Autoregressive AR Research Articles

Diagnostic Measures in Ridge Regression Model with AR(1) Errors under the Stochastic Linear Restrictions

Outliers and influential observations have important effects on the regression analysis. The goal of this paper is to extend the mean-shift model for detecting outliers in case of ridge regression model in the presence of stochastic linear restrictions when the error terms follow by an autoregressive AR(1) process. Furthermore, extensions of measures for diagnosing influential observations are derived. A numerical example of a real data set is used to illustrate the findings. Finally, a simulation study is conducted to evaluate the performance of the proposed procedure and measures. Results of this study show the efficiency of the proposed mean-shift outlier model for the proposed model. Also, the study resulted in some findings about the behavior of suggested measures for the specified model. In fact, these measures are affected by the degree of collinearity and the size of autocorrelation.

Global estimation of long-term persistence in annual river runoff

Abstract Long-term persistence (LTP) of annual river runoff is a topic of ongoing hydrological research, due to its implications to water resources management. Here, we estimate its strength, measured by the Hurst coefficient H, in 696 annual, globally distributed, streamflow records with at least 80 years of data. We use three estimation methods (maximum likelihood estimator, Whittle estimator and least squares variance) resulting in similar mean values of H close to 0.65. Subsequently, we explore potential factors influencing H by two linear (Spearman's rank correlation, multiple linear regression) and two non-linear (self-organizing maps, random forests) techniques. Catchment area is found to be crucial for medium to larger watersheds, while climatic controls, such as aridity index, have higher impact to smaller ones. Our findings indicate that long-term persistence is weaker than found in other studies, suggesting that enhanced LTP is encountered in large-catchment rivers, were the effect of spatial aggregation is more intense. However, we also show that the estimated values of H can be reproduced by a short-term persistence stochastic model such as an auto-regressive AR(1) process. A direct consequence is that some of the most common methods for the estimation of H coefficient, might not be suitable for discriminating short- and long-term persistence even in long observational records.

Simulation of Cycle-to-Cycle Instabilities in SiOx- Based ReRAM Devices Using a Self-Correlated Process with Long-Term Variation

Cycle-to-cycle (C2C) current variability occurring in ReRAM devices is not only a stochastic feature inherent to electron transport in low-dimensional conducting structures but also a consequence of the measurement protocol used to characterize the device evolution during resistance switching. In such latest case, C2C changes depend on the particular arrangement of the ions or vacancies that form the conducting filament spanning the dielectric film. In this letter, a discrete first-order autoregressive model AR(1) with long-term variation is used to represent both the random and the “deterministic” behaviors of the high resistance state current. Simulation of C2C instabilities in SiO x is carried out through the quantum point-contact model for filamentary electron transport in dielectrics with fluctuating confinement potential barrier height. Simplicity is of utmost importance, since the proposed approach is aimed for circuit simulation environments in which complex and time-consuming computations need to be avoided.

Adjustment of growth models in broiler chickens

Abstract: The objective of this work was to investigate adjustments of the Gompertz, Logistic, von Bertalanffy, and Richards growth models, in male and female chickens of the Cobb 500, Ross 308, and Hubbard Flex lines. Initially, 1,800 chickens were randomly housed in 36 pens, with six replicates per lineage and sex, fed ad libitum with feed according to gender, and bred until 56 days of age. Average weekly body weight for each line and sex was used to estimate model parameters using the ordinary least squares, weighted by the inverse variance of the body weight and weighted with a first-order autocorrelated error structure. Weighted models and weighted autocorrelated error models showed different parameter values when compared with the unweighted models, modifying the inflection point of the curve and according to the adjusted coefficient of determination, and the standard deviation of the residue and Akaike information criteria exhibited optimal adjustments. Among the models studied, the Richards and the Gompertz models had the best adjustments in all situations, with more realistic parameter estimates. However, the weighted Richards model, with or without ponderation with the autoregressive first order model AR (1), exhibited the best adjustments in females and males, respectively.

Fractional Gaussian noise: Prior specification and model comparison

Fractional Gaussian noise (fGn) is a stationary stochastic process used to model antipersistent or persistent dependency structures in observed time series. Properties of the autocovariance function of fGn are characterised by the Hurst exponent (H), which, in Bayesian contexts, typically has been assigned a uniform prior on the unit interval. This paper argues why a uniform prior is unreasonable and introduces the use of a penalised complexity (PC) prior for H. The PC prior is computed to penalise divergence from the special case of white noise and is invariant to reparameterisations. An immediate advantage is that the exact same prior can be used for the autocorrelation coefficient ϕ of a first‐order autoregressive process AR(1), as this model also reflects a flexible version of white noise. Within the general setting of latent Gaussian models, this allows us to compare an fGn model component with AR(1) using Bayes factors, avoiding the confounding effects of prior choices for the two hyperparameters H and ϕ. Among others, this is useful in climate regression models where inference for underlying linear or smooth trends depends heavily on the assumed noise model.

