First-order Autoregressive Process Research Articles

Noise Analysis of Average Blood Pressure in Terms of Aggregation of First-Order Autoregressive Process Models

Noise Analysis of Average Blood Pressure in Terms of Aggregation of First-Order Autoregressive Process Models

On MSE estimators of EBLUP of domain total under some longitudinal model

Żądlo (2012) proposed a certain unit-level longitudinal model which was a special case of the General Linear Mixed Model. Two vectors of random components included in the model obey assumptions of simultaneous spatial autoregressive process (SAR) and temporal first-order autoregressive process (AR(1)) respectively. Moreover, it is assumed that the population can change in time and the population elements can change its domains’ (subpopulations’) affiliation in time. Under the proposed model, Żądlo (2012) derived the Empirical Best Linear Unbiased Predictor (EBLUP) of the domain total. What is more (based on the theorem proved by Żądlo (2009)), the approximate equation of the mean squared error (MSE) was derived and its estimator based on the Taylor approximation was proposed. The proposed MSE estimator was derived under some assumptions including that the variance-covariance matrix can be decomposed into linear combination of variance components. The assumption was not met under the proposed model. In the paper the jackknife MSE estimator for the derived EBLUP will be proposed based on the results presented by Jiang, Lahiri, Wan (2002). The bias of the jackknife MSE estimator will be compared in the simulation study with the bias of the MSE estimator based on the Taylor approximation.

Large deviations for posterior distributions on the parameter of a multivariate $$\text{ AR}(p)$$ process

We prove the large deviation principle for the posterior distributions on the (unknown) parameter of a multivariate autoregressive process with i.i.d. Normal innovations. As a particular case, we recover a previous result for univariate first-order autoregressive processes. We also show that the rate function can be expressed in terms of the divergence between two spectral densities.

Systematic tuning of dispersion models for simulation of evaporating sprays

In this study, via an Eulerian–Lagrangian framework, the performance of two recent dispersion models, i.e. a first-order autoregressive process and the PDF model, is compared. The appropriate relations for the turbulence scales and the drift correction term are suggested and the tuned values for the constants of the models are proposed in a systematic approach by starting with the simplest case, i.e. particle-laden stationary isotropic turbulence and adding more complexities in the subsequent cases, including the homogeneous anisotropic shear flow, decaying grid turbulence, and inhomogeneous gas–solid spray. Also, the isotropic relation for the effect of inertia in the Lagrangian turbulence time scale seen by particles is extended to the anisotropic case while it remains consistent in the isotropic limit. Finally, the performance of the tuned models is evaluated for the simulation of an evaporating spray. It is observed that, the tuned constants for the evaporating spray are close to the ones obtained for the homogeneous shear flow.

Assessing One-Step-Ahead Prediction Error Based on the Median for First-Order Autoregressive Models in the Presence Of Outliers

The prediction of the one-step-ahead observation of the first-order autoregressive process in the presence of outliers is considered. The mean square of the prediction error is obtained based on the median estimator of the model parameter for a stationary process. Monte Carlo simulation methods are employed to investigate the performance of the proposed estimator as well as the conventional ordinary least squares estimators proposed by Zhang and Shaman (1995) and Kabaila and He (1999) for a process without outliers. The results show that the proposed method outperforms the conventional method. These conclusions are substantiated with results from actual datasets.

D-Optimal Chemical Balance Weighing Designs with N ≡ 0 (mod 4) and 3 Objects

In this article, the problem of estimation of the individual weights of three objects using a chemical balance weighing design is considered. We use the criterion of D-optimality. We assume that the covariance matrix of errors is the matrix of first-order autoregressive process. Such problems were discussed in Li and Yang (2005) and also in Yeh and Lo Huang (2005). We present some results of D-optimal designs in certain class of designs with the design matrix X ∈ M n×3(±1) such that each column of matrix X has at least one 1 and one −1.

Functional central limit theorems for sums of nearly nonstationary processes*

We study some Holderian functional central limit theorems for the polygonal partial-sum processes built on a first-order autoregressive process yn,k = φnyn,k−1 + ek with ϕn converging to 1 and i.i.d. centered square-integrable innovations. In the case where ϕn = eγ/n with a negative constant γ, we prove that the limiting process is an integrated Ornstein–Uhlenbeck one. In the case where ϕn = 1− γn/n, with γn tending to infinity slower than n, the convergence to Brownian motion is established in Holder space in terms of the rate of γn and the integrability of the eks.

