An exponential continuous time GARCH process

In this paper we introduce an exponential continuous time GARCH(p,q) process. It is defined in such a way that it is a continuous time extension of the discrete time EGARCH(p,q) process. We investigate stationarity and moment properties of the new model. An instantaneous leverage effect can be shown for the exponential continuous time GARCH(p,p) model

Mixed effect model for absolute log returns of ultra high frequency data

The influence of covariates on absolute log returns of ultra high frequency data is analysed. Therefore we construct a mixed effect model for the absolute log returns. The parameters are estimated in a state space approach. To analyse the correlation in these irregularly spaced data empirically, the variogram, known mainly from spatial statistics, will be used. In a small simulation study the performance of the estimators will be analysed. In the end we apply the model to IBM trade data and analyse the influence of the covariates

Quasi maximum likelihood estimation and prediction in the compound Poisson ECOGARCH(1,1) model

This paper deals with the problem of estimation and prediction in a compound Poisson ECOGARCH(1,1) model. For this we construct a quasi maximum likelihood estimator under the assumption that all jumps of the log-price process are observable. Since these jumps occur at unequally spaced time points, it is clear that the estimator has to be computed for irregularly spaced data. Assuming normally distributed jumps and a recursion to estimate the volatility allows to define and compute a quasi-likelihood function, which is maximised numerically. The small sample behaviour of the estimator is analysed in a small simulation study. Based on the recursion for the volatility process a one-step ahead prediction of the volatility is defined as well as a prediction interval for the log-price process. Finally the model is fitted to tick-by-tick data of the New York Stock Exchange

A fractionally integrated ECOGARCH process

In this paper we introduce a fractionally integrated exponential continuous time GARCH(p,d,q) process. It is defined in such a way that it is a continuous time extension of the discrete time FIEGARCH(p,d,q) process. We investigate stationarity and moment properties of the new model. It is also shown that the long memory effect introduced in the log-volatility propagates to the volatility process

Estimating the COGARCH(1,1) model - a first go

We suggest moment estimators for the parameters of a continuous time GARCH(1,1) process based on equally spaced observations. Using the fact that the increments of the COGARCH(1,1) process are ergodic, the resulting estimators are consistent. We investigate the quality of our estimators in a simulation study based on the compound Poisson driven COGARCH model. The estimated volatility with corresponding residual analysis is also presented

Eumetazoan cryptochrome phylogeny and evolution

Cryptochromes (Crys) are light sensing receptors that are present in all eukaryotes. They mainly absorb light in the UV/blue spectrum. The extant Crys consist of two subfamilies, which are descendants of photolyases but are now involved in the regulation of circadian rhythms. So far, knowledge about the evolution, phylogeny, and expression of cry genes is still scarce. The inclusion of cry sequences from a wide range of bilaterian species allowed us to analyze their phylogeny in detail, identifying six major Cry subgroups. Selective gene inactivations and stabilizations in multiple chordate as well as arthropod lineages suggest several sub- and/or neofunctionalization events. An expression study performed in zebrafish, the model organism harboring the largest amount of crys, showed indeed only partially overlapping expression of paralogous mRNA, supporting gene sub- and/or neofunctionalization. Moreover, the daily cry expression in the adult zebrafish retina indicated varying oscillation patterns in different cell types. Our extensive phylogenetic analysis provides for the first time an overview of cry evolutionary history. Although several, especially parasitic or blind species, have lost all cry genes, crustaceans have retained up to three crys, teleosts possess up to seven, and tetrapods up to four crys. The broad and cyclic expression pattern of all cry transcripts in zebrafish retinal layers implies an involvement in retinal circadian processes and supports the hypothesis of several autonomous circadian clocks present in the vertebrate retina

Helical stability of the GnTV transmembrane domain impacts on SPPL3 dependent cleavage

Signal-Peptide Peptidase Like-3 (SPPL3) is an intramembrane cleaving aspartyl protease that causes secretion of extracellular domains from type-II transmembrane proteins. Numerous Golgi-localized glycosidases and glucosyltransferases have been identified as physiological SPPL3 substrates. By SPPL3 dependent processing, glycan-transferring enzymes are deactivated inside the cell, as their active site-containing domain is cleaved and secreted. Thus, SPPL3 impacts on glycan patterns of many cellular and secreted proteins and can regulate protein glycosylation. However, the characteristics that make a substrate a favourable candidate for SPPL3-dependent cleavage remain unknown. To gain insights into substrate requirements, we investigated the function of a GxxxG motif located in the transmembrane domain of N-acetylglucosaminyltransferase V (GnTV), a well-known SPPL3 substrate. SPPL3-dependent secretion of the substrate’s ectodomain was affected by mutations disrupting the GxxxG motif. Using deuterium/hydrogen exchange and NMR spectroscopy, we studied the effect of these mutations on the helix flexibility of the GnTV transmembrane domain and observed that increased flexibility facilitates SPPL3-dependent shedding and vice versa. This study provides first insights into the characteristics of SPPL3 substrates, combining molecular biology, biochemistry, and biophysical techniques and its results will provide the basis for better understanding the characteristics of SPPL3 substrates with implications for the substrates of other intramembrane proteases