Autoregressive Time Series Models Research Articles

The effect of oil rent on economic development in Saudi Arabia: Comparing the role of globalization and the international geopolitical risk

We explored the effect of globalization and international geopolitical risks on Saudi Arabia's economic development via the channel of Saudi's oil rent during the period 1970–2018. In addition, we tested if globalization and international geopolitical risk can strengthen or weaken the impact of oil rent on Saudi Arabia's economic development. A time series autoregressive distributed lag model with moderation effects was used to achieve the paper's objective. Our results revealed that the direct short and long run effects of oil rent and globalization are statistically significant and positive, while the influence of international geopolitical risk is statistically insignificant in the short and long run. However, adding the moderation effects to the analysis reversed the results. The interaction terms of our paper are significant and negative. It implies that the interaction terms deflate the direct positive effects. Therefore, the final effect of oil rent and globalization could be either positive or negative, while the final effect of the international geopolitical risk is negative. The findings from the current paper confirms that globalization effect is dominant on economic development, compared to geopolitical risk. The policy implication of our paper focuses on diversifying Saudi's economy and strengthen Saudi Arabia's institutional framework.

Feedback adjustment using exponentially weighted moving average schemes

In this study, we discuss the use of exponentially weighted moving average (EWMA) schemes in feedback adjustment for process improvement. By application the different measures of dispersion yield different optimal values. In particular it is suggested that a robust statistic based on the median is more appropriate than the usual mean of square error (MSE).We also consider an autoregressive time series model for modeling the deviations from target and this model is compared with the usual EWMA model. The problem of applying feedback adjustment to a controllable process is discussed and it is shown via a simulation that correlation structure of the data of interest play a critical role on whether the MSE after adjustment is lower than the MSE before adjustment.

Evaluating Forecasts from State-Dependent Autoregressive Models for US GDP Growth Rate. Comparison with Alternative Approaches

Abstract The aim of the paper is to compare the forecasting performance of a class of statedependent autoregressive (SDAR) models for univariate time series with two alternative families of nonlinear models, such as the SETAR and the GARCH models. The study is conducted on US GDP growth rate using quarterly data. Two methods of forecast comparison are employed. The first method consists in evaluation the average performance by using two measures such as the root mean square error (RMSE) and the mean absolute error (MAE) over different forecast horizons, while the second method make use of one of the most used statistical test to compare the accuracy of two forecast methods such as the Diebold-Mariano test. JEL classification numbers: C22, E37, F47. Keywords: Nonlinear models for time series, GDP growth rate, Forecasting accuracy.

Wasserstein Regression

The analysis of samples of random objects that do not lie in a vector space is gaining increasing attention in statistics. An important class of such object data is univariate probability measures defined on the real line. Adopting the Wasserstein metric, we develop a class of regression models for such data, where random distributions serve as predictors and the responses are either also distributions or scalars. To define this regression model, we use the geometry of tangent bundles of the space of random measures endowed with the Wasserstein metric for mapping distributions to tangent spaces. The proposed distribution-to-distribution regression model provides an extension of multivariate linear regression for Euclidean data and function-to-function regression for Hilbert space-valued data in functional data analysis. In simulations, it performs better than an alternative transformation approach where one maps distributions to a Hilbert space through the log quantile density transformation and then applies traditional functional regression. We derive asymptotic rates of convergence for the estimator of the regression operator and for predicted distributions and also study an extension to autoregressive models for distribution-valued time series. The proposed methods are illustrated with data on human mortality and distributional time series of house prices.

