Order Autoregressive Process Research Articles

A cautionary tale on the effects of different covariance structures in linear mixed effects modeling of fMRI data.

With the steadily increasing abundance of longitudinal neuroimaging studies with large sample sizes and multiple repeated measures, questions arise regarding the appropriate modeling of variance and covariance. The current study examined the influence of standard classes of variance-covariance structures in linear mixed effects (LME) modeling of fMRI data from patients with pediatric mild traumatic brain injury (pmTBI; N = 181) and healthy controls (N = 162). During two visits, participants performed a cognitive control fMRI paradigm that compared congruent and incongruent stimuli. The hemodynamic response function was parsed into peak and late peak phases. Data were analyzed with a 4-way (GROUP×VISIT×CONGRUENCY×PHASE) LME using AFNI's 3dLME and compound symmetry (CS), autoregressive process of order 1 (AR1), and unstructured (UN) variance-covariance matrices. Voxel-wise results dramatically varied both within the cognitive control network (UN>CS for CONGRUENCY effect) and broader brain regions (CS>UN for GROUP:VISIT) depending on the variance-covariance matrix that was selected. Additional testing indicated that both model fit and estimated standard error were superior for the UN matrix, likely as a result of the modeling of individual terms. In summary, current findings suggest that the interpretation of results from complex designs is highly dependent on the selection of the variance-covariance structure using LME modeling.

Process capability index Cpm under autoregressive process AR (2)

PurposeThe paper aims to identify the effect of ignorance of correlatedness among process observations and to implement new sampling schemes; skip and mixed sampling, in order to reduce the effect of autocorrelation on process capability index (PCI) Cpm.Design/methodology/approachAutocorrelated observations are generated using autoregressive process of order two (AR (2)) using Monte Carlo simulations. The PCI is computed based on these observations assuming the independence. The skip and mixed sampling schemes are then used to form sub-groups among correlated observations. The PCI obtained using sub-groups from skip and mixed sampling schemes are assessed using sample mean and sample standard deviation.FindingsThe paper provides empirical insights into how the effect of autocorrelation decreases in the estimated value of PCI Cpm. The use of new sampling schemes, skip and mixed sampling, reduces the effect of autocorrelation on estimates of PCI Cpm.Originality/valueThis paper fulfills an identified need to study how to reduce the effect of autocorrelation on PCI Cpm.

Insecurity and political uncertainty: Factors that Influence the Fall of Foreign Direct Investment in Mexico

One of the fundamental aspects of any government is to have a national development plan that establishes the guidelines that will guide the destiny of the nation. In the case of Mexico, each six-year presidential term has a national development plan that may or may not have continuity, where one of its main objectives is economic growth. The attraction of foreign direct investment is one of the pillars of economic growth, however, it can be affected by various national and international factors. This research analyzes the behavior of foreign direct investment during four presidential terms in Mexico from 1999 to date. The first twelve years were governed by the national action party (PAN, right wing political party), from 2012 to 2018 by the institutional revolutionary party (PRI, center-right political party) and from 2019 to date by the MORENA political party (left wing political party). The methodology applied for this research was an autoregressive process of order one. We highlight that the arrival to the presidency by the PAN in the year 2000 brought large flows of foreign capital during it´s six-year term, however, during the period from 2006 to 2012 also governed by the PAN there is a decrease in the attraction of FDI of 27% in relation to the previous period. Likewise, a 16% drop in FDI is also observed during the period from 2012 to 2018 governed by the PRI and a drop of almost 5% from 2019 to date, a period governed by the political party MORENA. As a conclusion, we can argue that the drop in FDI in the period studied can be attributed to various factors such as organized crime as well as the distrust of investors derived from the arrival of a leftist political party to the government.

Conformal prediction bands for two-dimensional functional time series

Time evolving surfaces can be modeled as two-dimensional Functional time series, exploiting the tools of Functional data analysis. Leveraging this approach, a forecasting framework for such complex data is developed. The main focus revolves around Conformal Prediction, a versatile nonparametric paradigm used to quantify uncertainty in prediction problems. Building upon recent variations of Conformal Prediction for Functional time series, a probabilistic forecasting scheme for two-dimensional functional time series is presented, while providing an extension of Functional Autoregressive Processes of order one to this setting. Estimation techniques for the latter process are introduced, and their performance are compared in terms of the resulting prediction regions. Finally, the proposed forecasting procedure and the uncertainty quantification technique are applied to a real dataset, collecting daily observations of Sea Level Anomalies of the Black Sea.

Cumulative residual fisher information of a general k-th order autoregressive process

In this work, we consider cumulative residual Fisher information and Bayes-cumulative residual Fisher information for a general k-th order autoregressive and their corresponding stationary equilibrium distributions and develop some associated results. We establish several interesting connections between these measures and some known informational measures such as chi-square divergence, Gini?s mean difference, cumulative residual Kullback-Leibler, Jeffreys and Jensen-cumulative residual entropy divergences.

