High frequency sampling of a continuous-time ARMA process

Continuous-time autoregressive moving average (CARMA) processes have recently been used widely in the modeling of non-uniformly spaced data and as a tool for dealing with high-frequency data of the form $Y_{n\Delta}, n=0,1,2,...$, where $\Delta$ is small and positive. Such data occur in many fields of application, particularly in finance and the study of turbulence. This paper is concerned with the characteristics of the process (Y_{n\Delta})_{n\in\bbz}, when $\Delta$ is small and the underlying continuous-time process (Y_t)_{t\in\bbr} is a specified CARMA process.Comment: 13 pages, submitte

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

Sequential Monte Carlo pricing of American-style options under stochastic volatility models

We introduce a new method to price American-style options on underlying investments governed by stochastic volatility (SV) models. The method does not require the volatility process to be observed. Instead, it exploits the fact that the optimal decision functions in the corresponding dynamic programming problem can be expressed as functions of conditional distributions of volatility, given observed data. By constructing statistics summarizing information about these conditional distributions, one can obtain high quality approximate solutions. Although the required conditional distributions are in general intractable, they can be arbitrarily precisely approximated using sequential Monte Carlo schemes. The drawback, as with many Monte Carlo schemes, is potentially heavy computational demand. We present two variants of the algorithm, one closely related to the well-known least-squares Monte Carlo algorithm of Longstaff and Schwartz [The Review of Financial Studies 14 (2001) 113-147], and the other solving the same problem using a "brute force" gridding approach. We estimate an illustrative SV model using Markov chain Monte Carlo (MCMC) methods for three equities. We also demonstrate the use of our algorithm by estimating the posterior distribution of the market price of volatility risk for each of the three equities.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS286 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Continuous-time GARCH processes

A family of continuous-time generalized autoregressive conditionally heteroscedastic processes, generalizing the $\operatorname {COGARCH}(1,1)$ process of Kl\"{u}ppelberg, Lindner and Maller [J. Appl. Probab. 41 (2004) 601--622], is introduced and studied. The resulting $\operatorname {COGARCH}(p,q)$ processes, $q\ge p\ge 1$, exhibit many of the characteristic features of observed financial time series, while their corresponding volatility and squared increment processes display a broader range of autocorrelation structures than those of the $\operatorname {COGARCH}(1,1)$ process. We establish sufficient conditions for the existence of a strictly stationary nonnegative solution of the equations for the volatility process and, under conditions which ensure the finiteness of the required moments, determine the autocorrelation functions of both the volatility and the squared increment processes. The volatility process is found to have the autocorrelation function of a continuous-time autoregressive moving average process.Comment: Published at http://dx.doi.org/10.1214/105051606000000150 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

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

Higher Moments and Prediction Based Estimation for the COGARCH(1,1) model

COGARCH models are continuous time version of the well known GARCH models of financial returns. They are solution of a stochastic differential equation driven by a L\'evy process. The first aim of this paper is to show how the method of Prediction-Based Estimating Functions (PBEFs) can be applied to draw statistical inference from a discrete sample of observations of a COGARCH(1,1) model as far as the higher order structure of the process is clarified. Motivated by the search for an optimal PBEF, a second aim of the paper is to provide recursive expressions for the joint moments of any fixed order of the process, whenever they exist. Asymptotic results are given and a simulation study shows that the method of PBEF outperforms the other available estimation methods

Self-management in Bronchiectasis: barriers and opportunities

A 2018 Cochrane systematic review of self-management for bronchiectasis found scarce, poor quality evidence. National Bronchiectasis Guidelines recommend self-management including ‘basic principles of disease management’, recognition of exacerbation through health changes requiring action - either by self-initiation of treatment (airway clearance or antibiotic therapy) or seeking healthcare assistance. Existing information sources and a new mixed-method randomised control trial were considered. The intervention aimed to improve self-efficacy in self-managing bronchiectasis. Outcomes were; quantitative patient reported outcomes; qualitative findings thematically analysed from participant focus groups, professional interviews and insights from participants during education. 220 people from 6 East of England hospitals with one or more exacerbations of bronchiectasis within 12 months participated. Randomisation was to treatment as usual alone or in addition to the Bronchiectasis Empowerment Tool (BET). Four brief telephone calls introduced BET which comprised an action plan, four educational sections: sputum, health changes, medications and health interactions (with notepads). Primary outcome at 12 months was the 6-item Self-Efficacy to Manage Chronic Disease Scale (SEMCD). Quantitative/economic data were collected quarterly via mailed self-reported questionnaires for one year. Participant focus groups investigated intervention acceptability and education comments exposed participants’ self-management experiences. Under-powered, with 12% greater than expected withdrawal the BET intervention did not measurably improve self-efficacy or secondary outcomes. BET did not affect SEMCD (mean difference (0.14 (95% confidence interval (95%CI) -0.37 to 0.64), p=0.59) and showed no significant difference in overall cost to NHS or in QALYs though participants valued the telephone education. Recruitment success illustrates participant requirement for self-management support, withdrawals raise methodological questions such as literacy burdens (intervention and trial outcome measures). My contribution questions current evaluation methods for quality of life and self-efficacy in bronchiectasis, examining participant motivational needs, their healthcare and social insights, to elucidate the barriers and opportunities for self-efficacy and empowerment in future collaborative self-management

