A Mathematical Investigation of a Continuous Covariance Function Fitting with Discrete Covariances of an AR Process

In this paper, we want to find a continuous function fitting through the discrete covariance sequence generated by a stationary AR process. This function can be determined as soon as the Yule–Walker equations are found. The procedure consists of two steps. At first the inverse zeros of the characteristic polynomial of the AR process must be fixed. The second step is based on the fact that an AR process can also be seen as a difference equation. By solving this difference equation, it is possible to determine a class of functions from which a candidate for a continuous covariance function can be determined. To analyze if this function is applicable as a positive definite covariance function, it is analyzed mathematically in view of the power spectral density compared to the characteristics of the power spectral density for the discrete covariances. Then it is shown that this function is positive semi-definite. At the end, a simulation of a stationary AR(3) process is elaborated to illustrate the derived properties.

Divergent reactivities of 2-pyridyl sulfonate esters. Exceptionally mild access to alkyl bromides and 2-substituted pyridines

A series of 2- and 3-pyridyl sulfonate and tosylate esters of primary and secondary alcohols were synthesized and evaluated in the bromination reaction with MgBr2·Et2O. The greater coordinating ability of the 2-pyridyl sulfonate esters accounted for its observed superior reactivity and selectivity. Reaction of neopentyl and phenyl 2-pyridyl sulfonates with a variety of aryl and heteroaryl Li reagents led to 2-substituted pyridines at temperatures as low as −78 °C via an SNAr process. Mechanistic considerations are discussed.

Hacia la inclusión del alumnado con TEA en educación física: investigación-acción en un programa piloto (Towards the inclusion of students with ASD in physical education: action-research in a pilot programme)

La prevalencia del trastorno del espectro autista (TEA) ha aumentado en las décadas recientes. Es necesario que el profesorado atienda la diversidad presente en las aulas, teniendo en consideración las características y necesidades que presentan las personas con TEA a la hora de diseñar propuestas educativas capaces de motivar la participación de todo el alumnado. El presente trabajo relata un proceso de investigación-acción (IA) abordado en el seno de un programa piloto de sesiones de Educación Física (EF) con alumnado con TEA. El objetivo consistió en testar un programa de actividades centrado en ofrecer pautas útiles para el profesorado, aplicables tanto en sesiones ordinarias de EF, como en unidades específicas de comunicación y lenguaje. Partiendo del compromiso con el enfoque de educación inclusivo, la propuesta de actividades se hizo teniendo como base de fundamentación la legislación vigente y se analizó a través de la metodología de IA. Los resultados obtenidos concretan que orientaciones como la utilización de pictogramas explicativos de las tareas, el modelaje, la introducción de temáticas de su interés o el uso de una metodología directiva, pueden mejorar la participación y servir como referencia para el diseño de futuras propuestas de EF. Abstract. The prevalence of Autism Spectrum Disorder (ASD) has increased in recent decades. It is necessary for teachers to attend to the diversity present in the classrooms, taking into account the characteristics and needs of people with ASD when designing educational proposals capable of motivating the inclusion of all students. The present work reports an action-research (AR) process approached within a pilot program of Physical Education (PE) sessions with students with ASD. The objective consisted of testing a program of activities focused on offering useful guidelines for teachers, applicable both in ordinary PE sessions, as well as in specific communication and language units. Based on the commitment to the inclusive education approach, the proposal of activities was based on the current legislation and analysed through the AR methodology. The results obtained show that guidelines such as the use of pictograms to explain the tasks, modelling, the introduction of topics of interest, and the use of a directive methodology can improve participation and serve as a reference for the design of future PE proposals.

GLM based auto-regressive process to model Covid-19 pandemic in Turkey

Objectives: Our objective is to propose a robust approach to model daily new cases and daily new deaths due to covid-19 infection in Turkey. Methods: We consider the generalized linear model (GLM) approach for the autoregressive process (AR) with log link for modelling. We study the data between March 11, 2020 that is the date first confirmed case occurred and October 20, 2020. After a month of the first outbreak in Turkey, the first official curfew has been imposed during the weekend. Since then there have been curfews each weekend till June 1st. Hence, we include intervention effects as well as some outlying data points in the model where necessary. We use the data between March 11 and September 15 to build the models, and test the performance on the data from September 16 till October 20. We also study the consistency of the model statistics. Results: Estimated models fit data quite well. Results reveal that after the first curfew daily new Covid-19 cases decrease 18.5%. As expected, effect of the curfew gets more significant once a month is past, and daily new cases cut down 24.9%. Our approach also gives a robust estimate for the effective reproduction number that is approximately 2 meaning as of October 20, 2020 there is still a risk for an infected person to cause 2 secondary infections despite all the interventions, preventions, and rules. Conclusion: The GLM approach for AR process with log link produces consistent and robust estimates for the daily new cases and daily new deaths for the data covering almost the first year of the pandemic in Turkey. The proposed approach can also be used to model the cases in other countries.