Symposium Title: Construction and Validation of an Event-Related Potential Platform

A model predictive control (MPC) system based on latent variables (LV) model generated by using partial least squares (PLS) method is developed. The difference in the performance of MPCs that use recursively updated LV models based on autoregressive time series modeling (with exogenous inputs - ARX) and PLS is studied. The effect of signal noise on MPC performance is also investigated for both types of models. MPC performance is evaluated by regulating the blood glucose concentration (BGC) of people with Type 1 diabetes mellitus (T1DM) in simulation studies. Signal noise in glucose concentration sensor data, delays caused by insulin absorption and action, and disturbances caused by consumption of meals make the regulation of BGC difficult. The proposed controller is evaluated with 10 in-silico adult subjects of the UVa/Padova simulator with different levels of signal noise. The results illustrate the effectiveness of the MPC based on LV model. The average time for BGC in the safe range (70-180 mg/dL) for the LV-based MPC is 83.23% compared to 79.68% for the MPC based on ARX model when intravenous BGC values are used. The average time in safe range decreases to 76.04% and 71.92%, respectively, when using the generic CGM sensor of the simulator. It is reduced further to 71.93% and 67.20% when additional noise is added to CGM readings.

Estimation of parameters in the MDDRCINAR(p) model

ABSTRACT This paper brings forward a pth-order mixed dependence-driven random coefficient integer-valued autoregressive time series model (MDDRCINAR(p)). Stationarity and ergodicity properties of the proposed model are derived. The unknown parameters are estimated by conditional least squares, weighted least squares and maximum quasi-likelihood and asymptotic characterization of the obtained parameter estimators is proved. The performances of the proposed estimate methods are checked via simulations, which present that maximum quasi-likelihood estimators perform better than the other two estimate methods considering the proportion of within-Ω estimates in certain regions of the parameter space. The applicability of the model is investigated using two real count data sets.

Modeling and forecasting the COVID-19 pandemic with heterogeneous autoregression approaches: South Korea

This paper deals with time series analysis for COVID-19 in South Korea. We adopt heterogeneous autoregressive (HAR) time series models and discuss the statistical inference for various COVID-19 data. Seven data sets such as cumulative confirmed (CC) case, cumulative recovered (CR) case and cumulative death (CD) case as well as recovery rate, fatality rate and infection rates for 14 and 21 days are handled for the statistical analysis. In the HAR models, model selections of orders are conducted by evaluating root mean square error (RMSE) and mean absolute error (MAE) as well as R2, AIC, and BIC. As a result of estimation, we provide coefficients estimates, standard errors and 95% confidence intervals in the HAR models. Our results report that fitted values via the HAR models are not only well-matched with the real cumulative cases but also differenced values from the fitted HAR models are well-matched with real daily cases. Additionally, because the CC and the CD cases are strongly correlated, we use a bivariate HAR model for the two data sets. Out-of-sample forecastings are carried out with the COVID-19 data sets to obtain multi-step ahead predicted values and 95% prediction intervals. As for the forecasting performances, four accuracy measures such as RMSE, MAE, mean absolute percentage error (MAPE) and root relative square error (RRSE) are evaluated. Contributions of this work are three folds: First, it is shown that the HAR models fit well to cumulative numbers of the COVID-19 data along with good criterion results. Second, a variety of analysis are studied for the COVID-19 series: confirmed, recovered, death cases, as well as the related rates. Third, forecast accuracy measures are evaluated as small values of errors, and thus it is concluded that the HAR model provides a good prediction model for the COVID-19.

Seasonal functional autoregressive models

Functional autoregressive models are popular for functional time series analysis, but the standard formulation fails to address seasonal behaviour in functional time series data. To overcome this shortcoming, we introduce seasonal functional autoregressive time series models. For the model of order one, we derive sufficient stationarity conditions and limiting behaviour, and provide estimation and prediction methods. Moreover, we consider a portmanteau test for testing the adequacy of this model, and we derive its asymptotic distribution. The merits of this model are demonstrated using simulation studies and via an application to hourly pedestrian counts.