Explained Variance and Intraclass Correlation in a Two-Level AR(1) Model

ABSTRACTThe total variance of a first-order autoregressive AR(1) time series is well known in time series literature. However, despite the increased use and interest in two-level AR(1) models, an equation for the total variance of these models does not exist. This paper presents an approximation of this total variance. It will be used to compute the unexplained and explained variance at each level of the model, the proportion of explained variance, and the intraclass correlation (ICC). The use of these variances and the ICC will be illustrated using an example concerning structured diary data about the positive affect of 96 married women.

EVIDENCE FOR INDUCED SEISMICITY FOLLOWING THE 2001 SKYROS MAINSHOCK

Estimation of the seismicity rate changes caused by a major earthquake is based upon the assumption that the earthquake occurrence can be described by stochastic processes. Three stochastic models are applied to the data, i.e. the homogeneous Poisson model, the non-homogeneous Poisson model with two different rate functions, and the Autoregressive model AR(2). The two latter models seem to be adequate to properly simulate the earthquake production in a given area. The identification of the model which best fits the data, enables the estimations of the seismicity rate changes and the numbers of the earthquakes following a specific main shock.

Hourly forecasting of global solar radiation based on multiscale decomposition methods: A hybrid approach

This paper introduces a new approach for the forecasting of solar radiation series at 1 h ahead. We investigated on several techniques of multiscale decomposition of clear sky index Kc data such as Empirical Mode Decomposition (EMD), Ensemble Empirical Mode Decomposition (EEMD) and Wavelet Decomposition. From these differents methods, we built 11 decomposition components and 1 residu signal presenting different time scales. We performed classic forecasting models based on linear method (Autoregressive process AR) and a non linear method (Neural Network model). The choice of forecasting method is adaptative on the characteristic of each component. Hence, we proposed a modeling process which is built from a hybrid structure according to the defined flowchart. An analysis of predictive performances for solar forecasting from the different multiscale decompositions and forecast models is presented. From multiscale decomposition, the solar forecast accuracy is significantly improved, particularly using the wavelet decomposition method. Moreover, multistep forecasting with the proposed hybrid method resulted in additional improvement. For example, in terms of RMSE error, the obtained forecasting with the classical NN model is about 25.86%, this error decrease to 16.91% with the EMD-Hybrid Model, 14.06% with the EEMD-Hybid model and to 7.86% with the WD-Hybrid Model.

An optimal k of kth MA-ARIMA models under AR(p) models

ABSTRACTIn this article, we discuss finding the optimal k of (i) kth simple moving average, (ii) kth weighted moving average, and (iii) kth exponential weighted moving average based on simulated autoregressive AR(p) model. We run a simulation using the three above examining method under specific conditions. The main finding is that the optimal k = 4 and then k = 3. Especially, the fourth WMA ARIMA model, fourth EWMA ARIMA model, and third EWMA ARIMA model are the best forecasting models among others, respectively. For all the six real data reveal the similar results of simulation study.

Bayesian inference and forecasting in the stationary bilinear model

ABSTRACTA stationary bilinear (SB) model can be used to describe processes with a time-varying degree of persistence that depends on past shocks. This study develops methods for Bayesian inference, model comparison, and forecasting in the SB model. Using monthly U.K. inflation data, we find that the SB model outperforms the random walk, first-order autoregressive AR(1), and autoregressive moving average ARMA(1,1) models in terms of root mean squared forecast errors. In addition, the SB model is superior to these three models in terms of predictive likelihood for the majority of forecast observations.

Asymptotics of self-weighted M-estimators for autoregressive models

In this paper, we consider a stationary autoregressive AR(p) time series \(y_t=\phi _0+\phi _1y_{t-1}+\cdots +\phi _{p}y_{t-p}+u_t\). A self-weighted M-estimator for the AR(p) model is proposed. The asymptotic normality of this estimator is established, which includes the asymptotic properties under the innovations with finite or infinite variance. The result generalizes and improves the known one in the literature.