An Empirical Analysis of a Stock Market Index of a Developing Country: Case of the Main Index of the Casablanca Stock Exchange MASI

Purpose: Managing stock market risk and making an optimal investment decision in a stock market requires study- ing the dynamics of this market and analyzing the fluctuations of its benchmark index in order to avoid heavy damage in the event of crises. This paper aims to study and analyze the fluctuations of the main index of the Casablanca Stock Exchange "MASI" to explore its efficiency and stability in the normal financial context (especially before the recent pandemic crisis). Design/methodology/approach: To carry out this study, two methods are proposed, the first one, how evolves this index over time depending on some random data generation processes widely used for stock prices: A Random Walk with a drift RW(α) and an autoregressive process of order 1 AR(1). Based on the actual MASI returns series used (2007-2018), we estimate each equation parameter according to the process chosen to generate the artificial MASI returns series to know the most relevant data generation process in the case of The Moroccan financial market. The second method focuses on the technique of "simple moving average" as a method of stock prices fluctuation analysis to make its investment decision, choosing the proper order on the same series. Findings: The results and findings of our econometric study show, in the first method, that either the RW(α) or the AR(1) process cannot adequately model MASI fluctuation. However, the results of the second method affirm the utility of the simple moving average to identify trends, their strength and buy / sell signals, using some techniques known in this field, in order to make decisions and draw interpretations in investment terms and risk management, which can prove that the market is less efficient and stable. Research limitations/implications: An important implication of this study is the need to explore the efficient models to describe the MASI return series. Originality/value: This study offers empirical evidence in relation to the estimation of the econometric model to describe MASI and how to make adequate investment decisions in the Moroccan stock market. Moreover, contributes to future research to find other more appropriate models.

Model Averaging Multistep Prediction in an Infinite Order Autoregressive Process

Model Averaging Multistep Prediction in an Infinite Order Autoregressive Process

Moment estimator for an AR(1) model driven by a long memory Gaussian noise

In this paper, we consider an inference problem for the first order autoregressive process driven by a given long memory stationary Gaussian noise. Suppose that the covariance function of the noise is positive and can be expressed as |k|2H−2 times a positive function slowly varying at infinity. The fractional Gaussian noise and the fractional ARIMA(0, d, 0) model with d∈(0,12) and some others Gaussian noise are special examples that satisfy this assumption. We propose a moment estimator and prove the strong consistency, the asymptotic normality and the almost sure central limit theorem. Moreover, we give the upper Berry–Esséen bound by means of Fourth moment theorem.

On the Paradox of the Duality of Autoregressive and Moving Average Processes

A widely held view in time series analysis is the concept of duality that a finite order stationary autoregressive process of order p (AR(p)) is equivalent to an infinite order moving average (MA) process and a finite order invertible moving average of order q (MA(q)) is equivalent to an infinite order autoregressive (AR) process. The purpose of this paper is to demonstrate that the concept is not universally true. Thus, a finite order stationary autoregressive process of order p (AR(p)) can be written as an finite order moving average process and a finite order moving average process of order q (MA(q)) can be written as a finite order stationary autoregressive process. The regions of breakdown of concept of duality were determined for p = q = 1,2 using method of moments. The method involves equating non-zero autocovariances of the stationary AR(p) to the equivalent non-zero autocovariances of the invertible MA(p) to determine the region of non-duality. In such region of breakdown in duality, 1) both the Autocorrelation function and the Partial Autocorrelation function of the AR process and MA process cuts off after equal lags 2) a finite AR model can be adequately represented by a finite MA model of equal order and conversely with the same error variance and 3) negative values of the parameters of the AR process are equal in magnitude but opposite in direction to the parameters of the equivalent MA process and conversely. Empirical examples (simulation and real life examples) were used to illustrate these. Therefore, it has been recommended that caution should be exercised in using the concept of duality in time series analysis until future research proves otherwise.

Finite-sample properties of estimators for first and second order autoregressive processes

The class of autoregressive (AR) processes is extensively used to model temporal dependence in observed time series. Such models are easily available and routinely fitted using freely available statistical software like R. A potential problem is that commonly applied estimators for the coefficients of AR processes are severely biased when the time series are short. This paper studies the finite-sample properties of well-known estimators for the coefficients of stationary AR(1) and AR(2) processes and provides bias-corrected versions of these estimators which are quick and easy to apply. The new estimators are constructed by modeling the relationship between the true and originally estimated AR coefficients using weighted orthogonal polynomial regression, taking the sampling distribution of the original estimators into account. The finite-sample distributions of the new bias-corrected estimators are approximated using transformations of skew-normal densities, combined with a Gaussian copula approximation in the AR(2) case. The properties of the new estimators are demonstrated by simulations and in the analysis of a real ecological data set. The estimators are easily available in our accompanying R-package for AR(1) and AR(2) processes of length 10–50, both giving bias-corrected coefficient estimates and corresponding confidence intervals.

