First-order Autoregressive Model Research Articles

Estimated model-based robust optimization of closed-loop supply chain under uncertain carbon tax rates and demand

Due to the growing interest in sustainable development, the importance of research on closed-loop supply chain is being emphasized more and more. The main objective of this study is to develop a robust optimization model for a closed-loop supply chain that reflects uncertain demand and the time-series patterns of uncertain carbon tax rates on the basis of historical data. This study incorporates the first-order autoregressive model into a set-based robust optimization model to find a less conservative solution. Two novel uncertainty sets reflecting the time-series pattern using the historical data are proposed and tractable robust counterparts are developed. The results of numerical experiments conducted herein indicate that the optimal solutions of the proposed models are less conservative than those of the conventional robust optimization model, with a slight loss in robustness to the parameter uncertainty. Moreover, according to the experimental results, the stronger the autocorrelation of the uncertain parameter, the greater are the benefits of the proposed models. Furthermore, the smaller the size of the historical data, the higher are the conservatism and robustness of the proposed model. In addition, when the exact support set is known, the proposed model can be less conservative than that when it is not known, but both proposed models outperform the conventional robust optimization model.

New bivariate Poisson extended exponential distributions and associated BINAR(1) processes with applications

This study proposes two types of bivariate Poisson extended exponential distributions: the basic bivariate Poisson extended exponential distribution and the Sarmanov-based bivariate Poisson extended exponential distribution. The two bivariate Poisson extended exponential distributions are then introduced as joint innovation distributions in a bivariate first-order integer-valued autoregressive process based on binomial thinning. The model parameters are estimated using maximum likelihood in basic bivariate Poisson extended exponential and Sarmanov-based bivariate Poisson extended exponential distributions. Conditional maximum likelihood is applied to the bivariate first-order integer-valued autoregressive process. Simulation experiments are used to evaluate the performance of small and large samples. In addition, the newly developed bivariate first-order integer-valued autoregressive models are then applied to the Pittsburgh crime series data and candies data. We show that they fit better than existing bivariate first-order integer-valued autoregressive models described in the literature.

An Observation-Driven Random Parameter INAR(1) Model Based on the Poisson Thinning Operator.

This paper presents a first-order integer-valued autoregressive time series model featuring observation-driven parameters that may adhere to a particular random distribution. We derive the ergodicity of the model as well as the theoretical properties of point estimation, interval estimation, and parameter testing. The properties are verified through numerical simulations. Lastly, we demonstrate the application of this model using real-world datasets.

A novel geometric AR(1) model and its estimation

This paper proposes a first-order geometric autoregressive model based on a new thinning operator. The parameters of the model are estimated by the method of Two-Stage Conditional Least Squares and Saddlepoint Approximation. Simulation studies demonstrate that the saddlepoint approximation estimator performs well, even in the case of small sample sizes. To illustrate the significance of the model, a real data analysis of the number of downloads of a TeX editor is presented.

Autoregressive optimal transport models.

Series of univariate distributions indexed by equally spaced time points are ubiquitous in applications and their analysis constitutes one of the challenges of the emerging field of distributional data analysis. To quantify such distributional time series, we propose a class of intrinsic autoregressive models that operate in the space of optimal transport maps. The autoregressive transport models that we introduce here are based on regressing optimal transport maps on each other, where predictors can be transport maps from an overall barycenter to a current distribution or transport maps between past consecutive distributions of the distributional time series. Autoregressive transport models and their associated distributional regression models specify the link between predictor and response transport maps by moving along geodesics in Wasserstein space. These models emerge as natural extensions of the classical autoregressive models in Euclidean space. Unique stationary solutions of autoregressive transport models are shown to exist under a geometric moment contraction condition of Wu & Shao [(2004) Limit theorems for iterated random functions. Journal of Applied Probability 41, 425-436)], using properties of iterated random functions. We also discuss an extension to a varying coefficient model for first-order autoregressive transport models. In addition to simulations, the proposed models are illustrated with distributional time series of house prices across U.S. counties and annual summer temperature distributions.

Efficient Data Augmentation Techniques for Some Classes of State Space Models

Data augmentation improves the convergence of iterative algorithms, such as the EM algorithm and Gibbs sampler by introducing carefully designed latent variables. In this article, we first propose a data augmentation scheme for the first-order autoregression plus noise model, where optimal values of working parameters introduced for recentering and rescaling of the latent states, can be derived analytically by minimizing the fraction of missing information in the EM algorithm. The proposed data augmentation scheme is then utilized to design efficient Markov chain Monte Carlo (MCMC) algorithms for Bayesian inference of some non-Gaussian and nonlinear state space models, via a mixture of normals approximation coupled with a block-specific reparametrization strategy. Applications on simulated and benchmark real data sets indicate that the proposed MCMC sampler can yield improvements in simulation efficiency compared with centering, noncentering and even the ancillarity-sufficiency interweaving strategy.

