak over threshold method to potential storm losses. The estimated losses for ECHAM5 20C and reanalysis events show similar statistical features in terms of return periods. Under future climate conditions, all climate scenarios show an increase in both frequency and magnitude of potential losses caused by windstorms for Core Europe. Future losses that are double the highest ECHAM5 20C loss are identified for some countries. While positive changes of ranking are significant for many countries and multiple scenarios, significantly shorter RPs are mostly found under the A2 scenario for return levels correspondent to 20 yr losses or less. The emergence time of the statistically significant changes in loss varies from 2027 to 2100. These results imply an increased risk of occurrence of windstorm-associated losses, which can be largely attributed to changes in the meteorological severity of the events. Additionally, factors such as changes in the cyclone paths and in the location of the wind signatures relative to highly populated areas are also important to explain the changes in estimated losses.

Effect of high dose selenium enriched yeast diets on the distribution of total selenium and selenium species within lamb tissues

The objective of this study was to determine the distribution of total selenium (Se) and of the proportion of total Se comprised as the selenized amino acids selenomethionine (SeMet) and selenocysteine (SeCys) within the post mortem tissues of lambs that were fed high dose selenized enriched yeast (SY), derived from a specific strain of Saccharomyces cerevisae CNCM (Collection Nationale de Culture de Micro-organism) I-3060. Thirty two Texel X Suffolk lambs (6.87 ± 0.23 kg BW) were offered both reconstituted milk replacer and a pelleted diet, both of which had been either supplemented with high SY (6.30 ± 0.18 mg Se/kg DM) or unsupplemented (0.13 ± 0.01 mg Se/kg of DM), depending on treatment designation, for a continuous period of 91 d. At enrollment and 28, 56 and 91 d following enrollment lambs were blood sampled. At the completion of the treatment period, five lambs from each treatment group were euthanased and samples of heart, liver, kidney and skeletal muscle (Longissimus Dorsi and Psoas Major) were retained for Se analysis. The inclusion of high SY increased (P < 0.001) whole blood Se concentration, reaching a maximum mean value of 815.2 ± 19.1 ng Se/mL compared with 217.8 ± 9.1 ng Se/mL in control animals. Tissue total Se concentrations were significantly (P < 0.001) higher in SY supplemented animals than in controls irrespective of tissue type; values were 26, 16, 8 and 3 times higher in skeletal muscle, liver, heart and kidney tissue of HSY lambs when compared to controls. however, the distribution of total Se and the proportions of total Se comprised as either SeMet or SeCys differed between tissue types. Selenocysteine was the predominant selenized amino acid in glandular tissues, such the liver and kidney. irrespective of treatment, although absolute values were markedly higher in HSY lambs. Conversely selenomethionine was the predominat selenized amino acid in cardiac and skeletal muscle (Longissimus Dorsi, and Psoas Major) tissues in HSY animals, although the same trend was not apparent for control lambs in which SeCys was the predominant selenized amino acid. It was concluded that there were increases in both whole blood and tissue total Se concentrations as a result of dietary supplementation with high dose of SY. Furthermore, distribution of total Se and Se species differed between both treatment designation and tissue type.

Trust and governance of global value chains: The case of a Brazilian beef processor

Purpose - The purpose of this paper is to offer an exploratory case study comparing one Brazilian beef processor's relationships supplying two different distribution channels, an EU importer and an EU retail chain operating in Brazil. Design/methodology/approach - The paper begins with a short review of global value chains and the recent literature on trust. It gives the background to the Brazilian beef chain and presents data obtained through in-depth interviews, annual reports and direct observation with the Brazilian beef processor, the EU importer and the retailer. The interviews were conducted with individual firms, but the analysis places them in a chain context, identifying the links and relationships between the agents of the chains and aiming to describe each distribution channel. Findings - Executive chain governance exercised by the domestic retailer stimulates technical upgrading and transferring of best practices to local. suppliers. Consequently, this kind of relationship results in more trust within the global value chain. Practical implications - There are difficulties and challenges facing this Brazilian beef processor that are party related to the need to comply with increasingly complex and demanding food safety and food quality standards. There is still a gap between practices adopted for the export market and practices adopted locally. The strategies of transnational retailers in offering differentiated beef should be taken in account. Originality/value - The research outlines an interdisciplinary framework able to explain chain relationships and the kind of trust that emerges in relationships between EU importer/retail and a developing country supplier.

The air distribution index as an indicator for energy consumption and performance of ventilation systems

This paper deals with the energy consumption and the evaluation of the performance of air supply systems for a ventilated room involving high- and low-level supplies. The energy performance assessment is based on the airflow rate, which is related to the fan power consumption by achieving the same environmental quality performance for each case. Four different ventilation systems are considered: wall displacement ventilation, confluent jets ventilation, impinging jet ventilation and a high level mixing ventilation system. The ventilation performance of these systems will be examined by means of achieving the same Air Distribution Index (ADI) for different cases. The widely used high-level supplies require much more fan power than those for low-level supplies for achieving the same value of ADI. In addition, the supply velocity, hence the supply dynamic pressure, for a high-level supply is much larger than for low-level supplies. This further increases the power consumption for high-level supply systems. The paper considers these factors and attempts to provide some guidelines on the difference in the energy consumption associated with high and low level air supply systems. This will be useful information for designers and to the authors' knowledge there is a lack of information available in the literature on this area of room air distribution. The energy performance of the above-mentioned ventilation systems has been evaluated on the basis of the fan power consumed which is related to the airflow rate required to provide equivalent indoor environment. The Air Distribution Index (ADI) is used to evaluate the indoor environment produced in the room by the ventilation strategy being used. The results reveal that mixing ventilation requires the highest fan power and the confluent jets ventilation needs the lowest fan power in order to achieve nearly the same value of ADI.

