Nonlinearity, Nonstationarity, and Thick Tails: How They Interact to Generate Persistency in Memory

We consider nonlinear transformations of random walks driven by thick-tailed innovations that may have infinite means or variances. These three nonstandard characteristics: nonlinearity, nonstationarity, and thick tails interact to generate a spectrum of asymptotic autocorrelation patterns consistent with long-memory processes. Such autocorrelations may decay very slowly as the number of lags increases or may not decay at all and remain constant at all lags. Depending upon the type of transformation considered and how the model error is speci- fied, the autocorrelation functions are given by random constants, deterministic functions that decay slowly at hyperbolic rates, or mixtures of the two. Such patterns, along with other sample characteristics of the transformed time series, such as jumps in the sample path, excessive volatility, and leptokurtosis, suggest the possibility that these three ingredients are involved in the data generating processes of many actual economic and financial time series data. In addition to time series characteristics, we explore nonlinear regression asymptotics when the regressor is observable and an alternative regression technique when it is unobservable. To illustrate, we examine two empirical applications: wholesale electricity price spikes driven by capacity shortfalls and exchange rates governed by a target zone.persistency in memory, nonlinear transformations, random walks, thick tails, stable distributions, wholesale electricity prices, target zone exchange rates

Analysis of opposed jet hydrogen-air counter flow diffusion flame

A computational simulation of the opposed-jet diffusion flame is performed to study its structure and extinction limits. The present analysis concentrates on the nitrogen-diluted hydrogen-air diffusion flame, which provides the basic information for many vehicle designs such as the aerospace plane for which hydrogen is a candidate as the fuel. The computer program uses the time-marching technique to solve the energy and species equations coupled with the momentum equation solved by the collocation method. The procedure is implemented in two stages. In the first stage, a one-step forward overal chemical reaction is chosen with the gas phase chemical reaction rate determined by comparison with experimental data. In the second stage, a complete chemical reaction mechanism is introduced with detailed thermodynamic and transport property calculations. Comparison between experimental extinction data and theoretical predictions is discussed. The effects of thermal diffusion as well as Lewis number and Prandtl number variations on the diffusion flame are also presented

Extracting a Common Stochastic Trend: Theories with Some Applications

This paper investigates the statistical properties of the Kalman filter for state space models including integrated time series. In particular, we derive the full asymptotics of maximum likelihood estimation for some prototypical class of such models, i.e., the models with a single latent common stochastic trend. Indeed, we establish the consistency and asymptotic mixed normality of the maximum likelihood estimator and show that the conventional method of inference is valid for this class of models. The models considered explicitly in the paper comprise a special, yet useful, class of models that we may use to extract the common stochastic trend from multiple integrated time series. As we show in the paper, the models can be very useful to obtain indices that represent fluctuations of various markets or common latent factors that affect a set of economic and financial variables simultaneously. Moreover, our derivation of the asymptotics of this class makes it clear that the asymptotic Gaussianity and the validity of the conventional inference for the maximum likelihood procedure extends to a larger class of more general state space models involving integrated time series. Finally, we demonstrate the utility of the state space model by extracting a common stochastic trend in three empirical analyses: interest rates, return volatility and trading volume, and Dow Jones stock prices.

Extracting a Common Stochastic Trend:Theories with Some Applications

This paper investigates the statistical properties of the Kalman filter for state space models including integrated time series. In particular, we derive the full asymptotics of maximum likelihood estimation for some prototypical class of such models, i.e., the models with a single latent common stochastic trend. Indeed, we establish the consistency and asymptotic mixed normality of the maximum likelihood estimator and show that the conventional method of infer- ence is valid for this class of models. The models considered explicitly in the paper comprise a special, yet useful, class of models that we may use to extract the common stochastic trend from multiple integrated time series. As we show in the paper, the models can be very useful to obtain indices that represent fluctuations of various markets or common latent factors that affect a set of economic and financial variables simultaneously. Moreover, our derivation of the asymptotics of this class makes it clear that the asymptotic Gaussianity and the validity of the conventional inference for the maximum likelihood procedure extends to a larger class of more general state space models involving integrated time series. Finally, we demonstrate the utility of the state space model by ex- tracting a common stochastic trend in three empirical analyses: interest rates, return volatility and trading volume, and Dow Jones stock prices.state space model, Kalman filter, common stochastic trend, maximum likelihood estimation, stock price index, interest rates, return volatility and trading volume.

Spatial distribution patterns of snow water equivalent data for the accumulation phase across the southern Rocky Mountains, The