Estimation of Heritability under Correlated Errors Using the Full-Sib Model

In plant and animal breeding, sometimes observations are not independently distributed. There may exist a correlated relationship between the observations. In the presence of highly correlated observations, the classical premise of independence between observations is violated. Plant and animal breeders are particularly interested to study the genetic components for different important traits. In general, for estimating heritability, a random component in the model must adhere to specific assumptions, such as random components, including errors, having a normal distribution, and being identically independently distributed. However, in many real-world situations, all of the assumptions are not fulfilled. In this study, correlated error structures are considered errors that are associated to estimate heritability for the full-sib model. The number of immediately preceding observations in an autoregressive series that are used to predict the value at the current observation is defined as the order of the autoregressive models. First-order and second-order autoregressive models i.e., AR(1) and AR(2) error structures, have been considered. In the case of the full-sib model, theoretical derivation of Expected Mean sum square (EMS) considering AR(1) structure has been obtained. A numerical explanation is provided for the derived EMS considering AR(1) structure. The predicted mean squares error (MSE) is obtained after including the AR(1) error structures in the model, and heritability is estimated using the resulting equations. It is noticed that correlated errors have a major influence on heritability estimation. Different correlation patterns, such as AR(1) and AR(2), can be inferred to change heritability estimates and MSE values. To attain better results, several combinations are offered for various scenarios.

Estimating the Topology of Preferential Attachment Graphs Under Partial Observability

This work addresses the problem of learning the topology of a network from the signals emitted by the network nodes. These signals are generated over time through a linear diffusion process, where neighboring nodes exchange messages according to the underlying network topology, and aggregate them according to a certain combination matrix. We consider the demanding setting of graph learning under partial observability, where signals are available only from a limited fraction of nodes, and we want to establish whether the topology of these nodes can be estimated faithfully, despite the presence of possibly many latent nodes. Recent results examined this problem when the network topology is generated according to an Erdős-Rényi random model. However, Erdős-Rényi graphs feature homogeneity across nodes and independence across edges, while, over several real-world networks, significant heterogeneity is observed between very connected “hubs” and scarcely connected peripheral nodes, and the edge construction process entails significant dependencies across edges. Preferential attachment random graphs were conceived primarily to fill these gaps. We tackle the problem of graph learning over preferential attachment graphs by focusing on the following setting: first-order vector autoregressive models equipped with a stable Laplacian combination matrix, and a network topology drawn according to the popular Bollobás-Riordan preferential attachment model. The main result established in this work is that a combination-matrix estimator known as Granger estimator achieves graph learning under partial observability.

Эффекты неликвидности на российском рынке акций

This work examines the impact of expected and unexpected illiquidity of Russian stockstraded on the Moscow Exchange on their ex ante and simultaneous excess returns. Following quantitative predictions of the market microstructure invariance hypothesis, I calculate the ex­pected ruble costs of executing a bet in the Russian stock market. This estimate is used to compute the invariance-implied low-frequency illiquidity measure for individual stocks. The expec­ted market illiquidity is estimated by a first-order autoregressive model, and the surprise illiquidity is the residuals from this model. We use two weighting methods (equal-weighting and value-wei­ghting) to calculate market returns, market illiquidity, as well as returns on size-based portfolios. According to the empirical analysis over the period from January 2010 to December 2020, the market premium for expected illiquidity in the Russian equity market was insignificant in most specifications, unlike the effect of unexpected market illiquidity. The negative effect of market illiquidity shocks on market returns is insignificant only in the case of using equal-weighted procedure over the period from January 2010 to June 2015. The weak form of the hypothesis that illiquidity effects are stronger for small-cap stocks is confirmed only in the case of using equal-weighting method over the period from July 2015 to December 2020.

Approximate bias for first-order autoregressive model with uniform innovations. Small sample case

Approximate bias for first-order autoregressive model with uniform innovations. Small sample case

Effects of Microstate Dynamic Brain Network Disruption in Different Stages of Schizophrenia.