A neutrosophic student’s t –type of statistic for AR (1) random processes

Neutrosophic statistics are used when one is dealing with imprecise and indeterminate data or parameters. In the present paper we propose a method for performing a neutrosophic Student’s t –type of statistical test that concerns the population mean when data arise from an autoregressive process of order 1 (AR(1)). In classical statistics data obtained through this process are not independent when the autocorrelation coefficient of the process is not equal to 0, and hence the usual Student’s t distribution is inadequate for inferring about the population mean; however a result obtained in earlier literature states that a Student’s t –type of statistic, which is asymptotically normally distributed, can be used instead. Our method is based on the neutrosophic version of this result and it is implemented using simulated data.

A Bayesian algorithm with second order autoregressive errors for B-WIM weight estimation

Bridge weigh-in-motion (B-WIM) systems are employed for estimating axle weights of vehicles traveling over the bridge structure, providing useful information for many applications regarding structural health monitoring. In this regard, the improvement of single axle weight estimates is a major concern, since B-WIM systems in general have more difficulties with such quantities when compared to the prediction of the total weight, mainly for closely spaced axles. The main goal of the present work is to develop a weigh strategy for B-WIM systems that prevents the occurrence of spurious values, improving the overall accuracy of estimates for single axle weights. For reaching this goal, prior beliefs regarding axle weights, such as their order of magnitude and similarity for closely spaced axles, are employed. Bayesian modeling is well suited for the present problem, since it allows the suitable combination of prior beliefs and experimental data for providing proper weight estimates. In addition, a covariance matrix based on a second order autoregressive process is employed for modeling the error between theoretical and measured responses aiming to overcome the negative effects due to the presence of serial correlation in such errors. Both simulated signals and an example of B-WIM system calibration data are employed for assessing the suitability of the proposed approach. Moreover, sensitivity analyses are conducted aiming to check the robustness of the strategy to its own model parameters. For all analyses, the overall accuracy of the proposed approach, when considering both single axle as well as gross vehicle weight (GVW) estimates, outperforms the baseline algorithms. Furthermore, the sensitivity analyses indicate that the conclusions are the same for distinct prior distributions based on the same prior information.

On simultaneous limits for aggregation of stationary randomized INAR(1) processes with poisson innovations

Abstract We investigate joint temporal and contemporaneous aggregation of N independent copies of strictly stationary INteger-valued AutoRegressive processes of order 1 (INAR(1)) with random coefficient α ∈ (0, 1) and with idiosyncratic Poisson innovations. Assuming that α has a density function of the form ψ(x) (1 − x) β , x ∈ (0, 1), with β ∈ (−1, ∞) and lim x ↑ 1 ψ ( x ) = ψ 1 ∈ ( 0 , ∞ ) $\lim\limits_{x\uparrow 1} \psi(x) = \psi_1 \in (0, \infty)$ , different limits of appropriately centered and scaled aggregated partial sums are shown to exist for β ∈ (−1, 0] in the so-called simultaneous case, i.e., when both N and the time scale n increase to infinity at a given rate. The case β ∈ (0, ∞) remains open. We also give a new explicit formula for the joint characteristic functions of finite dimensional distributions of the appropriately centered aggregated process in question.

On the generalization of the central limit theorem for the least-squares estimator of the unknown parameter in the autoregressive process of order one (AR(1))

In this work it is proved central limit theorem for the least-squares estimator of the unknown parameter in the generalization autoregressive process of order one (AR(1)).

A tale of two sentiment scales: disentangling short-run and long-run components in multivariate sentiment dynamics

The digitalization of news and social media provides an unprecedented source to investigate the role of information on market dynamics. However, the observed sentiment time-series represent a noisy proxy of the true investor sentiment. Moreover, modeling the joint dynamics of different sentiment series can be beneficial for the assessment of their economic relevance. The main methodological contribution of this paper is twofold: (i) we filter the latent sentiment signals in a genuinely multivariate model; (ii) we propose a decomposition into a long-term random walk component, named long-term sentiment, and a short-term component driven by a stationary Vector Autoregressive process of order one, named short-term sentiment. The proposed framework is a dynamic factor model describing the joint evolution of the observed sentiments of a portfolio of assets. Empirically, we find that the long-term sentiment co-integrates with the market price factor, while the short-term sentiment captures transient and firm-specific swings. By means of quantile regressions, we assess the significance of the explanatory power of filtered present sentiment on future returns. Then, we demonstrate how the lagged relation can be successfully exploited in a portfolio allocation exercise.

