A New First-Order Integer-Valued Autoregressive Model with Bell Innovations

A Poisson distribution is commonly used as the innovation distribution for integer-valued autoregressive models, but its mean is equal to its variance, which limits flexibility, so a flexible, one-parameter, infinitely divisible Bell distribution may be a good alternative. In addition, for a parameter with a small value, the Bell distribution approaches the Poisson distribution. In this paper, we introduce a new first-order, non-negative, integer-valued autoregressive model with Bell innovations based on the binomial thinning operator. Compared with other models, the new model is not only simple but also particularly suitable for time series of counts exhibiting overdispersion. Some properties of the model are established here, such as the mean, variance, joint distribution functions, and multi-step-ahead conditional measures. Conditional least squares, Yule–Walker, and conditional maximum likelihood are used for estimating the parameters. Some simulation results are presented to access these estimates’ performances. Real data examples are provided.     

Count Data Time Series Modelling in Julia—The CountTimeSeries.jl Package and Applications

A new software package for the Julia language, CountTimeSeries.jl, is under review, which provides likelihood based methods for integer-valued time series. The package’s functionalities are showcased in a simulation study on finite sample properties of Maximum Likelihood (ML) estimation and three real-life data applications. First, the number of newly infected COVID-19 patients is predicted. Then, previous findings on the need for overdispersion and zero inflation are reviewed in an application on animal submissions in New Zealand. Further, information criteria are used for model selection to investigate patterns in corporate insolvencies in Rhineland-Palatinate. Theoretical background and implementation details are described, and complete code for all applications is provided online. The CountTimeSeries package is available at the general Julia package registry.     

A New Extension of Thinning-Based Integer-Valued Autoregressive Models for Count Data

The thinning operators play an important role in the analysis of integer-valued autoregressive models, and the most widely used is the binomial thinning. Inspired by the theory about extended Pascal triangles, a new thinning operator named extended binomial is introduced, which is a general case of the binomial thinning. Compared to the binomial thinning operator, the extended binomial thinning operator has two parameters and is more flexible in modeling. Based on the proposed operator, a new integer-valued autoregressive model is introduced, which can accurately and flexibly capture the dispersed features of counting time series. Two-step conditional least squares (CLS) estimation is investigated for the innovation-free case and the conditional maximum likelihood estimation is also discussed. We have also obtained the asymptotic property of the two-step CLS estimator. Finally, three overdispersed or underdispersed real data sets are considered to illustrate a superior performance of the proposed model.     

Comparative Analysis of Different Univariate Forecasting Methods in Modelling and Predicting the Romanian Unemployment Rate for the Period 2021–2022

Unemployment has risen as the economy has shrunk. The coronavirus crisis has affected many sectors in Romania, some companies diminishing or even ceasing their activity. Making forecasts of the unemployment rate has a fundamental impact and importance on future social policy strategies. The aim of the paper is to comparatively analyze the forecast performances of different univariate time series methods with the purpose of providing future predictions of unemployment rate. In order to do that, several forecasting models (seasonal model autoregressive integrated moving average (SARIMA), self-exciting threshold autoregressive (SETAR), Holt–Winters, ETS (error, trend, seasonal), and NNAR (neural network autoregression)) have been applied, and their forecast performances have been evaluated on both the in-sample data covering the period January 2000–December 2017 used for the model identification and estimation and the out-of-sample data covering the last three years, 2018–2020. The forecast of unemployment rate relies on the next two years, 2021–2022. Based on the in-sample forecast assessment of different methods, the forecast measures root mean squared error (RMSE), mean absolute error (MAE), and mean absolute percent error (MAPE) suggested that the multiplicative Holt–Winters model outperforms the other models. For the out-of-sample forecasting performance of models, RMSE and MAE values revealed that the NNAR model has better forecasting performance, while according to MAPE, the SARIMA model registers higher forecast accuracy. The empirical results of the Diebold–Mariano test at one forecast horizon for out-of-sample methods revealed differences in the forecasting performance between SARIMA and NNAR, of which the best model of modeling and forecasting unemployment rate was considered to be the NNAR model.     