Forecasting interval-valued crude oil prices using asymmetric interval models

Practitioners and policy makers rely on accurate crude oil forecasting to avoid price risks and grasp investment opportunities, but the core of existing predictive models for such prices is based on point-valued inputs and outputs, which may suffer from informational loss of volatility. This paper addresses this issue by proposing a modified threshold autoregressive interval-valued models with interval-valued factors (MTARIX), as extended by Sun et al. [Threshold autoregressive models for interval-valued time series. J. Econom., 2018, 206, 414–446], to analyze and forecast interval-valued crude oil prices. In contrast to point-valued data methods, MTARIX models simultaneously capture nonlinear features in price trend and volatility, and this informational gain can produce more accurate forecasts. Several interval-valued factors and point-valued threshold variables are analyzed, including supply and demand, speculation, stock market, monetary market, technical factor, and search query data. Empirical results suggest that MTARIX models with appropriate threshold variables outperform other competing forecast models (ACIX, CR-SETARX, ARX, and VARX). The findings indicate that oil price range information is more valuable than oil price level information in forecasting crude oil prices.

A Modeling Study on the Estimation of COVID-19 Daily and Weekly Cases and Reproduction Number Using the Adaptive Kalman Filter: The Example of Ziraat Bank, Turkey

Abstract Since the beginning of 2020, the world has been struggling with a viral epidemic (COVID-19), which poses a serious threat to the collective health of the human race. Mathematical modeling of epidemics is critical for developing such policies, especially during these uncertain times. In this study, the reproduction number and model parameters were predicted using AR(1) (autoregressive time-series model of order 1) and the adaptive Kalman filter (AKF). The data sample used in the study consists of the weekly and daily number of cases amongst the Ziraat Bank personnel between March 11, 2020, and April 19, 2021. This sample was modeled in the state space, and the AKF was used to estimate the number of cases per day. It is quite simple to model the daily and weekly case number time series with the time-varying parameter AR(1) stochastic process and to estimate the time-varying parameter with online AKF. Overall, we found that the weekly case number prediction was more accurate than the daily case number (R2 = 0.97), especially in regions with a low number of cases. We suggest that the simplest method for reproduction number estimation can be obtained by modeling the daily cases using an AR(1) model. JEL classification numbers: C02, C22, C32. Keywords: COVID-19, Modeling, Reproduction number estimation, AR(1), Kalman filter.

A multivariate statistical approach to predict COVID-19 count data with epidemiological interpretation and uncertainty quantification.

For the analysis of COVID‐19 pandemic data, we propose Bayesian multinomial and Dirichlet‐multinomial autoregressive models for time‐series of counts of patients in mutually exclusive and exhaustive observational categories, defined according to the severity of the patient status and the required treatment. Categories include hospitalized in regular wards (H) and in intensive care units (ICU), together with deceased (D) and recovered (R). These models explicitly formulate assumptions on the transition probabilities between these categories across time, thanks to a flexible formulation based on parameters that a priori follow normal distributions, possibly truncated to incorporate specific hypotheses having an epidemiological interpretation. The posterior distribution of model parameters and the transition matrices are estimated by a Markov chain Monte Carlo algorithm that also provides predictions and allows us to compute the reproduction number Rt. All estimates and predictions are endowed with an accuracy measure obtained thanks to the Bayesian approach. We present results concerning data collected during the first wave of the pandemic in Italy and Lombardy and study the effect of nonpharmaceutical interventions. Suitable discrepancy measures defined to check and compare models show that the Dirichlet‐multinomial model has an adequate fit and provides good predictive performance in particular for H and ICU patients.

Smooth-transition autoregressive models for time series of bounded counts

The binomial smooth-transition autoregressive (BSTAR) model is proposed as a non-linear model for time series of bounded counts. The BSTAR(1) model enhances the first-order binomial autoregressive model by a smooth-transition mechanism between two regimes. Apart from this basic BSTAR model, also model extensions with more than two regimes, with higher-order autoregression, or with extra-binomial variation are discussed. Moreover, parameter estimation is addressed. We analyze the asymptotic and the finite-sample properties of the maximum likelihood estimator, which also covers the BSTAR’s threshold parameter. The BSTAR model is applied to two real-world data examples from the fields of epidemiology and meteorology.