Nonlinear Trends, Long-Range Dependence, and Climate Noise Properties of Surface Temperature

Abstract This study investigates the significance of trends of four temperature time series—Central England Temperature (CET), Stockholm, Faraday-Vernadsky, and Alert. First the robustness and accuracy of various trend detection methods are examined: ordinary least squares, robust and generalized linear model regression, Ensemble Empirical Mode Decomposition (EEMD), and wavelets. It is found in tests with surrogate data that these trend detection methods are robust for nonlinear trends, superposed autocorrelated fluctuations, and non-Gaussian fluctuations. An analysis of the four temperature time series reveals evidence of long-range dependence (LRD) and nonlinear warming trends. The significance of these trends is tested against climate noise. Three different methods are used to generate climate noise: (i) a short-range-dependent autoregressive process of first order [AR(1)], (ii) an LRD model, and (iii) phase scrambling. It is found that the ability to distinguish the observed warming trend from stochastic trends depends on the model representing the background climate variability. Strong evidence is found of a significant warming trend at Faraday-Vernadsky that cannot be explained by any of the three null models. The authors find moderate evidence of warming trends for the Stockholm and CET time series that are significant against AR(1) and phase scrambling but not the LRD model. This suggests that the degree of significance of climate trends depends on the null model used to represent intrinsic climate variability. This study highlights that in statistical trend tests, more than just one simple null model of intrinsic climate variability should be used. This allows one to better gauge the degree of confidence to have in the significance of trends.

Generalized RCINAR(1) Process with Signed Thinning Operator

A generalized random coefficient first-order integer-valued autoregressive process with signed thinning operator is introduced, this kind of process is appropriate for modeling negative integer-valued time series. Strict stationarity and ergodicity of process are established. Estimators of the parameters of interest are derived and their properties are studied via simulation. At last, we use bootstrap method in the real data analysis.

D-optimal chemical balance weighing designs with autoregressive errors

In this paper, we consider the estimation problem of individual weights of three objects. For the estimation we use the chemical balance weighing design and the criterion of D-optimality. We assume that the error terms \({\varepsilon_{i}, i=1,2,\dots,n,}\) are a first-order autoregressive process. This assumption implies that the covariance matrix of errors depends on the known parameter ρ. We present the chemical balance weighing design matrix \({\widetilde{\bf X}}\) and we prove that this design is D-optimal in certain classes of designs for \({\rho\in[0,1)}\) and it is also D-optimal in the class of designs with the design matrix \({{\bf X} \in M_{n\times 3}(\pm 1)}\) for some ρ ≥ 0. We prove also the necessary and sufficient conditions under which the design is D-optimal in the class of designs \({M_{n\times 3}(\pm 1)}\) , if \({\rho\in[0,1/(n-2))}\) . We present also the matrix of the D-optimal factorial design with 3 two-level factors.

Sequential interval estimation of the limiting interval availability for a bivariate stationary dependent sequence

In this paper, we consider the sequential confidence interval estimation of the limiting interval availability of a repairable system when the sequences of failure and repair times are generated by a bivariate stationary dependent sequence. The confidence interval and the proposed stopping rule are shown to be asymptotically consistent and efficient as the width of the interval approaches zero. In particular, we consider the sequential interval estimation of the limiting interval availability for a first-order bivariate exponential autoregressive process. A simulation study is also conducted to asses the performance of the proposed confidence interval.

Estimation for Nonnegative First-Order Autoregressive Processes with an Unknown Location Parameter

Consider a first-order autoregressive processes , where the innovations are nonnegative random variables with regular variation at both the right endpoint infinity and the unknown left endpoint θ. We propose estimates for the autocorrelation parameter f and the unknown location parameter θ by taking the ratio of two sample values chosen with respect to an extreme value criteria for f and by taking the minimum of over the observed series, where represents our estimate for f. The joint limit distribution of the proposed estimators is derived using point process techniques. A simulation study is provided to examine the small sample size behavior of these estimates.

Identifying the mean step change of UBM chart

The traditional control charts are developed based on the assumption that the successive observations are independent and identically distributed. In some processes, the independence assumption is violated when there is autocorrelation between observations. To solve this problem, two methods, classified as model-based and model-free, could be applied. When a control chart alarms an assignable cause, it is essential to detect the process change point in order to remove the root cause. In the presence of autocorrelated data, different methods for change-point identification have been applied only for model-based methods. Hence, this is considered as the research gap and an attempt is made to fill this gap by applying maximum likelihood function in unweighted batch mean control chart, one of the most applied model-free methods. In this article, an estimator is presented to determine the change point for the first-order autoregressive process, AR(1). When a real change occurs, the performance of proposed estimator is evaluated through simulation.

