Parametric estimation of the driving L\'evy process of multivariate CARMA processes from discrete observations

We consider the parametric estimation of the driving L\'evy process of a multivariate continuous-time autoregressive moving average (MCARMA) process, which is observed on the discrete time grid $(0,h,2h,...)$. Beginning with a new state space representation, we develop a method to recover the driving L\'evy process exactly from a continuous record of the observed MCARMA process. We use tools from numerical analysis and the theory of infinitely divisible distributions to extend this result to allow for the approximate recovery of unit increments of the driving L\'evy process from discrete-time observations of the MCARMA process. We show that, if the sampling interval $h=h_N$ is chosen dependent on $N$, the length of the observation horizon, such that $N h_N$ converges to zero as $N$ tends to infinity, then any suitable generalized method of moments estimator based on this reconstructed sample of unit increments has the same asymptotic distribution as the one based on the true increments, and is, in particular, asymptotically normally distributed.Comment: 38 pages, four figures; to appear in Journal of Multivariate Analysi

A Continuous Time GARCH Process of Higher Order

A continuous time GARCH model of order (p,q) is introduced, which is driven by a single Lévy process. It extends many of the features of discrete time GARCH(p,q) processes to a continuous time setting. When p=q=1, the process thus defined reduces to the COGARCH(1,1) process of Klüppelberg, Lindner and Maller (2004). We give sufficient conditions for the existence of stationary solutions and show that the volatility process has the same autocorrelation structure as a continuous time ARMA process. The autocorrelation of the squared increments of the process is also investigated, and conditions ensuring a positive volatility are discussed

A double-helix neutron detector using micron-size B-10 powder

A double-helix electrode configuration is combined with a $^{10}$B powder coating technique to build large-area (9 in $\times$ 36 in) neutron detectors. The neutron detection efficiency for each of the four prototypes is comparable to a single 2-bar $^3$He drift tube of the same length (36 in). One unit has been operational continuously for 18 months and the change of efficiency is less than 1%. An analytic model for pulse heigh spectra is described and the predicted mean film thickness agrees with the experiment to within 30%. Further detector optimization is possible through film texture, power size, moderator box and gas. The estimated production cost per unit is less than 3k US\$ and the technology is thus suitable for deployment in large numbers

Linear prediction of ARMA processes with infinite variance

AbstractIn order to predict unobserved values of a linear process with infinite variance, we introduce a linear predictor which minimizes the dispersion (suitably defined) of the error distribution. When the linear process is driven by symmetric stable white noise this predictor minimizes the scale parameter of the error distribution. In the more general case when the driving white noise process has regularly varying tails with index α, the predictor minimizes the size of the error tail probabilities. The procedure can be interpreted also as minimizing an appropriately defined lα-distance between the predictor and the random variable to be predicted. We derive explicitly the best linear predictor of Xn+1 in terms of X1,..., Xn for the process ARMA(1, 1) and for the process AR(p). For higher order processes general analytic expressions are cumbersome, but we indicate how predictors can be determined numerically

Prediction of the Translocation Kinetics of a Protein from Its Mechanical Properties

AbstractProteins are actively unfolded to pass through narrow channels in macromolecular complexes that catalyze protein translocation and degradation. Catalyzed unfolding shares many features that characterize the mechanical unfolding of proteins using the atomic force microscope (AFM). However, simulations of unfolding induced by the AFM and when a protein is translocated through a pore suggest that each process occurs by distinct pathways. The link, if any, between each type of unfolding, therefore, is not known. We show that the mechanical unfolding energy landscape of a protein, obtained using an atomistic molecular model, can be used to predict both the relative mechanical strength of proteins when unfolded using the AFM and when unfolded by translocation into a pore. We thus link the two processes and show that the import rate through a pore not only depends on the location of the initiation tag but also on the mechanical properties of the protein when averaged over all the possible geometries that are relevant for a given translocation initiation site