Depreciation, income distribution and the UK REIT

Purpose – The purpose of this paper is to consider prospects for UK REITs, which were introduced on 1 January 2007. It specifically focuses on the potential influence of depreciation and expenditure on income and distributions. Design/methodology/approach – First, the ways in which depreciation can affect vehicle earnings and value are discussed. This is then set in the context of the specific rules and features of REITs. An analysis using property income and expenditure data from the Investment Property Databank (IPD) then assesses what gross and net income for a UK REIT might have been like for the period 1984-2003. Findings – A UK REIT must distribute at least 90 per cent of net income from its property rental business. Expenditure therefore plays a significant part in determining what funds remain for distribution. Over 1984-2003, expenditure has absorbed 20 per cent of gross income and been a source of earnings volatility, which would have been exacerbated by gearing. Practical implications – Expenditure must take place to help UK REITs maintain and renew their real estate portfolios. In view of this, investors should moderate expectations of a high and stable income return, although it may well still be so relative to alternative investments. Originality/value – Previous literature on depreciation has not quantified amounts spent on portfolios to keep depreciation at those rates. Nor, to our knowledge, has its ideas been placed in the indirect investor context.

A comparison of extreme value theory approaches for determining value at risk

This paper compares a number of different extreme value models for determining the value at risk (VaR) of three LIFFE futures contracts. A semi-nonparametric approach is also proposed, where the tail events are modeled using the generalised Pareto distribution, and normal market conditions are captured by the empirical distribution function. The value at risk estimates from this approach are compared with those of standard nonparametric extreme value tail estimation approaches, with a small sample bias-corrected extreme value approach, and with those calculated from bootstrapping the unconditional density and bootstrapping from a GARCH(1,1) model. The results indicate that, for a holdout sample, the proposed semi-nonparametric extreme value approach yields superior results to other methods, but the small sample tail index technique is also accurate.

The effect of asymmetries on stock index return value-at-risk estimates

It is widely accepted that equity return volatility increases more following negative shocks rather than positive shocks. However, much of value-at-risk (VaR) analysis relies on the assumption that returns are normally distributed (a symmetric distribution). This article considers the effect of asymmetries on the evaluation and accuracy of VaR by comparing estimates based on various models.

An extreme value theory approach to calculating minimum capital risk requirements

This paper investigates the frequency of extreme events for three LIFFE futures contracts for the calculation of minimum capital risk requirements (MCRRs). We propose a semiparametric approach where the tails are modelled by the Generalized Pareto Distribution and smaller risks are captured by the empirical distribution function. We compare the capital requirements form this approach with those calculated from the unconditional density and from a conditional density - a GARCH(1,1) model. Our primary finding is that both in-sample and for a hold-out sample, our extreme value approach yields superior results than either of the other two models which do not explicitly model the tails of the return distribution. Since the use of these internal models will be permitted under the EC-CAD II, they could be widely adopted in the near future for determining capital adequacies. Hence, close scrutiny of competing models is required to avoid a potentially costly misallocation capital resources while at the same time ensuring the safety of the financial system.

Initial distribution spread: A density forecasting approach

Ensemble forecasting of nonlinear systems involves the use of a model to run forward a discrete ensemble (or set) of initial states. Data assimilation techniques tend to focus on estimating the true state of the system, even though model error limits the value of such efforts. This paper argues for choosing the initial ensemble in order to optimise forecasting performance rather than estimate the true state of the system. Density forecasting and choosing the initial ensemble are treated as one problem. Forecasting performance can be quantified by some scoring rule. In the case of the logarithmic scoring rule, theoretical arguments and empirical results are presented. It turns out that, if the underlying noise dominates model error, we can diagnose the noise spread.

Geoarchaeology and the value of multidisciplinary palaeoenvironmental approaches: a case study from the Tehran Plain, Iran

Tepe Pardis, a significant Neolithic–Chalcolithic site on the Tehran Plain in Iran, is, like many sites in the area, under threat from development. The site contains detailed evidence of (1) the Neolithic–Chalcolithic transition, (2) an Iron Age cemetery and (3) how the inhabitants adapted to an unstable fan environment through resource exploitation (of clay deposits for relatively large-scale ceramic production by c. 5000 BC, and importantly, possible cutting of artificial water channels). Given this significance, models have been produced to better understand settlement distribution and change in the region. However, these models must be tied into a greater understanding of the impact of the geosphere on human development over this period. Forming part of a larger project focusing on the transformation of simple, egalitarian Neolithic communities into more hierarchical Chalcolithic ones, the site has become the focus of a multidisciplinary project to address this issue. Through the combined use of sedimentary and limited pollen analysis, radiocarbon and optically stimulated luminescence dating (the application of the last still rare in Iran), a greater understanding of the impact of alluvial fan development on human settlement through alluviation and the development of river channel sequences is possible. Notably, the findings presented here suggest that artificial irrigation was occurring at the site as early as 6.7±0.4 ka (4300–5100 BC).