A wavelet-based approach to the analysis and modelling of financial time series exhibiting strong long-range dependence: the case of Southeast Europe

This paper demonstrates the utilization of wavelet-based tools for the analysis and prediction of financial time series exhibiting strong long-range dependence (LRD). Commonly emerging markets' stock returns are characterized by LRD. Therefore, we track the LRD evolvement for the return series of six Southeast European stock indices through the application of a wavelet-based semi-parametric method. We further engage the á trous wavelet transform in order to extract deeper knowledge on the returns term structure and utilize it for prediction purposes. In particular, a multiscale autoregressive (MAR) model is fitted and its out-of-sample forecast performance is benchmarked to that of ARMA. Additionally, a data-driven MAR feature selection procedure is outlined. We find that the wavelet-based method captures adequately LRD dynamics both in calm as well as in turmoil periods detecting the presence of transitional changes. At the same time, the MAR model handles with the complicated autocorrelation structure implied by the LRD in a parsimonious way achieving better performance.     

ROBUST ESTIMATION IN PARAMETRIC TIME SERIES MODELS UNDER LONG- AND SHORT-RANGE-DEPENDENT STRUCTURES

This paper studies the asymptotic behaviour of an M-estimator of regression parameters in the linear model when the design variables are either stationary short-range dependent (SRD), α-mixing or long-range dependent (LRD), and the errors are LRD. The weak consistency and the asymptotic distributions of the M-estimator are established. We present some simulated examples to illustrate the efficiency of the proposed M-estimation method.     

Some results on random design regression with long memory errors and predictors

This paper studies nonparametric regression with long memory (LRD) errors and predictors. First, we formulate general conditions which guarantee the standard rate of convergence for a nonparametric kernel estimator. Second, we calculate the mean integrated squared error (MISE). In particular, we show that LRD of errors may influence MISE. On the other hand, an estimator for a shape function is typically not influenced by LRD in errors. Finally, we investigate properties of a data-driven bandwidth choice. We show that averaged squared error (ASE) is a good approximation of MISE; however, this is not the case for a cross-validation criterion.     

Nonparametric regression for dependent data in the errors-in-variables problem

We consider the nonparametric estimation of the regression functions for dependent data. Suppose that the covariates are observed with additive errors in the data and we employ nonparametric deconvolution kernel techniques to estimate the regression functions in this paper. We investigate how the strength of time dependence affects the asymptotic properties of the local constant and linear estimators. We treat both short-range dependent and long-range dependent linear processes in a unified way and demonstrate that the long-range dependence (LRD) of the covariates affects the asymptotic properties of the nonparametric estimators as well as the LRD of regression errors does.     

Estimation of long-range dependence in gappy Gaussian time series

Statistics and Computing - Knowledge of the long-range dependence (LRD) parameter is critical to studies of self-similar behavior. However, statistical estimation of the LRD parameter becomes...     

Long-Range Dependence of Markov Renewal Processes

This paper examines long‐range dependence (LRD) and asymptotic properties of Markov renewal processes generalizing results of Daley for renewal processes. The Hurst index and discrepancy function, which is the difference between the expected number of arrivals in (0, t] given a point at 0 and the number of arrivals in (0, t] in the time stationary version, are examined in terms of the moment index. The moment index is the supremum of the set of r > 0 such that the rth moment of the first return time to a state is finite, employing the solidarity results of Sgibnev. The results are derived for irreducible, regular Markov renewal processes on countable state spaces. The paper also derives conditions to determine the moment index of the first return times in terms of the Markov renewal kernel distribution functions of the process.     

Cellular telephones and motor-vehicle collisions: Some variations on matched-pairs analysis

We describe the analysis of some matched-pair binary data arising from a study designed to investigate whether cellular-telephone use is associated with motor-vehicle collisions. Conditional and random effects approaches to the problem are derived and compared. Driving intermittency is a potential confounder whose effect is assessed by strategic choices of the control period and by application of the bootstrap. The marked discrepancy between the conditional and random approaches merits further study.     

