Autoregressive Parameters Research Articles

PREDICTING REGIME SHIFTS IN JOHANNESBURG STOCK EXCHANGE ALLSHARE INDEX (JSE-ALSI): A MARKOV-SWITCHING APPROACH

It has been proven several times that linear models are unable to encapsulate nonlinear dynamics of macroeconomic and financial data such as inflation rates, exchange rates and stock prices to mention fewer. As a result, to overcome this problem, this current study adopted the nonlinear models due to the fact that they have required qualities to apprehend nonlinearity in a dataset. In order to predict a regime shifts, a five-day Johannesburg stock exchange allshare index (JSE-ALSI) spanning period from 02 January 2003 to 28 June 2019 was used as an experimental unit. This current study firstly employed Terasvirta neural network test to detect the presence of nonlinearity and proceeded to estimate a two regime Markov-Switching autoregressive (MS-AR). The results of Terasvirta neural network test revealed a highly significant nonlinearity with permanent seasonality as demonstrated by Kruskal-Wallis test. The predicted regime shifts by a latent dynamic allowed the autoregressive and variance parameters to promptly react to vital systemic shocks. As a result, this current study allowed volatility to oscillate between high and low volatility regimes that produced an expected duration of high volatility of two year and two months. This was a clear indication that there is a regime shifts in JSE-ALI which are modeled using Markov-Chain (MC) stochastic process. These findings may be used to inform robust policy making with the aim of safeguarding both the JSE and other global stock markets from the episodes of stock market crash. Moreover, other researchers can utilize the results of this study to calculate the risk associated with structural breaks and high volatility periods.

ESL-Based Robust Estimation for Mean-Covariance Regression with Longitudinal Data

When longitudinal data contains outliers, the classical least-squares approach is known to be not robust. To solve this issue, the exponential squared loss (ESL) function with a tuning parameter has been investigated for longitudinal data. However, to our knowledge, there is no paper to investigate the robust estimation procedure against outliers within the framework of mean-covariance regression analysis for longitudinal data using the ESL function. In this paper, we propose a robust estimation approach for the model parameters of the mean and generalized autoregressive parameters with longitudinal data based on the ESL function. The proposed estimators can be shown to be asymptotically normal under certain conditions. Moreover, we develop an iteratively reweighted least squares (IRLS) algorithm to calculate the parameter estimates, and the balance between the robustness and efficiency can be achieved by choosing appropriate data adaptive tuning parameters. Simulation studies and real data analysis are carried out to illustrate the finite sample performance of the proposed approach.

Does nature make us happier? A spatial error model of greenspace types and mental wellbeing

Exposure to nature is thought to benefit mental health and wellbeing. However, many studies consider greenspace as a single entity, which overlooks the potential significance of the various forms of greenspace, and natural greenspaces in particular. This study was designed to investigate the association between different types of greenspace and mental wellbeing. Drawing wellbeing and socioeconomic data from the Annual Population Survey (2012–2015), and shapefiles from the Greenspace Information for Greater London group, the amount of greenspace accessible within a 300 m walk of individual’s postcodes was calculated, and categorised according to type. Spatial Error Models were used to account for spatial patterns in the data. Natural greenspace was significantly associated with improved life satisfaction ( B = 0.028, p < 0.001) and happiness ( B = 0.023, p = 0.019) scores. The spatial autoregressive parameter ([Formula: see text]) was small but significant ( p < 0.001), implying slight second-order spatial variation in the model. These results imply that natural areas may be more important for hedonic mental wellbeing than other greenspaces. Future research is needed on exploring causal relationships between exposure to greenspace and mental wellbeing outcomes.

Local Power of Kolmogorov’s and Omega-Squared Type Criteria in Autoregression

A stationary AR(p) model is considered. The autoregression parameters are unknown as well as the distribution of innovations. Based on the residuals from the parametric estimates, an analog of the empirical distribution function is defined and tests of Kolmogorov’s and ω2 type are constructed for testing hypotheses on the distribution of innovations. The asymptotic power of these tests under local alternatives is obtained.

RS-CAE-Based AR-Wiener Filtering and Harmonic Recovery for Speech Enhancement

By taking into account temporal correlation of speech feature. In this paper, a novel structure of convolutional Auto Encoder CAE was proposed. In this structure, the historical output of the CAE was fed into a CAE stack recurrently. We name this structure as Recurrent Stack Convolutional Auto Encoder RS-CAE. In the training stage, the training feature maps of the RS-CAE comprise of log power spectrum LPS of noisy speech and an additional feature map derived from the LPS of the enhanced speech in the history. In this way, the temporal correlation is incorporated as much as possible in the RS-CAE. The training target is a concatenated vector of auto-regressive AR model parameters of speech and noise. At online stage, the LPS of noisy speech and the LPS of the enhanced speech from the history make up input feature maps together. The outputs of the RS-CAE are the AR model parameters of speech and noise, which are used to construct the AR-Wiener filter. Because the estimated AR model parameters are not completely accurate and some harmonics may be lost in the enhanced speech, the codebook-based harmonic recovery technique was proposed to reconstruct harmonic structure of the enhanced speech. The test results confirmed that the proposed method achieved better performance compared with some existing approaches.

