Generalized Extreme Value Distribution with Time-Dependence Using the AR and MA Models in State Space Form

A new state space approach is proposed to model the time- dependence in an extreme value process. The generalized extreme value distribution is extended to incorporate the time-dependence using a state space representation where the state variables either follow an autoregressive (AR) process or a moving average (MA) process with innovations arising from a Gumbel distribution. Using a Bayesian approach, an efficient algorithm is proposed to implement Markov chain Monte Carlo method where we exploit a very accurate approximation of the Gumbel distribution by a ten-component mixture of normal distributions. The methodology is illustrated using extreme returns of daily stock data. The model is fitted to a monthly series of minimum returns and the empirical results support strong evidence for time-dependence among the observed minimum returns.Extreme values, Generalized extreme value distribution, Markov chain Monte Carlo, Mixture sampler, State space model, Stock returns

Identification of alleles of carotenoid pathway genes important for zeaxanthin accumulation in potato tubers

We have investigated the genetics and molecular biology of orange flesh colour in potato (Solanum tuberosum L.). To this end the natural diversity in three genes of the carotenoid pathway was assessed by SNP analyses. Association analysis was performed between SNP haplotypes and flesh colour phenotypes in diploid and tetraploid potato genotypes. We observed that among eleven beta-carotene hydroxylase 2 (Chy2) alleles only one dominant allele has a major effect, changing white into yellow flesh colour. In contrast, none of the lycopene epsilon cyclase (Lcye) alleles seemed to have a large effect on flesh colour. Analysis of zeaxanthin epoxidase (Zep) alleles showed that all (diploid) genotypes with orange tuber flesh were homozygous for one specific Zep allele. This Zep allele showed a reduced level of expression. The complete genomic sequence of the recessive Zep allele, including the promoter, was determined, and compared with the sequence of other Zep alleles. The most striking difference was the presence of a non-LTR retrotransposon sequence in intron 1 of the recessive Zep allele, which was absent in all other Zep alleles investigated. We hypothesise that the presence of this large sequence in intron 1 caused the lower expression level, resulting in reduced Zep activity and accumulation of zeaxanthin. Only genotypes combining presence of the dominant Chy2 allele with homozygosity for the recessive Zep allele produced orange-fleshed tubers that accumulated large amounts of zeaxanthin

Handbuch des Hülsenfruchterbaues

von C. Fruwirt