Includes bibilographical references.Plan B M.S. project, also called Engineering report.2020 Fall.The spatial characteristics and patterns of snow accumulation and ablation are used to estimate runoff volume, and timing of snowpack in mountainous regions across the western United States. This paper focuses on quantifying and characterizing the snow accumulation phase to investigate the spatio-temporal snow water equivalent (SWE) distribution in the Southern Rocky Mountains (SRM). Average daily SWE data were obtained from 90 Natural Resources Conservation Service (NRCS) Snow Telemetry (SNOTEL) data stations from southern Wyoming to northern New Mexico for the snow years between from 1982 to 2015. The stations range in elevation between 2268 and 3536 meters, and they were aggregated into seven sub-sets, based on elevation (high-low), latitude (north-south) and annual maximum SWE (above average, average, below average snow years). For the entire dataset and the seven data sub-sets, the standard deviation versus mean trajectories were developed. Each trajectory was comprised of average daily data points across the snow year, and each data point represented the standard deviation and mean SWE values from a sub-set of the SNOTEL stations. The trajectory can be used to describe and represent the change in the snowpack over the water year. Within each trajectory, the accumulation (increasing snowpack), hysteretic (increasing and decreasing snowpack) and ablation (decreasing snowpack) phases can be observed, characterized and modeled. For this paper, regression techniques were applied to the accumulation phase only. The regression form, average slope, maximum slope, minimum slope, and coefficient of determination values were extracted. These data were aggregated across elevation, latitude and snow year sub-sets, and spatial patterns were evaluated. Although the prior study (Egli and Jonas, 2009) used snow depth data, SWE data were the focus for this study. SWE data were available for a longer period of record than snow depth data in the SRM, and since SWE measures the mass of water rather than depth snow, the physical effects of snow settling were eliminated from the analysis. The snow settling signature appeared in the data as noise in the standard deviation versus mean depth trajectory plots, compared to SWE trajectory plots. The removal of this noise, i.e., use of SWE trajectory plots, yielded stronger correlations than were produced using snow depth data. The accumulation phase data most closely fit a truncated linear regression model, with the average slopes ranging between 0.36 to 0.40 (seven sub-sets), and the average standard deviation values ranging between 0.042 to 0.097. While the average accumulation slopes were fairly similar across all seven sub-sets, latitude impacted snowpack variability more significantly than did elevation. Within individual years, the accumulation snowpack in the south region was frequently more homogenous than the north region, but when aggregated across the 34-year study, the accumulation snowpack in the south region was less consistent on an inter-annual basis. In contrast to original hypotheses, when SWE were discretized by both elevation and latitude, the standard deviation of the accumulation slopes increased, rather than decreased. Snow year (above average, average, below average) was found to have a negligible impact on spatial homogeneity of the accumulation snowpack, except within the south-high sub-set, where range in average accumulation slope was 0.10. Generally, the snowpack was found to be more homogenous for below average snow years 3 compared to average or above average snow years, because below average snow years exhibited the lowest average accumulation slopes of the three categories

Casimir Invariants from Quasi-Hopf (Super)algebras

We show how to construct, starting from a quasi-Hopf (super)algebra, central elements or Casimir invariants. We show that these central elements are invariant under quasi-Hopf twistings. As a consequence, the elliptic quantum (super)groups, which arise from twisting the normal quantum (super)groups, have the same Casimir invariants as the corresponding quantum (super)groups.Comment: 24 pages, Latex fil

Conceptual Exploration of the Rites of Passage With The Kumasi Central Market

As a concept, the Rites of Passage –a phrase which was coined by the French anthropologist and folklorist Arnold van Gennep, is represented with paintings to depict the stages of life from the time of birth to death. This write-up, conceptually represents the behavioural tendencies at each stage of life with scenes captured from the Kumasi Central Market at the four major periods of the day which are morning, afternoon, evening and night. The captured scenes were selected based on the effect of light on the particular scene, specifically, the brightness of the hues, and its capability of portraying the specific period of the day. To achieve the exact optical effect, the selected scenes were photographically painted on canvasses. Descriptions were made of the scenes and were finally analysed. Thus Observatory, Participatory, Descriptive and Analytical methodologies were utilized to observe and capture snapshots of the scenes from the Kumasi Central Market, then painted the scenes, described them and finally analysed them respectively. The analyses resulted in conceptually portraying the Rites of Passage theory with the paintings. The statement or morals is that in nature, everything passes through the four stages of life and eventually dies. It is therefore concluded that nothing is permanent in life as it goes through several challenges and changes before finally deteriorating and dying or annihilating. Keywords: Conceptual, Exploration, Rites of passage, Kumasi Central Market. DOI: 10.7176/JCSD/66-03 Publication date:August 31st 2021

Utilization of Colour for Visual Representation of Nature, Form, Space and Time

In nature, everything has a form, occupies a space, and is susceptible to change in a matter of time. Nature, form, space and time could well be classified as theoretical and the problem of intangibility of the said terms is addressed with the application of colour to visually represent them through paintings. Through application of colour, this article pulls the said incorporeities from their abstract realm for visual perception. Methodology of Observation was applied to observe some scenes at the same time, but a particular scene or spot was studied at four different periods of the day namely; morning, afternoon, evening and night. Participatory methodology was utilized to capture the scenes with a camera and, through the application of colour, painted the captured scenes on canvasses. Analyses of the painted scenes were finally made to result in conceptually representing nature, form and space with painted objects. Four of the scenes visually present the four periods or time of the day which are morning, afternoon, evening and night. The analyses have subsequently resulted in visually bringing about the concept of nature, form, space and time. In conclusion, if the intangibilities of nature, form, space and time could be concretized for visual conception, then any theory could be practically materialized. Keywords: colour, visual representation, nature, form, space, time DOI: 10.7176/ADS/94-01 Publication date:July 31st 202

Cavity approach for real variables on diluted graphs and application to synchronization in small-world lattices

We study XY spin systems on small world lattices for a variety of graph structures, e.g. Poisson and scale-free, superimposed upon a one dimensional chain. In order to solve this model we extend the cavity method in the one pure-state approximation to deal with real-valued dynamical variables. We find that small-world architectures significantly enlarge the region in parameter space where synchronization occurs. We contrast the results of population dynamics performed on a truncated set of cavity fields with Monte Carlo simulations and find excellent agreement. Further, we investigate the appearance of replica symmetry breaking in the spin-glass phase by numerically analyzing the proliferation of pure states in the message passing equations.Comment: 10 pages, 3 figure