Palladium-catalyzed C8–H arylation and annulation of 1-naphthalene carboxylic acid derivatives with aryl iodides

Disclosed herein is palladium-catalyzed C8–H arylation and annulation of 1-naphthoic acid derivatives with aryl iodides in a low reactant molar ratio via an electrophilic aromatic substitution (SEAr) process.

The Tail Behavior due to the Presence of the Risk Premium in AR-GARCH-in-Mean, GARCH-AR, and Double-Autoregressive-in-Mean Models*

We extend the results in Borkovec (2000), Basrak, David, and Mikosch (2002a), Lange (2011), and Francq and Zakoïan (2015) by describing the tail behavior when a risk premium component is added in the mean equation of different conditional heteroskedastic processes. We study three types of parametric models: the traditional generalized autoregressive conditional heteroskedastic (GARCH)-M model, the double autoregressive (AR) model with risk premium, and the GARCH-AR model. We find that if an AR process is introduced in the mean equation of a traditional GARCH-M process, the tail behavior is the same as if it is not introduced. However, if we add a risk premium component to the double AR model, then the tail behavior changes with respect to the GARCH-M. The GARCH-AR model also has a different tail index than the traditional AR-GARCH model. In a simulation study, we show that larger tail indexes are associated with the traditional GARCH-M model. When the size of the risk premium component increases, the tail index tends to fall. The only exception to this rule occurs in the double AR model when the risk premium depends on log-volatility. Parameter configurations where the strong stationarity condition of the risk premium models fails are also illustrated and discussed.

Forecasting the Growth of Structures from NMR and X-Ray Crystallography Experiments Released Per Year

In this paper, we present a forecasting scheme for the growth of molecular structures from NMR and X-ray Crystallography experimental techniques released every year by employing an autoregressive (AR) process. The proposed scheme maximises the forecasting accuracy by utilising the optimal AR process order. The optimal model order was derived as the model with the least prediction error. Therefore, the proposed scheme has been efficiently employed to model and predict the annual growth of structures-based NMR and X-ray Crystallography experimental data for the next decade 2019–2028 using the time series of the past 43 years of both experimental datasets. The experimental results showed that the optimal model order to estimate both datasets was [Formula: see text] which belongs to a forecasting accuracy of [Formula: see text], for both datasets. Indeed, such a high level of accuracy referred to the amount of linearity between the consecutive elements of the original times series. Hence, the forecasting results reveals of an exponential increasing behaviour in the future growth in the annual structures released from both NMR and X-ray Crystallography experiments.

Cognitive Decision Process: The Context of Auditors' Diagnostic Reasoning

Based on a cognitive psychology framework, this article provides an insight into how auditors perform diagnostic reasoning tasks through an analytical review (AR) process. AR refers to the diagnostic process of identifying, investigating, and resolving unexpected fluctuations in account balances and other financial relationships in financial statements. Auditors perfuming AR typically follow four distinct components of a diagnostic, sequential and iterative (DS1) process, namely: mental representation, hypothesis generation, information search, and hypothesis evaluation. Through the DS1 process, auditors are able to recognize and detect errors and irregularities in financial statements for the purpose of presenting a true and fair view of financial reporting, with the intention of communicating quality and reliable economic information of an enterprise to users.

COINTEGRATION IN FUNCTIONAL AUTOREGRESSIVE PROCESSES

This article defines the class of ${\cal H}$-valued autoregressive (AR) processes with a unit root of finite type, where ${\cal H}$ is a possibly infinite-dimensional separable Hilbert space, and derives a generalization of the Granger–Johansen Representation Theorem valid for any integration order $d = 1,2, \ldots$. An existence theorem shows that the solution of an AR process with a unit root of finite type is necessarily integrated of some finite integer order d, displays a common trends representation with a finite number of common stochastic trends, and it possesses an infinite-dimensional cointegrating space when ${\rm{dim}}{\cal H} = \infty$. A characterization theorem clarifies the connections between the structure of the AR operators and (i) the order of integration, (ii) the structure of the attractor space and the cointegrating space, (iii) the expression of the cointegrating relations, and (iv) the triangular representation of the process. Except for the fact that the dimension of the cointegrating space is infinite when ${\rm{dim}}{\cal H} = \infty$, the representation of AR processes with a unit root of finite type coincides with the one of finite-dimensional VARs, which can be obtained setting ${\cal H} = ^p $ in the present results.