Schizophrenia is a heterogeneous mental disorder with unknown etiology or pathological characteristics. Microstate analysis of the electroencephalogram (EEG) signal has shown significant potential value for clinical research. Importantly, significant changes in microstate-specific parameters have been extensively reported; however, these studies have ignored the information interactions within the microstate network in different stages of schizophrenia. Based on recent findings, since rich information about the functional organization of the brain can be revealed by functional connectivity dynamics, we use the first-order autoregressive model to construct the functional connectivity of intra- and intermicrostate networks to identify information interactions among microstate networks. We demonstrate that, beyond abnormal parameters, disrupted organization of the microstate networks plays a crucial role in different stages of the disease by 128-channel EEG data collected from individuals with first-episode schizophrenia, ultrahigh-risk, familial high-risk, and healthy controls. According to the characteristics of the microstates of patients at different stages, the parameters of microstate class A are reduced, those of class C are increased, and the transitions from intra- to intermicrostate functional connectivity are gradually disrupted. Furthermore, decreased integration of intermicrostate information might lead to cognitive deficits in individuals with schizophrenia and those in high-risk states. Taken together, these findings illustrate that the dynamic functional connectivity of intra- and intermicrostate networks captures more components of disease pathophysiology. Our work sheds new light on the characterization of dynamic functional brain networks based on EEG signals and provides a new interpretation of aberrant brain function in different stages of schizophrenia from the perspective of microstates.

Pain and physical activity for one individual

Aims: there is increasing awareness that for effective patient care we need more than only randomized controlled trials with groups of participants and that carefully collected single case (N = 1) data have several important advantages over traditional group-level studies. With the advance of technology, collecting relevant data from a single case is becoming easier by the day, and this offers tremendous opportunities for understanding how behaviors displayed by an individual can be influenced by one or several key variables. For example, how pain experienced influences the amount of time spent on physical exercise. Method: using publicly available observational single case data, five models are compared: a classical ordinary least squares (OLS) linear regression model; a dynamic regression model (DRM); a two-level random-intercepts model (2LRI); a continuous covariate first-order autoregressive correlation model (CAR1); and an ordinary least squares model with time trend (OLST). These models are compared in terms of overall model fit statistics, estimates of the relation between physical activity (response variable of interest) and pain (covariate of interest), and residual statistics. Results: 2LRI outperforms all other models on both overall model fit and residual statistics, and provides covariate estimates that are in between the relative extremes provided by other models. CAR1 and OLST demonstrate an almost identical performance and one that is substantially better than OLS – which performs worst – and DRM. Conclusion: for observational single case data, DRM, CAR1, OLST, and 2LRI account for the serial correlation that is typically present in single case data in somewhat different ways under somewhat different assumptions, and all perform better than OLS. Implications of these findings for observational, quasi-experimental, and experimental single case studies are discussed.

Controlled Parameter Estimation for The AR(1) Model with Stationary Gaussian Noise

This paper deals with the maximum likelihood estimator for the parameter of first-order autoregressive models driven by the stationary Gaussian noises (Colored noise) together with an input. First, we will find the optimal input that maximizes the Fisher information, and then, with the method of the Laplace transform, both the asymptotic properties and the asymptotic design problem of the maximum likelihood estimator will be investigated. The results of the numerical simulation confirm the theoretical analysis and show that the proposed maximum likelihood estimator performs well in finite samples.

Modified Two-Stage Sampling Around the Mean of the First-Order Autoregressive Model

Modified Two-Stage Sampling Around the Mean of the First-Order Autoregressive Model

Semantic Metrics for Non Real-Time Applications

In this work, we investigate the issue of semantics in non real-time communication scenarios, that is, without stringent information delivery constraints. While semantics has been widely used in the context of communications, the definition of the semantic metrics has been limited to the real-time applications. We thus revise the basic concepts of the timeliness and the accuracy and propose their formal definitions in the case of non real-time applications characterized by a possibility of non-causal signal reconstruction at the destination. In particular, we link the concept of accuracy to the canonical first-order auto-regressive model of the signal, while the timeliness is defined by the time difference to reference samples of the signal. We compare the proposed semantic metrics in the case of different buffer management strategies and using numerical examples we show that the optimality of the transmission strategy changes when the real-time or non real-time applications are considered.