Communication in Statistics-Theory and methods improved GQL estimation method for the generalised BINMA(1) model

In a recent research, the quasi-likelihood estimation methodology was developed to estimate the regression effects in the Generalized BINMA(1) (GBINMA(1)) process. The method provides consistent parameter estimates but, in the intermediate computations, moment estimating equations were used to estimate the serial- and cross-correlation parameters. This procedure may not result optimal parameter estimates, in particular, for the regression effects. This paper provides an alternative simpler GBINMA(1) process based on multivariate thinning properties where the main effects are estimated via a robust generalized quasi-likelihood (GQL) estimation approach. The two techniques are compared through some simulation experiments. A real-life data application is studied.     

Type-I intermittency from Markov binary block visibility graph perspective

In this work, the type-I intermittency is studied from the optimized Markov binary visibility graphs perspective. We consider a local Poincaré map such as the logistic map that is a simple model for exhibiting this type of intermittency. To consider the acceptance gate as G≪0.01, we show that the transition between laminar and non-laminar zones in type-I intermittency takes distinct phases and regions. According to their behavioral characteristics, we call them as pure, switching, threshold, trapping, and transforming phases for the laminar zone and initial, terminal reinjection, and chaotic burst regions for non-laminar zone. We investigate their properties based on statistical tools such as the maximum and the mean length of the laminar zone and also length distributions of the laminar zone. For further investigation, we study degree distribution of the complex network generated by type-I intermittency time series and finally, predict various behaviors of phases and regions by proposed theoretical degree distributions.KEYWORDS: Type-I intermittency, binary block design, Markov binary visibility graph, chaos

We study the effect of the acceptance gate on the type-I intermittency derived from a local Poincaré map such as the logistic map. Then, based on system behaviors during the transition between laminar and non-laminar zones, we consider them as dynamic states such as pure, switching, threshold, trapping, and transforming phases for laminar zone and initial, terminal reinjection, and chaotic burst regions for non-laminar zone. We define an optimized Markov binary visibility graphs using the binary block design in order to describe the type-I intermittency from the complex network perspective. Statistical results proved this claim and in order to further illustrate this claim, we use from network properties of the optimized Markov binary visibility graphs.     

固定效应面板线性回归模型的移动分块经验似然估计

本文针对固定效应面板线性回归模型中特意误差项为任意形式序列相关情形,提出了移动分块经验似然估计方法,并给出了大样本性质。模拟研究表明：该方法适用于特意误差项序列相关形式已知和形式未知两种情形,较Baltagi和Li（1994）以及Gon?alves（2011）提出的方法有效。本文采用该方法对CO2排放量与城市化水平之间的关系进行了实证分析,结果表明：城市化水平对CO2排放量有显著影响,不同城市化阶段对CO2排放量影响不同。     

On the complex dynamics of functional-coefficients nonlinear autoregressive time series models

In this article, a new chaotic functional-coefficient nonlinear autoregressive time series model is formulated. Asymptotic stability of the equilibria of the skeleton is studied. Complex dynamics of the proposed model are investigated by means of the bifurcations, time series diagrams, and phase portraits. The effects of noise intensity on its dynamics and the intermittency phenomenon are also discussed via simulation. Two chaotic indicators, namely, the fractal dimension and the Lyapunov exponent methods are investigated for the model.     

Two parameter cuscore qualty control procedures

This paper is concerned with the problem of simultaneously monitoring the process mean and process variability of continuous production processes using combined Shewhart-cumulative score (cuscore) quality control procedures developed by Ncube and Woodall (1984). Two methods of approach are developed and their properties are investigated. One method uses two separate Shewhart-cuscore control charts, one for determining shifts in the process mean and the other for detecting shifts in process variability. The other method uses a single combined statistic which is sensitive to shifts in both the mean and the variance. Each procedure is compared to the corresponding Shewhart schemes. It will be shown by average run length calculations that the proposed Shewhart- cuscore schemes are considerably more efficient than the comparative Shewhart procedures for certain shifts in the process mean and process variability for the case when the underlying process control variable is assumed to be normally distributed.     

