Increasing Domain Infill Asymptotics for Stochastic Differential Equations Driven by Fractional Brownian Motion

Although statistical inference in stochastic differential equations (SDEs) driven by Wiener process has received significant attention in the literature, inference in those driven by fractional Brownian motion seem to have seen much less development in comparison, despite their importance in modeling long range dependence. In this article, we consider both classical and Bayesian inference in such fractional Brownian motion based SDEs. In particular, we consider asymptotic inference for two parameters in this regard; a multiplicative parameter associated with the drift function, and the so-called "Hurst parameter" of the fractional Brownian motion, when the time domain tends to infinity. For unknown Hurst parameter, the likelihood does not lend itself amenable to the popular Girsanov form, rendering usual asymptotic development difficult. As such, we develop increasing domain infill asymptotic theory, by discretizing the SDE. In this setup, we establish consistency and asymptotic normality of the maximum likelihood estimators, as well as consistency and asymptotic normality of the Bayesian posterior distributions. However, classical or Bayesian asymptotic normality with respect to the Hurst parameter could not be established. We supplement our theoretical investigations with simulation studies in a non-asymptotic setup, prescribing suitable methodologies for classical and Bayesian analyses of SDEs driven by fractional Brownian motion.Comment: Feedback welcom

Bidding structure, market efficiency and persistence in a multi-time tariff setting

The purpose of this study is to examine the fractal dynamics of day ahead electricity prices by using parametric and semi parametric approaches for each time zone in a multi-time tariff setting in the framework of bidding strategies, market efficiency and persistence of exogenous shocks. We find that that electricity prices have long term correlation structure for the first and third time zones indicating that market participants bid hyperbolically and not at their marginal costs, market is not weak form efficient at these hours and exogenous shocks to change the mean level of prices will have permanent effect and be effective. On the other hand, for the second time zone we find that price series does not exhibit long term memory. This finding suggests the weak form efficiency of the market in these hours and that market participants bid at their marginal costs. Furthermore this indicates that exogenous shocks will have temporary effect on electricity prices in these hours. These findings constitute an important foundation for policy makers and market participants to develop appropriate electricity price forecasting tools, market monitoring indexes and to conduct ex-ante impact assessment. © 2015 Elsevier B.V

Sequence to Sequence Change-Point Detection in Single Particle Trajectories via Recurrent Neural Network for Measuring Self-Diffusion

Data Availability: The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.Copyright © The Author(s) 2023. A recurrent neural network is developed for segmenting between anomalous and normal diffusion in single-particle trajectories. Accurate segmentation infers a distinct change point that is used to approximate an Einstein linear regime in the mean-squared displacement curve via the transition density function, a unique physical descriptor for short-lived and delayed transiency. Through several artificial and simulated scenarios, we demonstrate the compelling accuracy of our model for dissecting linear and nonlinear behaviour. The inherent practicality of our model lies in its ability to substantiate the self-diffusion coefficient through offline trajectory segmentation, which is opposed to the common ‘best-guess’ linear fitting standard. Additionally, we show that the transition density function has fundamental implications and correspondence to underlying mechanisms that influence transition. In particular, we show that the known proportionality between salt concentration and diffusion of water also influences delayed anomalous behaviour.Engineering and Physical Sciences Research Council (EPSRC; Grant number EP/T033940/1); Royal Society (Grant number IES\R3\193152)

Surveillance of Complex Auction Markets: a Market Policy Analytics Approach

The dissertation consists of four essays that investigates the merits of big data-driven decision-making in the surveillance of complex auction markets. In the first essay, Avci and her co-researchers examine the aggregate-level bidding strategies and market efficiency in a multi-time tariff setting by using parametric and semi parametric methods. In the second essay, they address three key forecasting challenges; risk of selection of an inadequate forecasting method and transparency level of the market and market-specific multi-seasonality factors in a semi-transparent auction market. In the third essay, they demonstrate the effect of information feedback mechanisms on bidders’ price expectations in complex auction markets with the existence of forward contracts. They develop a research model that empirically tests the impact of bidders’ attitudes on their price expectation through their trading behavior and tested their hypotheses on real ex-ante forecasts, evaluated ex-post. In the fourth essay, they investigate characterization of bidding strategies in an oligopolistic multi-unit auction and then examine the interactions between different strategies and auction design parameters. This dissertation offers important implications to theory and practice of surveillance of complex auction markets. From the theoretical perspective, this is, to our best knowledge, the first research that systematically examines the interplay of different informational and strategic factors in oligopolistic multi-unit auction markets. From the policy perspective, Avci’s research shows that integration of big data analytics and domain-specific knowledge improves decision-making in surveillance of complex auction markets

Estimation of the Hurst parameter for fractional Brownian motion using the CMARS method

In this study, we develop an alternative method for estimating the Hurst parameter using the conic multivariate adaptive regression splines (CMARS) method. We concentrate on the strong solutions of stochastic differential equations (SDEs) driven by fractional Brownian motion (fBm). Our approach is superior to others in that it not only estimates the Hurst parameter but also finds spline parameters of the stochastic process in an adaptive way. We examine the performance of our estimations using simulated test data.TUBITAK Domestic Doctoral Scholarship Progra