Autoregressive models of random fields on the circle

At present, the vast majority of known image models are varieties of random fields defined on rectangular flat grids or grids of higher dimension. In some practical situations, images have a circular or radial-circular structure. For example, an image of a facies (a thin film of dried biological fluid), an eye, a biological cell, a flower, a slice of a tree trunk, etc. This circumstance requires the development of appropriate models of random fields describing images of this type. This paper proposes autoregressive models of homogeneous and inhomogeneous random fields defined on a circular spiral. The problem of correlation analysis of such models is considered. Examples of imitation of circular images are given. This paper proposes linear autoregressive models of homogeneous and inhomogeneous random fields defined on a circle. The samples of these fields are defined on a circular or spiral grid. The next field value is a linear combination of several previous values and a standard random variable. Expressions of the correlation function of these fields are given depending on the values of the autoregression parameters. A graphic representation of the correlation function on a circle and examples of simulated images are presented in the figures.

The impact of demand parameter uncertainty on the bullwhip effect

The bullwhip effect is a very important issue for supply chains, impacting on costs and effectiveness. Academic researchers have studied this phenomenon and modelled it analytically, showing that it affects many real world industries. The analytical models generally assume that the final demand process and its parameters are known. This paper studies a two-echelon single-product supply chain with final demand distributed according to a known AR(1) process but with unknown parameters. The results show that the bullwhip effect is affected by unknown parameters and is influenced by the frequency with which parameter estimates are updated. For unknown parameters, the strength of the bullwhip effect is also influenced by the number of demand observations available to estimate the parameters. Furthermore, a negative autoregressive parameter does not always imply an anti-bullwhip effect when the parameters are unknown. An analytical approximation is proposed to mitigate the poor accuracy of existing models when the parameters of an AR(1) process are unknown, forecasts are updated but parameter estimates remain unchanged.

When will European Muslim population be majority and in which country?

Purpose The purpose of this paper is to estimate the years the European Muslim population will be majority among 30 European countries. Design/methodology/approach The methodology/approach is to forecast the population of 30 European countries with wavelet analysis combined with the Burg model which fits a pth order autoregressive model to the input signal by minimizing (least squares) the forward and backward prediction errors while constraining the autoregressive parameters to satisfy the Levinson–Durbin recursion, then relies on an infinite impulse response prediction error filter. Three scenarios are considered: the zero-migration scenario where the authors assume that the Muslim population has a higher fertility (one child more per woman, on average) than other Europeans, mirroring a global pattern; a 2017 migration scenario: to the Muslim population obtained in the zero-migration scenario, the authors add a continuous flow of migrants every year based on year 2017; the mid-point migration scenario is obtained by averaging the data of the two previous scenarios. Findings Among three scenarios, the most likely mid-point migration scenario identifies 13 countries where the Muslim population will be majority between years 2085 and 2215: Cyprus (in year 2085), Sweden (2125), France (2135), Greece (2135), Belgium (2140), Bulgaria (2140), Italy (2175), Luxembourg (2175), the UK (2180), Slovenia (2190), Switzerland (2195), Ireland (2200) and Lithuania (2215). The 17 remaining countries will never reach majority in the next 200 years. Originality/value The growing Muslim population will change the face of Europe socially, politically and economically. This paper will provide a better insight and understanding of Muslim population dynamics to European governments, policymakers, as well as social and economic planners.

Seasonal Autoregressive Integrated Moving Average (SARIMA) Model for the Analysis of Frequency of Monthly Rainfall in Osun State, Nigeria

The Seasonal Autoregressive Integrated Moving Average (SARIMA) model is proposed for Osun State monthly rainfall data and the analysis was based on probability time series modeling approach. The Plot of the original data shows that the time series is stationary and the Augmented Dickey-Fuller test did not suggest otherwise. The graph further displays evidence of seasonality and it was removed by seasonal differencing. The plots of the ACF and PACF show spikes at seasonal lags respectively, suggesting SARIMA (1, 0, 1) (2, 1, 1). Though the diagnostic check on the model favoured the fitted model, the Auto Regressive parameter was found to be statistically insignificant and this led to a reduced SARIMA (1, 0, 1) (1, 1, 1) model that best fit the data and was used to make forecast.

Characteristic changes in the EEG signals between microsleeps and preceding responsive states.