Pattern interdependent network of cross-correlation in multivariate time series

Cross-correlation of a bivariate time series induces interdependencies between local patterns in the two series, which cooperatively exhibit in turn the structure of the cross-correlation. However, this structure is lost in the procedure of statistical average in time series analysis. In this paper a new concept called pattern interdependent network is proposed to display the structure of cross-correlation, in which the nodes are unique local patterns and the linkages are co-occurring frequencies of the unique local patterns in the series. The performance is illustrated by the bivariate series generated with the Gaussian process and the auto-regressive fractionally integrated moving average (ARFIMA) model. It is found that the cross-correlation and the scaling behaviors dominate the pattern of backbone structure (the set of the nodes and the set of linkages) and the symmetry of the network, respectively. The ARFIMA model can reproduce the structural behaviors of cross-correlations in U.S. stock markets. This concept provides us with a new method for detecting the structure of couplings between time series in various fields, such as clinical pathological signals.     

Beam coupling and decoupling in degenerate two-wave mixing in a reflection geometry with photorefractive Bi2GeO20 crystals

The dependence of the effective gain on the incident angle of the beams and on the initial beam intensity ratio is studied in the experiment of degenerate two-wave mixing (TWM) in a reflection geometry with photorefractive Bi₁₂GeO₂₀ (BGO) crystals. A saturation value of the effective coupling constant ¦g¦-0.4 cm^–1 is obtained. In contrast to TWM operated in the drift mode (i.e. with a nonzero electric field applied to the crystal), for TWM operated in the diffusion mode (zero external electric field) as is our case, beam coupling is reduced by moving the crystal or the interference fringes at a constant speed. At high moving speeds, complete beam decoupling can be reached. A comparison between the theoretical and measured dependence of the effective gain on the moving speed is also made. Using this technique, complete isolation of two intersecting coherent beams inside a nonlinear medium can be achieved.     

Statistical Inference for Periodic Self-Exciting Threshold Integer-Valued Autoregressive Processes

This paper considers the periodic self-exciting threshold integer-valued autoregressive processes under a weaker condition in which the second moment is finite instead of the innovation distribution being given. The basic statistical properties of the model are discussed, the quasi-likelihood inference of the parameters is investigated, and the asymptotic behaviors of the estimators are obtained. Threshold estimates based on quasi-likelihood and least squares methods are given. Simulation studies evidence that the quasi-likelihood methods perform well with realistic sample sizes and may be superior to least squares and maximum likelihood methods. The practical application of the processes is illustrated by a time series dataset concerning the monthly counts of claimants collecting short-term disability benefits from the Workers’ Compensation Board (WCB). In addition, the forecasting problem of this dataset is addressed.     

Entropy Estimation Using a Linguistic Zipf–Mandelbrot–Li Model for Natural Sequences

Entropy estimation faces numerous challenges when applied to various real-world problems. Our interest is in divergence and entropy estimation algorithms which are capable of rapid estimation for natural sequence data such as human and synthetic languages. This typically requires a large amount of data; however, we propose a new approach which is based on a new rank-based analytic Zipf–Mandelbrot–Li probabilistic model. Unlike previous approaches, which do not consider the nature of the probability distribution in relation to language; here, we introduce a novel analytic Zipfian model which includes linguistic constraints. This provides more accurate distributions for natural sequences such as natural or synthetic emergent languages. Results are given which indicates the performance of the proposed ZML model. We derive an entropy estimation method which incorporates the linguistic constraint-based Zipf–Mandelbrot–Li into a new non-equiprobable coincidence counting algorithm which is shown to be effective for tasks such as entropy rate estimation with limited data.     

The Impact of Linear Filter Preprocessing in the Interpretation of Permutation Entropy

Permutation Entropy (PE) is a powerful tool for measuring the amount of information contained within a time series. However, this technique is rarely applied directly on raw signals. Instead, a preprocessing step, such as linear filtering, is applied in order to remove noise or to isolate specific frequency bands. In the current work, we aimed at outlining the effect of linear filter preprocessing in the final PE values. By means of the Wiener–Khinchin theorem, we theoretically characterize the linear filter’s intrinsic PE and separated its contribution from the signal’s ordinal information. We tested these results by means of simulated signals, subject to a variety of linear filters such as the moving average, Butterworth, and Chebyshev type I. The PE results from simulations closely resembled our predicted results for all tested filters, which validated our theoretical propositions. More importantly, when we applied linear filters to signals with inner correlations, we were able to theoretically decouple the signal-specific contribution from that induced by the linear filter. Therefore, by providing a proper framework of PE linear filter characterization, we improved the PE interpretation by identifying possible artifact information introduced by the preprocessing steps.     