Factor Augmented Artificial Neural Network Model

This paper brings together two important developments in forecasting literature; the artificial neural networks and factor models. The paper introduces the factor augmented artificial neural network (FAANN) hybrid model in order to produce a more accurate forecasting. Theoretical and empirical findings have indicated that integration of various models can be an effective way of improving on their predictive performance, especially when the models in the ensemble are quite different. The proposed model is used to forecast three time series variables using large South African monthly panel, namely, deposit rate, gold mining share prices and Long term interest rate, using monthly data over the in-sample period (training set) 1992:1---2006:12. The variables are used to compute out-of-sample (testing set) results for 3, 6 and 12 month-ahead forecasts for the period of 2007:1---2011:12. The out-of-sample root mean square error findings show that the FAANN model yields substantial improvements over the autoregressive AR benchmark model and standard dynamic factor model (DFM). The Diebold---Mariano test results also further confirm the superiority of the FAANN model forecast performance over the AR benchmark model and the DFM model forecasts. The superiority of the FAANN model is due to the ANN flexibility to account for potentially complex nonlinear relationships that are not easily captured by linear models.

Forecasting of Cairo Population using ARMA Model

The problem of large population is one of the most important factors influencing the economy and social advancement of Egypt. Population forecasts, when carefully and intelligently made, serves a valuable purpose in helping to direct the employment of labor and capital to places or projects where they are most needed. Firstly, the paper focuses on studying the population of the capital of Egypt (Cairo). By large numbers of sampling to the population data sequence, the increasing trend is found. Then, a time series model is given which can accurately forecast the population of Cairo. Multiple Autoregressive models AR (1), AR (2) are used the forecasting of the population in the next twenty years. The parameters of the model are calculated using the famous two methods: Yule-Walker and Burg. Before using the model to make predictions, the test of model response is verified and the MSE and MAPE are measured to verify the models. The result is a scary image of the population in this city. Full descriptions for the steps of selecting the suitable model and comprehensive MATLAB simulation are presented. Secondly, the total population density of Egypt is analyzing and forecasting with using the measured data from 1970 to 2013. The same steps of the first part are done with the population density and forecasting of the increasing of the population density of Egypt in the 20 next years is presented. The main reasons for the population problem are discussed and solution of this problem is presented.

Bullwhip Effect Analysis in Two-Level Supply Chain Distribution Network Using Different Demand Forecasting Technology

Following the basic work conducted by Lee et al. [(1997a), The bullwhip effect in supply chains. Sloan Management Review, 38(3), 93–102; (1997b), Information distribution in a supply chain: The bullwhip effect. Management Science, 43(4), 546–558] and using two first-order autoregressive AR(1) models, respectively, this paper provides three quantitative models of the bullwhip effect of the two-level supply chain distribution network consisting of a single manufacturer and two retailers. The paper assumes that two retailers adopt the order point method, uses three kinds of demand forecasting technology, i.e., moving average, exponential smoothing and minimum mean square error methods, respectively, provides three corresponding models for analyzing the impact of bullwhip effect of two-level supply chain distribution network. At the same time, this paper compares and analyzes the results of the three models through simulation.

Using quadratic mean diameter and relative spacing index to enhance height–diameter and crown ratio models fitted to longitudinal data

The inclusion of quadratic mean diameter (QMD) and relative spacing index (RSI) substantially improved the predictive capacity of height–diameter at breast height (d.b.h.) and crown ratio models (CR), respectively. Data were obtained from 208 permanent plots established in western Arkansas and eastern Oklahoma during 1985–1987 and remeasured for the sixth time (2012–2014). Existing height–d.b.h. and CR estimation models for naturally occurring shortleaf pine forests (Pinus echinata Mill.) were updated and modified for improved performance. Additionally, eight height–d.b.h. relationship models that use only d.b.h. (fundamental local models) were modified using covariates. The model performance was evaluated using fit statistics [root mean square error (RMSE), Fit index and Akaike information criteria (AIC)]. The results showed that the best model form which was an extended non-linear model with autoregressive first order AR (1) structure and power variance function performed better than extended mixed-effects models and predicted well as an ordinary least squares non-linear model. The autocorrelation within individual trees was larger for the height–d.b.h. relationship than for CR estimation. The addition of QMD to mean dominant height (HD) greatly improved height–d.b.h. relationship with a reduction of 8 per cent in RMSE, compared with the use of basal area per hectare. Similarly, multiplying a fundamental local model by using QMD raised to a parametric power reduced RMSE by 16 per cent, improved Fit index by 12 per cent and decreased the AIC value by 7 per cent. D.b.h., HD and RSI best explained the crown ratio relationship with an improved Fit index by 6.7 per cent compared with alternative non-linear models without RSI. The logistic model for CR also provided prediction accuracy similar to that of a commonly used non-linear model. A non-linear model with an application of remedial measures to enhance adherence to modelling assumptions can provide better parameter estimates than mixed-effects modelling approach.