This work aims at identifying characteristic features of EEG to demarcate a microsleep from preceding responsive states. The EEG signals, after reference electrode standardization technique (REST) re-referencing, were processed through a time-varying general linear Kalman filter (TVGLKF) to derive time-varying auto-regressive (TVAR) parameters. The time-varying effective connectivity measure of orthogonal partial directed coherence (OPDC) was obtained for every instant at 256 Hz. Effective connectivity matrices formed using these OPDC measures, with the scalp electrodes as nodes were processed further using graph theory. Community-based measures were investigated and statistical significances compared. Non-parametric Wilcoxon signed rank test was used for significance analysis, with Cohen-type and Common Language effect size (CLES) as measures of effect sizes. The results showed a decrease in directional modularity from anterior to posterior, in theta, alpha, and beta bands in microsleeps. The alpha band showed the highest significance with a Cohen-type effect size of 1.25 and a median percentage difference of 23% across subjects, with a range of 13-28%. Flexibility and integration also decreased with average percentage of 25% (17-35%) and 20% (16-32%), respectively, while recruitment increased on an average of 11% (3-16%), wherever significant across all bands. These community-based measures can help characterize and explain changes in brain mechanisms, and can also serve as potential biomarkers for microsleep detection.

Assessing the regional context of migration in the Brazilian Amazon through spatial regression modeling

The Brazilian Amazon contains the most active rainforest frontier in the world, and its socioeconomic, demographic and spatial dynamism has been a topic of interest for academics and policy makers for decades. In this paper, we use spatial statistical modeling to examine the context of migration in the Brazilian Amazon by investigating its socioeconomic, demographic, spatial and environmental heterogeneities at the municipal level between 2000 and 2010. First, we visualized the spatial distribution of net-migration, in-migration and out-migration rates among municipalities in the Brazilian Amazon. Then, we explored the presence of spatial autocorrelation using Global Moran's I Index, and use spatial modeling techniques to investigate the associations between response variables (in-migration and out-migration) and selected explanatory variables. We identified several in-migration frontiers in the region, especially in Center Mato Grosso and Southeast Pará, while out-migration seems more diffuse in the Amazonia territory. Global Moran's I scores indicate that most of the selected variables exhibit spatial dependence, and the spatial regression models present better estimates of the coefficients by incorporating the spatially lagged autoregressive parameter. Our results also confirm the spatial heterogeneity and multidimensional character of in-migration and out-migration in the Brazilian Amazon. Economic growth, regional inequality and the environmental dynamism of the rainforest frontier appear to be closely associated with the intensity of migration flows in the region. We also find that less-populated municipalities have a central role in regional migration dynamics, forming relevant in-migration frontiers and ensuring territorial robustness for migration in the region.

Robust inference in conditionally heteroskedastic autoregressions

We consider robust inference for an autoregressive parameter in a stationary linear autoregressive model with GARCH innovations. As the innovations exhibit GARCH, they are by construction heavy-tailed with some tail index κ. This implies that the rate of convergence as well as the limiting distribution of the least squares estimator depend on κ. In the spirit of Ibragimov and Müller (“t-statistic based correlation and heterogeneity robust inference”, Journal of Business & Economic Statistics, 2010, vol. 28, pp. 453–468), we consider testing a hypothesis about a parameter based on a Student’s t-statistic based on least squares estimates for a fixed number of groups of the original sample. The merit of this approach is that no knowledge about the value of κ nor about the rate of convergence and the limiting distribution of the least squares estimator is required. We verify that the two-sided t-test is asymptotically a level α test whenever for any which includes cases where the innovations have infinite variance. A simulation experiment suggests that the finite-sample properties of the test are quite good.

Robust Bayesian analysis of a multivariate dynamic model

Recently, a Bayesian approach has been widely used to infer parameters of complex models from finite sample data in business, finance, social and physical sciences. Bayesian applications in finance literature are growing due to their exposure to prior beliefs that macroeconomic variables influence the financial behavior of customers, investors and firm’s performance. This paper employs a robust Bayesian analysis model to capture a complex multi-dimensional process and estimate the required parameters of interest. It considers a class of prior distributions for the parameters that is a mixture of natural conjugate base priors and a contamination class of prior distributions. The conditional type-II maximum likelihood posterior densities and posterior means for the coefficients vector and autoregressive parameter are derived for the coefficients vector and autoregressive parameter of interest. The Markov Chain Monte Carlo (MCMC) method has been used for obtaining the marginal posterior densities and Bayes estimators for various combinations of the parameters. The usefulness of the model is demonstrated on Indian financial firms’ balance sheets data between 1992 to 2015 to observe the sensitivity of the proposed model. The result shows most of the corporate performance variables are significantly affecting the firm’s profitability with the exception of interest coverage ratio.