Change-point analysis through integer-valued autoregressive process with application to some COVID-19 data.

In this article, we consider the problem of change‐point analysis for the count time series data through an integer‐valued autoregressive process of order 1 (INAR(1)) with time‐varying covariates. These types of features we observe in many real‐life scenarios especially in the COVID‐19 data sets, where the number of active cases over time starts falling and then again increases. In order to capture those features, we use Poisson INAR(1) process with a time‐varying smoothing covariate. By using such model, we can model both the components in the active cases at time‐point t namely, (i) number of nonrecovery cases from the previous time‐point and (ii) number of new cases at time‐point t. We study some theoretical properties of the proposed model along with forecasting. Some simulation studies are performed to study the effectiveness of the proposed method. Finally, we analyze two COVID‐19 data sets and compare our proposed model with another PINAR(1) process which has time‐varying covariate but no change‐point, to demonstrate the overall performance of our proposed model.

MODELLING OF INTRADAY PHOTOVOLTAIC POWER PRODUCTION

Photovoltaic (PV) productions should occur within a time interval of sunlight. Time mismatches are detected between sunrise and first production hour as well as sunset and last production hour in a transmission system operator, Amprion, Germany. Hence, in this paper, we investigate this effect using an additive function of two seasonalities and a stochastic process. Both seasonalities are based on the mimicked locations, corrected by a weighing scale, depending on the first and last production hours' coordinates. The result shows that the proposed deterministic model could capture the effect of sunrise and sunset. Also, the dynamics of random components are sufficiently explained by an autoregressive process of order two. Finally, the Normal Inverse Gaussian distribution is shown as the best distribution in explaining noise behaviour, particularly heavy tails in the production's residuals, compared to the Gaussian distribution.

MANAJEMEN LABA, PROFITABILITAS, UKURAN BANK, DEWAN KOMISARIS DAN CORPORATE SOCIAL RESPONSIBILITY BANK SYARIAH

This study aims to examine the effect of Earnings Management, Profitability, Bank Size, and Board of Commissioners Size on Corporate Social Responsibility (CSR). The sample of this study consisted of 8 Sharia Commercial Banks registered in the Indonesian Sharia Banking Statistics. Testing the hypothesis in this study using multiple linear regression analysis by following the autoregressive process of order 1 or AR (1) which is estimated simultaneously using the Eviews application. The results of this study indicate that earnings management has a positive effect on Corporate Social Responsibility (CSR), while profitability, bank size, and board size do not affect Corporate Social Responsibility (CSR).

Time stable empirical best predictors under a unit-level model

Comparability as well as stability over time are highly desirable properties of regularly published statistics, specially when they are related to important issues such as people’s living conditions. For instance, poverty statistics displaying drastic changes from one period to the next for the same area have low credibility. In fact, longitudinal surveys that collect information on the same phenomena at several time points are indeed very popular, specially because they allow analyzing changes over time. Data coming from those surveys are likely to present correlation over time, which should be accounted for by the considered statistical procedures, and methods that account for it are expected to yield more stable estimates over time. A unit-level temporal linear mixed model is considered for small area estimation using historical information. The proposed model includes random time effects nested within the usual area effects, following an autoregressive process of order 1, AR(1). Based on the proposed model, empirical best predictors (EBPs) of small area parameters that are comparable for different time points and are expected to be more stable are derived. Explicit expressions are provided for the EBPs of some common poverty indicators. A parametric bootstrap method is also proposed for estimation of the mean square errors under the model. The proposed methods are studied through different simulation experiments, and are illustrated in an application to poverty mapping in Spanish provinces using survey data on living conditions from years 2004–2006.

A multiplicative version of the Lindley recursion

This paper presents an analysis of the stochastic recursion W_{i+1} = [V_iW_i+Y_i]^+ that can be interpreted as an autoregressive process of order 1, reflected at 0. We start our exposition by a discussion of the model’s stability condition. Writing Y_i=B_i-A_i, for independent sequences of nonnegative i.i.d. random variables {A_i}_{iin {mathbb N}_0} and {B_i}_{iin {mathbb N}_0}, and assuming {V_i}_{iin {mathbb N}_0} is an i.i.d. sequence as well (independent of {A_i}_{iin {mathbb N}_0} and {B_i}_{iin {mathbb N}_0}), we then consider three special cases (i) V_i equals a positive value a with certain probability pin (0,1) and is negative otherwise, and both A_i and B_i have a rational LST, (ii) V_i attains negative values only and B_i has a rational LST, (iii) V_i is uniformly distributed on [0, 1], and A_i is exponentially distributed. In all three cases, we derive transient and stationary results, where the transient results are in terms of the transform at a geometrically distributed epoch.