Short-term Electricity Load Forecasting Model and Bayesian Estimation for Thailand Data

This paper proposes multi-equation linear regression model with autoregressive AR(2) method for modelling and forecasting a day ahead electricity load. AR(2) is used to show the dependency of next data on its previous two days data because the nature of electricity load consumption for the next day follow the pattern of previous days. Since, we allocate one equation for particular half hour, we need 48 separate equations to predict for one complete day. Parameters of model are estimated based on two different approaches- (i) Classical approach, and (ii) Bayesian approach. Classical or Ordinary Least Square approach estimates the parameters in terms of single value and hence its forecast is also single value, where as Bayesian approach includes the predictive distribution of electricity load due to multiple values of parameters. So, we can forecast electricity load not only from mean, but median and with other percentile values. In this paper, we use 70-percentile value for forecasting because the performance for all models accounts better in this percentile than that of mean and median forecast. Finally, we compare the performances where Bayesian estimation provides better and consistent performance than that of OLS estimation

Robust newsvendor problem with autoregressive demand

This paper explores the single-item newsvendor problem under a novel setting which combines temporal dependence and tractable robust optimization. First, the demand is modeled as a time series which follows an autoregressive process AR(p), p≥1. Second, a robust approach to maximize the worst-case revenue is proposed: a robust distribution-free autoregressive method for the newsvendor problem, which copes with non-stationary time series, is formulated. A closed-form expression for the optimal solution is found for p=1; for the remaining values of p, the problem is expressed as a nonlinear convex optimization program, to be solved numerically. The optimal solution under the robust method is compared with those obtained under three versions of the classic approach, in which either the demand distribution is unknown, and autocorrelation is neglected, or it is assumed to follow an AR(p) process with normal error terms. Numerical experiments show that our proposal usually outperforms the previous benchmarks, not only with regard to robustness, but also in terms of the average revenue. Extensions to multiperiod and multiproduct models are also discussed.

Monte Carlo SSA to detect time-variable seasonal oscillations from GPS-derived site position time series

We explore the capability of singular spectrum analysis (SSA) to extract time-variable seasonal oscillations from continual GPS observations and demonstrate the statistical assessment on the colored noise (in particular the first-order autoregressive AR(1) noise) using Monte Carlo SSA (MCSSA) methodology. We provide example applications to ~15-year vertical coordinate time series for 36 globally distributed International GNSS Service (IGS) sites. We find the SSA-filtered seasonal signals can easily pass the confidence interval and hypothesis tests of MCSSA. However, maximum likelihood estimate (MLE) results show that 72% of sites have their flicker noise amplitudes reduced after removing SSA-filtered annual signal, implying that the SSA-filtered seasonal signals may contain an artificial signal driven by colored noise. Therefore, the AR(1) null hypothesis noise model may be misleading in surrogate data tests for GPS seasonal signals. Moreover, comparison between SSA-filtered GPS annual signals and joint geophysical model predictions (non-tidal atmospheric loading+non-tidal ocean loading+hydrological loading) confirms that seasonal signals are resulting from a combination of mass loading and systematic error.

Misspecification in Dynamic Panel Data Models and Model-Free Inferences

This paper discusses the issue of model misspecification and model-free methods in dynamic panel data analysis. We primarily review existing results, but also provide several new results. When the dynamics are homogeneous, we show that several widely used estimators for panel first-order autoregressive AR(1) models converge to first-order autocorrelation, even under misspecification. Under heterogeneity, these estimators converge to the ratio of the means of the first-order autocovariances and variances. We also discuss the estimation of autocovariances, the estimation of panel AR(∞) models, and the estimation of the distribution of the heterogeneous mean and autocovariances.

The fluctuation function of the detrended fluctuation analysis — investigation on the AR(1) process

We derive an analytical expression for the fluctuation function of the first order autoregressive process AR(1) by means of the detrended fluctuation analysis (DFA). This process is short-range correlated and therefore the fluctuation exponent should be α = 1/2. However, the fluctuation function exhibits a crossover between a region with α > 1/2 and the expected 1/2. We calculate the crossover point and compare it with the characteristic correlation time of the process. We conclude that DFA is data consuming and requires one to two orders of magnitude more data than the estimation of the autocorrelation function.