Spencer Wheatley

The Hawkes process with renewal immigration & its estimation with an EM algorithm

In its original form, the self-excited Hawkes process is a cluster process where immigrants follow a Poisson process, and each immigrant may form a cluster of multi-generational offspring. The Hawkes process is generalized by replacing the Poisson immigration process with a renewal process. This generalization makes direct MLE impossible. Thus, two EM algorithms are introduced: The first extends the existing EM algorithm for the Hawkes process to consider renewal immigration. It treats the entire branching structure-which points are immigrants, and which point is the parent of each offspring-as missing data. The second algorithm reduces the amount of missing data, considering only if a point is an immigrant or not as missing data. This significantly reduces computational complexity and memory requirements, enabling estimation on larger datasets. Both algorithms are found to perform well in simulation studies. A case study shows that the Hawkes process with renewal immigration is superior to the standard Hawkes process for the modeling of high-frequency price fluctuations. Further, it is demonstrated that misspecification of the immigration process can bias estimation of the branching ratio, which quantifies the degree of self-excitation.

Estimation of the Hawkes Process with Renewal Immigration Using the EM Algorithm

We introduce the Hawkes process with renewal immigration and make its statistical estimation possible with two Expectation Maximization (EM) algorithms. The standard Hawkes process introduces immigrant points via a Poisson process, and each immigrant has a subsequent cluster of associated offspring of multiple generations. We generalize the immigration to come from a Renewal process; introducing dependence between neighbouring clusters, and allowing for over/under dispersion in cluster locations. This complicates evaluation of the likelihood since one needs to know which subset of the observed points are immigrants. Two EM algorithms enable estimation here: The first is an extension of an existing algorithm that treats the entire branching structure - which points are immigrants, and which point is the parent of each offspring - as missing data. The second considers only if a point is an immigrant or not as missing data and can be implemented with linear time complexity. Both algorithms are found to be consistent in simulation studies. Further, we show that misspecifying the immigration process introduces significant bias into model estimation - especially the branching ratio, which quantifies the strength of self excitation. Thus, this extended model provides a valuable alternative model in practice.

Are Bitcoin Bubbles Predictable? Combining a Generalized Metcalfe's Law and the LPPLS Model

We develop a strong diagnostic for bubbles and crashes in bitcoin, by analyzing the coincidence (and its absence) of fundamental and technical indicators. Using a generalized Metcalfes law based on network properties, a fundamental value is quantified and shown to be heavily exceeded, on at least four occasions, by bubbles that grow and burst. In these bubbles, we detect a universal super-exponential unsustainable growth. We model this universal pattern with the Log-Periodic Power Law Singularity (LPPLS) model, which parsimoniously captures diverse positive feedback phenomena, such as herding and imitation. The LPPLS model is shown to provide an ex-ante warning of market instabilities, quantifying a high crash hazard and probabilistic bracket of the crash time consistent with the actual corrections; although, as always, the precise time and trigger (which straw breaks the camels back) being exogenous and unpredictable. Looking forward, our analysis identifies a substantial but not unprecedented overvaluation in the price of bitcoin, suggesting many months of volatile sideways bitcoin prices ahead (from the time of writing, March 2018).

Basics of Civilian Nuclear Fission

Uranium is by far the most concentrated available energy source, but with the downside that the physical process of fission generates a surplus of neutrons and radioactive fission products. Objectives exist to ensure the control of reactivity, confinement of radioactive substances and decay heat removal as well as long-term waste management, which are supported by mature methods and stringent safety requirements. Operators and regulators claim that the risk of well-designed and operated power plants with light-water reactors, which dominate the current worldwide fleet of 449 units, is justifiably small. The operating experience has accumulated to more than fifteen thousand years, with typical capacity factor now around 80%. Another 60 facilities are under construction in 15 countries; at the same time, some countries are phasing out nuclear while promoting renewables. New and future generation designs aim at further—in some cases radical—reduction of the risk of core melt accidents and minimize proliferation risks. New designs may also use advanced fuel cycles including thorium that extend and use fuel resources more efficiently and reduce reliance on husbandry of long-lived waste from millennia to centuries.

Severe Accidents: Singularity of Nuclear Disasters?

The risk of nuclear accidents has proven to be low in absolute and relative terms. Nevertheless, the high-energy density fission process and current technology make today’s reactors vulnerable to very severe albeit very rare accident scenarios. The three disasters experienced demonstrated the importance of site conditions, containment systems and severe accident management measures. Not being triggered by a single or combined technical failure in a classical sense, disasters experienced are partly explained as a product of five hierarchical levels of individual and societal human factors. The potentially severe consequences, including costs, of nuclear accidents have played a decisive role in the development of the nuclear power sector, and dominate nuclear risk analysis. However, in terms of cost or loss of life, these accidents are not singular—as other industrial and energy generation sectors have comparable severe accidents.