Modeling electricity loads in California: a continuous-time approach

In this paper we address the issue of modeling electricity loads and prices with diffusion processes. More specifically, we study models which belong to the class of generalized Ornstein-Uhlenbeck processes. After comparing properties of simulated paths with those of deseasonalized data from the California power market and performing out-of-sample forecasts we conclude that, despite certain advantages, the analyzed continuous-time processes are not adequate models of electricity load and price dynamics.Comment: To be published in Physica A (2001): Proceedings of the NATO ARW on Application of Physics in Economic Modelling, Prague, Feb. 8-10, 200

Markov processes follow from the principle of Maximum Caliber

Markov models are widely used to describe processes of stochastic dynamics. Here, we show that Markov models are a natural consequence of the dynamical principle of Maximum Caliber. First, we show that when there are different possible dynamical trajectories in a time-homogeneous process, then the only type of process that maximizes the path entropy, for any given singlet statistics, is a sequence of identical, independently distributed (i.i.d.) random variables, which is the simplest Markov process. If the data is in the form of sequentially pairwise statistics, then maximizing the caliber dictates that the process is Markovian with a uniform initial distribution. Furthermore, if an initial non-uniform dynamical distribution is known, or multiple trajectories are conditioned on an initial state, then the Markov process is still the only one that maximizes the caliber. Second, given a model, MaxCal can be used to compute the parameters of that model. We show that this procedure is equivalent to the maximum-likelihood method of inference in the theory of statistics.Comment: 4 page

Archaeological investigations of the Kakadu Wetlands, Northern Australia

Freshwater wetlands of tropical Australia are highly productive ecosystems. Along the floodplain margins of the Northern Territory’s South Alligator River, large open sites testify that in the past they were of significant economic importance to the prehistoric Aboriginal occupants. The sites are deflated and the only archaeological remains consist of stone artefacts. However, geomorphological investigations link the sites with the establishment of freshwater wetlands on the floodplains no more than 1500 years ago. Because the sites are flooded in the wet season, dry season occupation is implied. As wetland resources are available seasonally, sites may have been occupied at different times during the dry season according to the availability of resources. Historic evidence from comparable areas elsewhere in tropical Australia indicates that hunters in these areas maintained year-round residency on the floodplain margins, camping on higher ground and exploiting alternative resource bases during the wet season. The presence of mound sites in open woodland abutting the floodplains suggests that such settlement patterns also existed in the Kakadu region prehistorically. This thesis examines site use and settlement patterns on the South Alligator wetland margins through an analysis of the stone artefact assemblages. Stone raw materials and tool types were examined in terms of distributions both within and between sites. Differences in distribution of tool types between sites was linked to differences in site use and season of occupation. The assemblages of the South Alligator wetland sites were subsequently compared with those of nearby rockshelters located in the outliers and plateau valleys of the Arnhem Land escarpment. Differences between them were interpreted as reflecting different environmental locations and economic bases. These differences echoed the dichotomy found by other researchers between plateau valley and plain sites in northern Kakadu. Previously, it had been concluded that the emergence of estuarine conditions on the floodplains c.6000 years BP was the major environmental event to affect the economic strategies of the Kakadu inhabitants from mid Holocene times onwards. However, the development of large freshwater wetland systems in the Kakadu region c.1000 years BP implies a major restructuring of subsistence strategies and settlement patterns throughout the region at this time. A reassessment of the archaeological evidence from the rockshelter sites escarpment revealed that such was the case. Today, there are a number of Aboriginal people in Kakadu who recall living at the wetland sites while they were employed in the buffalo shooting industry during the 1930s and 40s. They were able to provide details about site use and seasonality, as well as information about seasonal movement throughout the region. In addition to the oral data, there is a large body of literature which includes details of wetland subsistence strategies both for Kakadu and other comparable areas of tropical Australia. Using these sources, historical models of site use and settlement on the wetland margins and regionally were constructed. The models were compared with those derived from the archaeological evidence, to determine whether pre-contact modes of behaviour have survived into the post-contact period, whether they have changed and why. It was demonstrated that considerable continuity exists. Differences relate mainly to methods of exploitation and change in resource availability due to environmental degradation of the wetlands as a result of buffalo damage