A new random permutation test in ANOVA models

This paper developed an exact method of random permutations when testing both interaction and main effects in the two-way ANOVA model. The method of this paper can be regarded as a much improved model when compared with those of the previous studies such as Still and White (1981) and ter Braak (1992). We further conducted a simulation experiment in order to check the statistical performance of the proposed method. The proposed method works relatively well for small sample sizes compare with the existing methods. This work was supported by Korea Science and Engineering Foundation Grant (R14-2003-002-0100)     

Vector autoregressive models with measurement errors for testing Granger causality

This paper develops a method for estimating the parameters of a vector autoregression (VAR) observed in white noise. The estimation method assumes that the noise variance matrix is known and does not require any iterative process. This study provides consistent estimators and the asymptotic distribution of the parameters required for conducting tests of Granger causality. Methods in the existing statistical literature cannot be used for testing Granger causality, since under the null hypothesis the model becomes unidentifiable. Measurement error effects on parameter estimates were evaluated by using computational simulations. The results suggest that the proposed approach produces empirical false positive rates close to the adopted nominal level (even for small samples) and has a satisfactory performance around the null hypothesis. The applicability and usefulness of the proposed approach are illustrated using a functional magnetic resonance imaging dataset.     

Spatio-temporal model for crop yield forecasting

This paper proposes a linear mixed model (LMM) with spatial effects, trend, seasonality and outliers for spatio-temporal time series data. A linear trend, dummy variables for seasonality, a binary method for outliers and a multivariate conditional autoregressive (MCAR) model for spatial effects are adopted. A Bayesian method using Gibbs sampling in Markov Chain Monte Carlo is used for parameter estimation. The proposed model is applied to forecast rice and cassava yields, a spatio-temporal data type, in Thailand. The data have been extracted from the Office of Agricultural Economics, Ministry of Agriculture and Cooperatives of Thailand. The proposed model is compared with our previous model, an LMM with MCAR, and a log transformed LMM with MCAR. We found that the proposed model is the most appropriate, using the mean absolute error criterion. It fits the data very well in both the fitting part and the validation part for both rice and cassava. Therefore, it is recommended to be a primary model for forecasting these types of spatio-temporal time series data.     

Combining Inverse Probability Weighting and Multiple Imputation to Improve Robustness of Estimation

Inverse probability weighting (IPW) and multiple imputation are two widely adopted approaches dealing with missing data. The former models the selection probability, and the latter models data distribution. Consistent estimation requires correct specification of corresponding models. Although the augmented IPW method provides an extra layer of protection on consistency, it is usually not sufficient in practice as the true data‐generating process is unknown. This paper proposes a method combining the two approaches in the same spirit of calibration in sampling survey literature. Multiple models for both the selection probability and data distribution can be simultaneously accounted for, and the resulting estimator is consistent if any model is correctly specified. The proposed method is within the framework of estimating equations and is general enough to cover regression analysis with missing outcomes and/or missing covariates. Results on both theoretical and numerical investigation are provided.     

A nonparametric estimation procedure for the Hawkes process: comparison with maximum likelihood estimation

In earlier work, Kirchner [An estimation procedure for the Hawkes process. Quant Financ. 2017;17(4):571–595], we introduced a nonparametric estimation method for the Hawkes point process. In this paper, we present a simulation study that compares this specific nonparametric method to maximum-likelihood estimation. We find that the standard deviations of both estimation methods decrease as power-laws in the sample size. Moreover, the standard deviations are proportional. For example, for a specific Hawkes model, the standard deviation of the branching coefficient estimate is roughly 20% larger than for MLE – over all sample sizes considered. This factor becomes smaller when the true underlying branching coefficient becomes larger. In terms of runtime, our method clearly outperforms MLE. The present bias of our method can be well explained and controlled. As an incidental finding, we see that also MLE estimates seem to be significantly biased when the underlying Hawkes model is near criticality. This asks for a more rigorous analysis of the Hawkes likelihood and its optimization.     

在不可忽略抽样机制下目标变量的估计问题

抽样调查是通过对有限总体的重复抽样,用样本数据对总体的目标变量进行估计,但是若样本的抽样过程与目标变量有关,则样本分布不能代表总体分布,此时用样本数据来估计总体会产生很大的偏差。针对这种在不可忽略的抽样机制下如何进行目标变量的估计问题展开讨论,详细介绍了三种处理该问题的方法并对这三种方法进行了比较,得出第三种概率密度函数的方法是处理该问题比较好的一种方法。