Strategic Aspects of Energy

The history of mankind is that of its ascent to unprecedented levels of comfort, productivity, and consumption—enabled by the increased mastery of the basic stocks and flows of energy. Intensive use of electricity in particular has enabled the 3rd and 4th industrial revolutions, the latter is on-going with the progressive fusion of the natural and digital worlds. Such innovations drive and are supported by a global urbanization trend, leading to futuristic mega-cities. And while about 20% of the global population are at the forefront of this development, the remaining 80% wish to attain the same standard. This requires a massive growth in the overall supply of electricity, in particular in concentrated form to power mega-cities and e-mobility.

Candidate Features and Technology Options

Nuclear power stations have become more efficient and safer inter alia due to learning from valuable operational experience, largely in reaction to major and near accidents. However, dread of rare but possible severe accidents, reliance upon unfailing human performance at various levels, and dependence on social stability, emphasize the importance of further safety improvements, for which challenging criteria were conveyed in Sect. 2.2. To achieve them, key design features (“building blocks”) are viewed and revisited and should be combined in a radically new way, to come up with “revolutionary” or even “exotic” system designs. To check whether such designs are feasible, we track most recent developments of reactor concepts focusing on differing (1) coolants, including liquid metals and molten salt, (2) neutron spectrum from thermal to fast, (3) power level, (4) fundamental design features (architecture) and purpose, and (5) ability to extend fuel reserves and “burn” waste. The designs selected are scored against the set of very stringent, highly ambitious criteria. The results show a high potential for far-reaching improvements compared to most advanced LWRs in use today. Small modular reactors emerge as being the most attractive. However, thus far, none of the candidate concepts fulfill all the criteria convincingly; avoiding criticality induced accidents and maximizing proliferation resistance appears most challenging. There is also a potential for new concept-specific risks to be introduced but this appears manageable. Although caution is warranted, a purely deterministic safety approach is tempting, in that we would like to absolutely exclude the possibility of severe accidents.

Risk in Nuclear Power Operation

Nuclear accidents are rare but costly and a common, but wrongly, held opinion is that, if the external cost of nuclear accidents were included in the price, then nuclear power would become economically unfeasible. Probabilistic Safety Analysis (PSA) is the standard method used to identify potential accident scenarios, estimate their probability, and their consequences with a focus on plant states as well as impact on health, the environmental, and certain direct costs. This methodology has developed substantially and is now used for regulatory purposes but is not without defects, notably when quantifying overall risk (level 3) and is best complemented and compared with statistical experience. More broadly, impacts of accidental releases are highly uncertain due to the difficulty of realistically estimating the effect of low doses of radiation to human health and mortality.

Potentials and Vision for the Future of Nuclear Energy

International treaties (Kyoto and Paris), EU and national legislation have created a growing demand for a larger share, and overall larger amount of concentrated de-carbonized electricity. With such high stakes, to rely on wind and solar as the only feasible solutions is a strategic error. To address the existential need for more and more energy of our growing and wealthier societies across the world, we argue for keeping the nuclear option open, supported by future revolutionary safe and clean nuclear technologies, which would be acceptable to an otherwise presently mostly nuclear-averse society. This proposal is further supported when one acknowledges the real problem of stewardship of already existing high-grade nuclear waste over time scales eclipsing that of stable societies. To realize this vision, substantial ongoing national and international R&D programs exist, although funding is at historically low levels, and the sufficiency of current policies and activities to meet expected energy demand at an acceptable level of emissions has been questioned. Moreover, in the nuclear industry, there is the risk of stagnation of essential human-capital and know-how. The promising concepts and designs presented in Chap. 6 provide the impulse to get us over the existing hurdles, but the scope is ambitious, and time delay from R&D to commercial deployment in general is too long, stemming in part from regulatory inertia. Therefore, we call for an urgent increase in government and international R&D funding by two orders of magnitude—i.e., of the order of hundreds of billions of USD per year, for an international civilian “super-Apollo” program. We emphasize that such a large-scale public program is not unprecedented in size, and experience indicates that such investments in fundamental technology are not only of immense public benefit but also enable revolutionary innovations to be spun out that would not otherwise ever have been attained.

Governance: Organizations and Management Issues

Energy effectively constitutes a global public good, and nuclear energy belongs to its provision. The potential risks of high consequence accidents and the importance of strong safety culture, regulation, and governance, have been recognized early, and to an increasing extent over time. As a result, exceptional and leading efforts into risk and reliability analysis have and continue to take place within the nuclear community. However, the adequacy of existing governance and control mechanisms can be questioned. Indeed, authoritative organizations, notably the IAEA, provide standards, best practices, and platforms for exchange at the international level. And strong regulatory bodies provide assurances and verification of safety at the national level. However, ultimately minimum standards are not trivial to impose because they will only be adopted by states that consent. Further, case studies of major accidents show the pervasiveness of distorted information and sometimes risk information concealment—a common organizational deficit, highly problematic in this safety-sensitive domain.