Collinearity Issues in Autoregressive Models with Time-Varying Serially Dependent Covariates

First-order autoregressive models are popular to assess the temporal dynamics of a univariate process. Researchers often extend these models to include time-varying covariates, such as contextual factors, to investigate how they moderate processes’ dynamics. We demonstrate that doing so has implications for how well one can estimate the autoregressive and covariate effects, as serial dependence in the variables can imply predictor collinearity. This is a noteworthy contribution, since in current practice serial dependence in a time-varying covariate is rarely considered important. We first recapitulate the role of predictor collinearity for estimation precision in an ordinary least squares context, by discussing how it affects estimator variances, covariances and correlations. We then derive a general formula detailing how predictor collinearity in first-order autoregressive models is impacted by serial dependence in the covariate. We provide a simulation study to illustrate the implications of the formula for different types of covariates. The simulation results highlight when the collinearity issue becomes severe enough to hamper interpretation of the effects. We also show that the effect estimates can be biased in small samples (i.e., 50 time points). Implications for study design, the use of time as a predictor, and related model variants are discussed.

Asymptotic normality of residual density estimator in stationary and explosive autoregressive models

The error density estimator in the first-order autoregressive model is considered based on α-mixing errors. Since the errors are not observed, the residual kernel density estimator is provided. The asymptotic normality of the residual estimator is obtained when the autoregressive model is a stationary process or an explosive process. Moreover, some simulations such as the fitted curves, mean integrated square errors and histograms are illustrated to the residual kernel estimator and residual histogram estimator. It is shown that the residual kernel estimator with smooth kernel is smoother than the residual histogram estimator.

First-order random coefficient mixed-thinning integer-valued autoregressive model

The paper develops a first-order random coefficient mixed-thinning integer-valued autoregressive time series model (RCMTINAR(1)) to deal with the data related to the counting of elements of variable character. Moments and autocovariance functions for this model are studied as the distribution of the innovation sequence is unknown. The conditional least squares and modified quasi-likelihood are adopted to estimate the model parameters. Asymptotic properties of the obtained estimators are established. The performances of these estimators are investigated and compared with false modified quasi-likelihood via simulations. Finally, the practical relevance of the model is illustrated by using two applications to a SIMpass data set and a burglary data set with a comparison with relevant models that exist so far in the literature.

The role of CEOs' human capital in sustaining superior performance–empirical evidence from China

PurposeFocusing on the important representative of firm intellectual capital (IC), this research explores the effects of chief executive officer’s (CEOs') managerial human capitals on sustaining superior performance in Chinese transition economy to prove the dynamic and strategic value of IC and fulfill the gap of lacking emerging market studies in this research field.Design/methodology/approachBased on dynamic managerial capability theoretical framework, the authors propose a dynamic management path to analyze the influencing mechanism of CEOs' managerial human capitals to firm performance persistence and the moderating effect of environment uncertainty. Using a panel data of Chinese publicly listed firms from 2008 to 2017, it adopts dynamic first-order autoregressive models to examine these hypotheses. Several tests are conducted to further analyze and ensure that the results are robust and reliable.FindingsThese managerial human capitals reveal heterogenous impacts on sustaining superior performance, and environment uncertainty is a valid moderating variable to further distinguish their dynamic values. The supplementary analyses show the integrating effect of an MBA degree and output functional experience is positive and significant, and the results in Chinese state-owned and private firm subsamples are distinct.Practical implicationsIt is beneficial for corporate stakeholders to judge and select CEOs and for policymakers to improve the efficiency advantage of IC in Chinese emerging market.Originality/valueThis study first explores the relationship between CEOs' managerial human capitals and superior performance persistence. Through introducing a dynamic perspective, it has extended existing performance persistence research into individual level and provided a new intellectual source of sustainable competitive advantages.

Dual CUSUM Charts for Monitoring Autocorrelated AR (1) Processes Mean With s-Skipping Sampling Scheme

In statistical process monitoring, it is often assumed that the sequential observations generated by processes are independent and identically distributed (iid). However, in real practice, these observations tend to exhibit an autocorrelation pattern. Thus, an autocorrelated process yields misleading results in terms of a high false alarm rate and slow detection of process changes if employing iid-based designed monitoring schemes. Therefore, in this article, we propose the dual cumulative sum (DCUSUM) and dual Crosier’s CUSUM (DCCUSUM) mean charts for monitoring the autocorrelated processes using a first-order autoregressive model. Monte Carlo simulations are extensively used to compute the performance measures: the average run length, standard deviation run length, extra quadratic loss, and relative average run length of the two-sided DCUSUM and DCCUSUM charts under both the zero-state and steady state cases. It is observed that as the level of autocorrelation increases, the performance of the studied charts deteriorates. Thus, a s-skipping sampling scheme is incorporated to reduce the negative effect of autocorrelation. To demonstrate the effect of autocorrelation and highlight implications further, a simulated dataset with a shift in the process mean is considered.