Odelling the Effect of Population on Rice Production, Consumption and Importation in Nigeria: Vector Autoregressive Model

One major factor of Economic Development of any nation is food security as the population is on increase in Nigeria. Imposition of barn and closure of border had led to increase in price, smuggling, and hoarding of rice among other problems. Diverse statistical studies had been carried out in many nation of Africa on how to improve rice production without much success. Vector Autoregressive time series modeling is proposed to analyse the relationship between population and rice production, importation, and consumption. The stationarity test reveals that only population got stationarity at first difference while others attain stationarity at zero differencing. Granger causality reported that population, rice production and importation Granger cause rate of rice consumption rate in Nigeria and in essence population, production, and importation of rice has significant effect on consumption. Important recommendation were made to enhance availability of rice for consumption

Auto-Regressive Integrated Moving-Average Machine Learning for Damage Identification of Steel Frames

Auto-regressive (AR) time series (TS) models are useful for structural damage detection in vibration-based structural health monitoring (SHM). However, certain limitations, e.g., non-stationarity and subjective feature selection, have reduced its wide-spread use. With increasing trends in machine learning (ML) technologies, automated structural damage recognition is becoming popular and attracting many researchers. In this paper, we combined TS modeling and ML classification to automatically extract damage features and overcome the limitation of non-stationarity. We propose a two-stage framework, namely auto-regressive integrated moving-average machine learning (ARIMA-ML) with modules for pre-processing, model parameter determination, feature extraction, and classification. Based on shaking table tests of a space steel frame, floor acceleration data were collected and labeled according to experimental observations and records. Subsequently, we designed three damage classification tasks for: (1) global damage detection, (2) local damage detection, and (3) local damage pattern recognition. The results from these three tasks indicated the robustness and accuracy of the proposed framework where 97%, 98%, and 80% average segment accuracy were achieved, respectively. The confusion matrix results showed the unbiased model performance even under an imbalanced-class distribution. In summary, the presented study revealed the high potential of the proposed ARIMA-ML framework in vibration-based SHM.

Fisher’s z Distribution-Based Mixture Autoregressive Model

We generalize the Gaussian Mixture Autoregressive (GMAR) model to the Fisher’s z Mixture Autoregressive (ZMAR) model for modeling nonlinear time series. The model consists of a mixture of K-component Fisher’s z autoregressive models with the mixing proportions changing over time. This model can capture time series with both heteroskedasticity and multimodal conditional distribution, using Fisher’s z distribution as an innovation in the MAR model. The ZMAR model is classified as nonlinearity in the level (or mode) model because the mode of the Fisher’s z distribution is stable in its location parameter, whether symmetric or asymmetric. Using the Markov Chain Monte Carlo (MCMC) algorithm, e.g., the No-U-Turn Sampler (NUTS), we conducted a simulation study to investigate the model performance compared to the GMAR model and Student t Mixture Autoregressive (TMAR) model. The models are applied to the daily IBM stock prices and the monthly Brent crude oil prices. The results show that the proposed model outperforms the existing ones, as indicated by the Pareto-Smoothed Important Sampling Leave-One-Out cross-validation (PSIS-LOO) minimum criterion.

Wasserstein autoregressive models for density time series

Data consisting of time‐indexed distributions of cross‐sectional or intraday returns have been extensively studied in finance, and provide one example in which the data atoms consist of serially dependent probability distributions. Motivated by such data, we propose an autoregressive model for density time series by exploiting the tangent space structure on the space of distributions that is induced by the Wasserstein metric. The densities themselves are not assumed to have any specific parametric form, leading to flexible forecasting of future unobserved densities. The main estimation targets in the order‐p Wasserstein autoregressive model are Wasserstein autocorrelations and the vector‐valued autoregressive parameter. We propose suitable estimators and establish their asymptotic normality, which is verified in a simulation study. The new order‐p Wasserstein autoregressive model leads to a prediction algorithm, which includes a data driven order selection procedure. Its performance is compared to existing prediction procedures via application to four financial return data sets, where a variety of metrics are used to quantify forecasting accuracy. For most metrics, the proposed model outperforms existing methods in two of the data sets, while the best empirical performance in the other two data sets is attained by existing methods based on functional transformations of the densities.