Monitoring the Zero-Inflated Time Series Model of Counts with Random Coefficient

In this research, we consider monitoring mean and correlation changes from zero-inflated autocorrelated count data based on the integer-valued time series model with random survival rate. A cumulative sum control chart is constructed due to its efficiency, the corresponding calculation methods of average run length and the standard deviation of the run length are given. Practical guidelines concerning the chart design are investigated. Extensive computations based on designs of experiments are conducted to illustrate the validity of the proposed method. Comparisons with the conventional control charting procedure are also provided. The analysis of the monthly number of drug crimes in the city of Pittsburgh is displayed to illustrate our current method of process monitoring.     

分层流体中移动动量源生成准二维偶极子涡街特性实验

采用水平移动射流方法模拟移动动量源,实验研究了该移动动量源在密度分层流体中生成准二维偶极子涡街的机理,分析了偶极子涡街的演化特性. 在系列实验基础上,获得了移动动量源在密度分层流体中能够演化为偶极子涡街的(Re,Fr)组合条件. 对不同的Re取值,获得了偶极子涡街无因次形成时间及其无因次涡街平均波长倒数与Fr之间的相关关系,表明它们不依赖于Re数,而与Fr近似为幂指数关系. 关键词： 分层流体 移动动量源 偶极子涡街 涡街形成时间     

Chaos game representation （CGR）-walk model for DNA sequences

Chaos game representation (CGR) is an iterative mapping technique that processes sequences of units, such as nucleotides in a DNA sequence or amino acids in a protein, in order to determine the coordinates of their positions in a continuous space. This distribution of positions has two features: one is unique, and the other is source sequence that can be recovered from the coordinates so that the distance between positions may serve as a measure of similarity between the corresponding sequences. A CGR-walk model is proposed based on CGR coordinates for the DNA sequences. The CGR coordinates are converted into a time series, and a long-memory ARFIMA (p, d, q) model, where ARFIMA stands for autoregressive fractionally integrated moving average, is introduced into the DNA sequence analysis. This model is applied to simulating real CGR-walk sequence data of ten genomic sequences. Remarkably long-range correlations are uncovered in the data, and the results from these models are reasonably fitted with those from the ARFIMA (p, d, q) model.     

Driven quasi-one-dimensional classical electron gas in the presence of a constriction: Pinning and depinning

We studied the properties of a quasi-one-dimensional system of charged particles in the presence of a local Lorentzian-shaped constriction. We investigated the response of the system when a time-independent external driving force is applied in the unconfined direction. Langevin molecular dynamics simulations for different values of the drive and temperature are performed. We found that the particles are pinned unless a threshold value of the driving force is reached. We investigated in detail the depinning phenomenon. The system can depin “elastically”, with particles moving together and keeping their neighbors, or “quasi-elastically”, with particles moving together through a complex net of conducting channels without keeping their neighbors. In the case of elastic depinning the velocity vs applied drive curves is characterized by a critical exponent β consistent with the value , while in the case of quasi-elastic depinning the critical exponent β has on average the value 0.94. The model is relevant e.g. for electrons on liquid helium, colloids and dusty plasma.     

The Z 0-Boson Contribution to the Anomalous Moments of an Electron in a Plane-Wave Electromagnetic Field

This paper considers the Z ⁰-boson contribution to the mass of an electron moving in a plane-wave field. The dependence of the Z ⁰-boson contribution to the anomalous magnetic moment (AMM) and anomalous electric moment (AEM) of the electron on the parameters of the external field is investigated in terms of the conventional Weinberg–Salam–Glashow model.     

Cross-Scale Causality and Information Transfer in Simulated Epileptic Seizures

An information-theoretic approach for detecting causality and information transfer was applied to phases and amplitudes of oscillatory components related to different time scales and obtained using the wavelet transform from a time series generated by the Epileptor model. Three main time scales and their causal interactions were identified in the simulated epileptic seizures, in agreement with the interactions of the model variables. An approach consisting of wavelet transform, conditional mutual information estimation, and surrogate data testing applied to a single time series generated by the model was demonstrated to be successful in the identification of all directional (causal) interactions between the three different time scales described in the model. Thus, the methodology was prepared for the identification of causal cross-frequency phase–phase and phase–amplitude interactions in experimental and clinical neural data.     