Semi-parametric estimation of the autoregressive parameter in non-Gaussian Ornstein–Uhlenbeck processes

ABSTRACTThis paper considers the problem of estimating the autoregressive parameter in discretely observed Ornstein–Uhlenbeck processes. Two consistent estimators are proposed: one obtained by maximizing a kernel-based likelihood function, and another by minimizing a Kolmogorov-type distance from independence. After establishing the consistency of these estimators, their finite-sample performance and possible normality in large samples, is investigated by means of extensive simulations. An illustrative example to credit rating is discussed.

On the Asymptotic Power of Tests of Fit under Local Alternatives in Autoregression

We consider a stationary AR(p) model. The autoregression parameters are unknown as well as the distribution of innovations. Based on the residuals from the parameter estimates, an analog of empirical distribution function is defined and the tests of Kolmogorov’s and ω2 type are constructed for testing hypotheses on the distribution of innovations. We obtain the asymptotic power of these tests under local alternatives.

Damage Analysis of Rolling Bearings Based on Model Correlation Dimension

Vibration signals of the rolling bearing are non-stationary, EEMD is occupied to decompose the signals; then ARMA model, which has higher accuracy, is established based on the signal principal components from the EEMD; then correlation dimension of the Auto-regressive (AR) parameters, taken from the ARMA model, serve as the feature vectors to be input to LSSVM for discriminating the actual conditions of rolling bearings. The results demonstrate that: the fault-patterns could be obtained accurately with the presented method, and it is an effective analysis method.

Damage Classification and Feature Extraction in Steel Moment-Resisting Frame Using Time-Varying Autoregressive Model

In this paper, the time-varying autoregressive (TVAR) model is integrated with the K-means—clustering technique to detect the damage in the steel moment-resisting frame. The damage is detected in the frame using nonstationary acceleration response of the structure excited using ambient white noise. The proposed technique identifies and quantifies the damage in the beam-to-column connection and column-to-column splice plate connection caused due to loosening of the connecting bolts. The algorithm models the nonstationary acceleration time history and evaluates the TVAR coefficients (TVARCs) for pristine and damage states. These coefficients are represented as a cluster in the TVARC subspace and segregated and classified using K-means—segmentation technique. The K-means—approach is adapted to simultaneously perform partition clustering and remove outliers. Eigenstructure evaluation of the segregated TVARC cluster is performed to detect the temporal damage. The topological and statistical parameters of the TVARC clusters are used to quantify the magnitude of the damage. The damage is quantified using the Mahalanobis distance (MD) and the Itakura distance (ID) serving as the statistical distance between the healthy and damage TVARC clusters. MD calculates a multidimensional statistical distance between two clusters using the covariance between the state vectors, whereas ID measures the dissimilarity of the autoregressive (AR) parameter between reference state and unknown states. These statistical distances are used as damage-sensitive feature (DSF) to detect and quantify the initiation and progression of the damage in the structure under ambient vibrations. The outcome of both the DSFs corroborate with the experimental investigation, thereby improving the robustness of the algorithm by avoiding false damage alarms.

A weak law for moments of pairwise stable networks

This paper studies the dependence structure of sparse networks realized according to a strategic model of network formation with homophilous agents. We argue that equilibrium selection and chains of indirect dependence generated by strategic interactions are the main drivers of network dependence. Drawing on results in random-graph theory, we derive weak-dependence conditions under which a law of large numbers holds for a general class of network moments. A key condition restricts the strength of strategic interactions, which constitutes the network analog of conventional weak-dependence assumptions in time series and spatial econometrics that bound the magnitude of autoregressive parameters. We apply our result to estimating models of strategic network formation and treatment effects under network interference.

Priors about observables in vector autoregressions

Standard practice in Bayesian VARs is to formulate priors on the autoregressive parameters, but economists and policy makers actually have priors about the behavior of observable variables. We show how to translate the prior on observables into a prior on parameters using strict probability theory principles, a posterior can then be formed with standard procedures. We state the inverse problem to be solved and we propose a numerical algorithm that works well in practical situations. We prove equivalence to a fixed point formulation and a convergence theorem for the algorithm. We use this framework in two well known applications in the VAR literature, we show how priors on observables can address some weaknesses of standard priors, serving as a cross check and an alternative formulation.

Identifying diffusive motions in single-particle trajectories on the plasma membrane via fractional time-series models.

In this paper we show that an autoregressive fractionally integrated moving average time-series model can identify two types of motion of membrane proteins on the surface of mammalian cells. Specifically we analyze the motion of the voltage-gated sodium channel Nav1.6 and beta-2 adrenergic receptors. We find that the autoregressive (AR) part models well the confined dynamics whereas the fractionally integrated moving average (FIMA) model describes the nonconfined periods of the trajectories. Since the Ornstein-Uhlenbeck process is a continuous counterpart of the AR model, we are also able to calculate its physical parameters and show their biological relevance. The fitted FIMA and AR parameters show marked differences in the dynamics of the two studied molecules.