Simulation of photo-voltaic power generation using copula autoregressive models for solar irradiance and air temperature time series

We propose a methodology for synthetic generation of solar irradiance (shortwave flux) and air temperature time series using copula functions. The use of copulas for the simulation gives flexibility to represent the serial stochastic variability of the solar irradiation and the air temperature affecting the photo-voltaic (PV) panel energy output. Moreover, it allows to have more control on the desired properties of the time series, not only in the temporal and cross-dependencies, but also in the marginal distributions. We use mixtures of zero mass adjusted density distributions to assess the nature of solar irradiance, alongside vector generalized linear models for the bivariate time series time marginal distributions. We found that the copula autoregressive methodology used, including the zero mass characteristics of the solar irradiance time series, accurately models the stochastic phenomena. Experimental analysis with observed data substantiates the usage and convenience of the proposed methodology to model solar irradiance time series and solar energy across the northern hemisphere, southern hemisphere and equatorial zones. These results will improve the understanding of the fluctuating nature of solar irradiance and also help to understand the underlying stochastic process of photo-voltaic energy production.

Gang-related crime in Los Angeles remained stable following COVID-19 social distancing orders.

Research SummaryThe onset of extreme social distancing measures is expected to have a dramatic impact on crime. Here, we examine the impact of mandated, city‐wide social distancing orders aimed at limiting the spread of COVID‐19 on gang‐related crime in Los Angeles. We hypothesize that the unique subcultural processes surrounding gangs may supersede calls to shelter in place and allow gang‐related crime to persist. If the normal guardianship of people and property is also disrupted by social distancing, then we expect gang violence to increase. Using autoregressive time series models, we show that gang‐related crime remained stable and crime hot spots largely stationary following the onset of shelter in place.Policy ImplicationsIn responding to disruptions to social and economic life on the scale of the present pandemic, both police and civilian organizations need to anticipate continued demand, all while managing potential reductions to workforce. Police are faced with this challenge across a wide array of crime types. Civilian interventionists tasked with responding to gang‐related crime need to be prepared for continued peacekeeping and violence interruption activities, but also an expansion of responsibilities to deal with “frontline” or “street‐level” management of public health needs.

Fuzzy Autoregressive Time Series Model Based on Symmetry Triangular Fuzzy Numbers

The symmetry triangular fuzzy number has been developed to build fuzzy autoregressive models by using various approaches such as low-high data, integer number, measurement error, and standard deviation data. However, most of these approaches are not simulated and compared between ordinary least square and fuzzy optimization in parameter estimation. In this paper, we are interested in implementation of measurement error and standard deviation data in construction symmetry triangular fuzzy numbers. Additionally, both types of triangular fuzzy numbers are deployed to build a fuzzy autoregressive model, especially the second order. The simulation result showed that the fuzzy autoregressive model produced the smaller mean square error and average width if compared with the ordinary autoregressive model. In the implementation, the high accuracy was also achieved by the fuzzy autoregressive model in consumer goods stock prediction. From the simulation and implementation, the proposed fuzzy autoregressive model is a competent approach for upper and lower forecasts.

Application of auto-regressive time series model to marginal oil field production in Nigeria

Some concern has been expressed over the continuous low production from Marginal oil field. This production problem has been ascribed to multitude of hindrances occasioned by the nature of earth formation in the zone. Attempts to ascertain the character or complexion of such problems have often eluded researchers and operators of the field. This study adopts the use of auto-regressive time series model to find out the root cause or the mechanism that generate high output or low output in marginal field. The correlogram that captures the memory of the mechanism that generated the output process was established. And by judiciously picking and choosing the right lags from the correlogram, model that replicates the production process mechanism was also established. The result obtained shows that there is a close tracking of the forecast with the actual. Evidently, the Mean absolute percentage error (MAPE) obtained is 5.07% showing that the errors in forecast are marginal suggesting that the forecast is robust if not sure-fire.