Modelling of solar magnetic fields using cellular automata models

Solar activity, including flares, CMEs, sunspots, global fleld reversal and, consequential to these, particle acceleration and X-ray emission result from the complexity of the atmospheric magnetic fields. These fields are driven into complex topologies by the continual stochastic photospheric motions and granulation flows. Significant energy is stored in the magnetic field however magnetic reconnection provides a mechanism for the relaxation and simplification of the field and release of this energy. Reconnection is capable of providing the observed plasma heating, field reorganisation and particle acceleration, although the relationship between reconnection and flaring is not yet understood. It is clear however that the field topology is key. Given fiare-size self-similarity, the short time-scales of hard X-ray emission and the observed apparent self-organisation, flaring models (Lu & Hamilton 1991) have been constructed based upon self-organised criticality (‘SOC’) with minimal physics and have produced plausible fiare-size distributions. The model by MacKinnon, Macpherson & Vlahos (1996) however assumed only local flare-triggering and made no statements regarding flare physics. This model reproduced the broad statistical features of flares yet without any implicit SOC. We speculate that the observed Solar activity arises from the self-interaction of the magnetic field, flux emergence/submergence and reconnection without the necessity for invoking SOC or power-law distributed convective flows. Our first model was a simple 1-D cellular automata (‘CA’) containing only formalised field connectivity, reconnection and flux emergence/submergence. The model produced self-similarity in fiare-sizes over four orders of magnitude. The following model built upon the first and included more realistic physics with continuous parameter values. The model gave power- law distributions in field density and fiare-sizes (up to seven orders of magnitude) without inclusion of SOC or power-law forcing. The results were robust and insensitive to details of the reconnection mechanism. We derive analytical explanations for the observed rapid decay curves of impulsive-phase X-ray emission and consider that the flares produced represent presently unresolvable reconnection events. It was found that, similar to large Solar flares, large events are rarely concurrent

Pandemic Potential of Reassortant Swine Influenza A Viruses

Influenza A viruses are capable of causing disease in several species, including birds, humans and swine. Host specificity of the viruses is not absolute, and is influenced by a range of factors. Swine play a pivotal role in the interspecies transmission of influenza A viruses, as they are susceptible to infection with both human and avian strains and have been implicated as a “mixing vessel” for the reassortment of influenza A viruses from different species. The reassortment of influenza A viruses of human and avian origin led to human influenza pandemics in 1957 and 1968. The dynamics of swine influenza viruses in North America changed drastically with the introduction of the avian-origin PA and PB2 and human-origin HA, NA, and PB1 gene segments and the creation of the triple reassortant swine virus lineage in 1998. While the previously circulating classical swine H1N1 influenza virus lineage was very stable in the swine population, triple reassortant lineage viruses have supplanted the classical H1N1 lineage and undergone repeated reassortment events, acquiring HA and NA genes from human, swine, and avian influenza viruses, while maintaining triple reassortant internal gene (TRIG) cassette. Viruses of the triple reassortant lineage have been very successful in the swine population, yet the mechanisms underlying their unique characteristics and increased fitness have not been elucidated. Here we address the pandemic potential of triple reassortant swine influenza A viruses, their transmissibility, and their relative fitness compared to classical and double reassortant swine influenza viruses. Several triple reassortant viruses, including one with avian-origin HA and NA, were characterized in the ferret, which is a commonly used model for human influenza infection. The effect of the TRIG cassette on the reassortment potential and temperature sensitivity of swine influenza viruses was determined in cell culture, and the replication and transmission of a classical and a reassortant swine virus were compared in pigs. We found that triple reassortant swine viruses replicated efficiently in the ferret model, although there was some variation in transmission efficiencies. An H2N3 virus with avian-origin HA and NA was transmissible in the ferret model, and this transmissibility could be abolished with a single amino acid change in the HA protein that altered its receptor binding specificity. Avian H2N3 viruses were also capable of replicating in ferrets without adaptation and could acquire transmissibility through a change in the receptor binding specificity of the HA protein. Both double and triple reassortant swine viruses had an advantage over the classical H1N1 swine virus at early timepoints in cell culture. Reassortant viruses also demonstrated less temperature sensitivity than the classical H1N1 swine virus. The triple reassortant H1N1 virus had an increased reassortment potential in cell culture compared to the classical swine H1N1 virus as determined by acquisition of a human HA gene. Triple reassortant swine viruses have an increased ability to establish infection, and an increased potential for reassortment, potentially introducing novel HA genes into a host population. This indicates that triple reassortant swine viruses may have an increased potential to cause human pandemics. In April 2009, a novel H1N1 pandemic virus containing five of the six genes of the TRIG cassette emerged in the human population, emphasizing the importance of reassortant swine influenza A viruses in the generation of human pandemics