A delayed demand supply chain: Incentives for upstream players

We study a decentralized supply chain where only delayed market demand information is available for making replenishment decisions. The impact of this delay is quantified in a serially linked two-level supply chain where each player exploits the order-up-to replenishment policy. The market demand is assumed to be a first-order autoregressive process. It is shown that the first level of the supply chain benefits from shorter time delays; however, the benefit for the second level is quite minor at best and can sometimes even be (counter-intuitively) detrimental. We conclude that the second level does not have a strong incentive to reduce the time delays in the shared market demand information.

Impact of forecasting methods on variance ratio in order-up-to level policy

This paper considers the impact of forecasting methods on the bullwhip effect for a simple replenishment system in which a first-order autoregressive process describes the customer demand and an order-up-to inventory policy characterizes the replenishment decision. The impact of exponential smoothing and minimum mean squared error forecasting is measured for both the bullwhip effect and inventory variances. Previous similar studies have focused on investigating the impact of forecasting methods on bullwhip effect. However, little research has been carried out to explore the impact of forecasting methods for both bullwhip effect and inventory variances. Through simulation experiments, it has been found that depending on the structure of the demand process, the appropriate selection of forecasting technique can reduce, or even eliminate (i.e., “dewhip”) the bullwhip effect. However, in terms of inventory variances it has been shown that the inventory variances for the exponential smoothing are greater than the minimum mean squared error forecasting method and that gap increases as lead time increases. These findings will help companies to choose the appropriate forecasting technique depending on the nature of demand. These guidelines can help companies to reduce the bullwhip effect and inventory variances across supply chain.

Time Series Properties of the Class of Generalized First-Order Autoregressive Processes with Moving Average Errors

A new class of time series models known as Generalized Autoregressive of order one with first-order moving average errors has been introduced in order to reveal some hidden features of certain time series data. The variance and autocovariance of the process is derived in order to study the behaviour of the process. It is shown that in special cases these new results reduce to the standard ARMA results. Estimation of parameters based on the Whittle procedure is discussed. We illustrate the use of this class of model by using two examples.

The Empirical Likelihood for First-Order Random Coefficient Integer-Valued Autoregressive Processes

This article studies the empirical likelihood method for the first-order random coefficient integer-valued autoregressive process. The limiting distribution of the log empirical likelihood ratio statistic is established. Confidence region for the parameter of interest and its coverage probabilities are given, and hypothesis testing is considered. The maximum empirical likelihood estimator for the parameter is derived and its asymptotic properties are established. The performances of the estimator are compared with the conditional least squares estimator via simulation.

Limit theory for random coefficient first-order autoregressive process under martingale difference error sequence

Phillips and Magdalinos (2007) [1] gave the asymptotic theory for autoregressive time series with a root of the form ρ n = 1 + c / k n , where k n is a deterministic sequence. In this paper, an extension to the more general case where the coefficients of an AR(1) model is a random variable and the error sequence is a sequence of martingale differences is discussed. A conditional least squares estimator of the autoregressive coefficient is derived and shown to be asymptotically normal. This extends the result of Phillips and Magdalinos (2007) [1] for stationary and near-stationary cases.

Long-Range Dependence and Climate Noise Characteristics of Antarctic Temperature Data

Abstract This study examines the long-range dependency, climate noise characteristics, and nonlinear temperature trends of eight Antarctic stations from the Reference Antarctic Data for Environmental Research (READER) dataset. Evidence is shown that Antarctic temperatures are long-range dependent. To identify possible nonlinear trends, the ensemble empirical mode decomposition (EEMD) method is used, and then the question of whether the observed trends can arise from internal atmospheric fluctuations is examined. To answer this question, surrogate data are generated from two paradigmatic null models: a standard first-order autoregressive process representing a short-range dependent process and a fractional integrated process representing a long-range dependent process. It is found that three of the eight stations show statistically significant trends when tested against the short-range dependent process while only the Faraday–Vernadsky station temperature time series shows a significant trend when tested against the long-range dependent null model. All other considered stations show no trends that are statistically significant against the two null models, and thus they can be explained by internal atmospheric variability. These results imply that more attention should be given to assessing the correlation structure of climate time series.

Asset-liability management under time-varying investment opportunities

Stochastic linear programming is a suitable numerical approach for solving practical asset-liability management problems. In this paper, we consider a multi-stage setting under time-varying investment opportunities and propose a decomposition of the benefits in dynamic re-allocation and predictability effects. We use a first-order unrestricted vector autoregressive process to model asset returns and state variables and include, in addition to equity returns and dividend-price ratios, Nelson/Siegel parameters to account for the evolution of the yield curve. The objective is to minimize the Conditional Value at Risk of shareholder value, i.e., the difference between the mark-to-market value of (financial) assets and the present value of future liabilities.