Statistics of count numbers from a photomultiplier tube and its implications for error estimation

We present investigations of counting statistics for five different luminescence-measuring systems. The dark current background and the counts obtained for a PM tube under constant illumination at various light intensities were measured. Where no divider is present in the counting system, the standard deviation of the number of counts exceeds the value predicted by a Poisson distribution but by different amounts in the different systems. This has implications for analysis of the uncertainties in the estimated equivalent doses and other quantitative analyses of luminescence measurements. We suggest how to account for the observed overdispersion of count numbers in uncertainty estimation.     

Local Lead–Lag Relationships and Nonlinear Granger Causality: An Empirical Analysis

The Granger causality test is essential for detecting lead–lag relationships between time series. Traditionally, one uses a linear version of the test, essentially based on a linear time series regression, itself being based on autocorrelations and cross-correlations of the series. In the present paper, we employ a local Gaussian approach in an empirical investigation of lead–lag and causality relations. The study is carried out for monthly recorded financial indices for ten countries in Europe, North America, Asia and Australia. The local Gaussian approach makes it possible to examine lead–lag relations locally and separately in the tails and in the center of the return distributions of the series. It is shown that this results in a new and much more detailed picture of these relationships. Typically, the dependence is much stronger in the tails than in the center of the return distributions. It is shown that the ensuing nonlinear Granger causality tests may detect causality where traditional linear tests fail.     

Progress in physical properties of Chinese stock markets

In the past two decades, statistical physics was brought into the field of finance, applying new methods and concepts to financial time series and developing a new interdiscipline “econophysics”. In this review, we introduce several commonly used methods for stock time series in econophysics including distribution functions, correlation functions, detrended fluctuation analysis method, detrended moving average method, and multifractal analysis. Then based on these methods, we review some statistical properties of Chinese stock markets including scaling behavior, long-term correlations, cross-correlations, leverage effects, antileverage effects, and multifractality. Last, based on an agent-based model, we develop a new option pricing model — financial market model that shows a good agreement with the prices using real Shanghai Index data. This review is helpful for people to understand and research statistical physics of financial markets.     

不同滤波方法在去趋势波动分析中去噪的应用比较

研究了连续噪声和尖峰噪声对去趋势波动分析的影响,发现噪声的存在使得双对数曲线在尺度较小时发生了"转折"现象.针对这一问题,文中采用三种不同滤波方法对理想时间序列进行了实验,结果表明,多级Vondrak滤波得到的高频序列与真实噪声序列无论是在强度还是在演变趋势上都展现出惊人的一致性,低频滤波序列的去趋势波动分析结果与真实信号十分接近,多级Vondrak滤波基本上能够消除由于噪声所引起的"转折"现象,而且这一研究结果对于滤波周期阈值的依赖性并不太大.多点滑动加权平均滤波虽然能够在一定程度上减轻噪声对于去趋势波动的影响,但不能从根本上消除由于噪声所引起的"转折"现象.快速傅里叶滤波在选择合适的滤波周期阈值时,能够基本消除噪声对去趋势波动分析的影响,但是由于其滤波结果对于滤波周期阈值的依赖较大,在实际应用中滤波周期阈值的选取比较困难.因此,多级Vondrak滤波是消除噪声对去趋势波动分析结果影响的一种有效的途径. 关键词： 多级Vondrak滤波 去趋势波动分析 多点滑动加权平均滤波 快速傅里叶滤波     

Conditional independence graph for nonlinear time series and its application to international financial markets

Conditional independence graphs are proposed for describing the dependence structure of multivariate nonlinear time series, which extend the graphical modeling approach based on partial correlation. The vertexes represent the components of a multivariate time series and edges denote direct dependence between corresponding series. The conditional independence relations between component series are tested efficiently and consistently using conditional mutual information statistics and a bootstrap procedure. Furthermore, a method combining information theory with surrogate data is applied to test the linearity of the conditional dependence. The efficiency of the methods is approved through simulation time series with different linear and nonlinear dependence relations. Finally, we show how the method can be applied to international financial markets to investigate the nonlinear independence structure.