Autoregressive Time Series Models Research Articles

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.

Parameter estimation for an exponential autoregressive time series model by the Newton search and multi-innovation theory

ABSTRACT This paper focuses on the recursive parameter estimation problem of the exponential autoregressive (ExpAR) model. Applying the Newton search and multi-innovation theory, a multi-innovation Newton recursive algorithm is presented for identifying the ExpAR model. In order to improve the computational efficiency, the hierarchical identification principle is employed to decompose an ExpAR model into two sub-models, and to derive a hierarchical multi-innovation Newton recursive algorithm. A simulation example is provided to demonstrate the effectiveness of the proposed algorithms.

Application of non-destructive sensors and big data analysis to predict physiological storage disorders and fruit firmness in ‘Braeburn’ apples

Physiological storage disorders affect a range of commercially important pomefruit and result in fruit losses and wastage of resources. Disorders can develop during and/or after storage and symptoms are strongly influenced by the growing environment and orchard management. Furthermore, fruit which receive similar orchard management and storage can vary greatly in disorder incidence and severity. Biological systems are complex and simple cause-and-effect approaches have not up until now resulted in robust methods to predict disorder risk. Reliable predictions are needed by fruit industries worldwide to better manage fruit production processes, to determine optimal harvest dates and long-term storage regimes. The current work proposes a new methodological approach to model ‘Braeburn’ apple disorder risk. Autoregressive time series (ARX) models via model identification techniques for chlorophyll, anthocyanins, soluble solids and dry matter content were obtained from weather conditions and different orchard management treatments and then served as input into a classifier for internal browning, cavities and fruit firmness after long-term controlled atmosphere storage. The classification results for internal browning disorder show a 90% agreement between two separate years and for fruit firmness an 80% success rate was obtained by training the classifier with two years of data.

92438 Symptom Dynamics and Biomarkers of Disease Progression in Older Adult Patient-Caregiver Dyads During Care Transitions after Heart Failure Hospitalization: Study Design and Anticipated Results

ABSTRACT IMPACT: This study is designed to address a critical gap in our understanding of how aging patients and caregivers recognize and respond to clinically important changes in heart failure symptoms during vulnerable transitions. OBJECTIVES/GOALS: Research on family involvement in heart failure (HF) symptom response is limited. Our objective is to examine HF symptom monitoring processes in couples after HF hospitalization, and quantify how coupled symptom assessments predict symptom response, patient clinical events, care strain, and dyad health during the high-risk post-discharge period. METHODS/STUDY POPULATION: This is an ongoing T2 translational study that employs an intensive longitudinal design. Adults aged ≥65 years hospitalized for HF and their caregiving spouse/partner are enrolled. The target n is 48 dyads. Over 5 weeks of follow-up, dyads complete daily diaries assessing patient HF symptoms. Clinical biomarkers of HF severity (NTproBNP, ST2) are also collected. Primary study endpoints are dyads’ HF symptom response behaviors and caregiver strain; secondary endpoints are dyads’ health status and patient clinical events. Dyadic dynamics of symptom assessment will first be characterized using dyadic autoregressive time series models. Subsequently, we will extract cross-partner effect parameters from the time series models and test whether dyadic effects predict the trajectories of each of our endpoints. RESULTS/ANTICIPATED RESULTS: This study is currently underway. In line with our study hypotheses, we anticipate that couples who assess patient symptoms similarly (dyadic agreement), and whose symptom assessments accurately reflect clinical severity, will be more likely to respond to symptoms appropriately with lower stress to the caregiving partner, and have better trajectories of health (self-reported and clinical). Characterizing dyadic symptom dynamics will provide important insight into the day-to-day process of symptom recognition in couples. Further, quantifying dyadic symptom dynamics in relation to our endpoints will provide information on the clinical value of dyadic symptom agreement, and whether it might be a target for future interventions to support better symptom response and health outcomes for both dyad members. DISCUSSION/SIGNIFICANCE OF FINDINGS: This project innovates on existing paradigms by applying family-level theory and techniques to better understand and support interventions for couples during post-discharge HF transitions - a vulnerable period for older adults that has traditionally been studied almost exclusively at the patient-level, with marginal success.

Variability in fluorescent dissolved organic matter concentrations across diel to seasonal time scales is driven by water temperature and meteorology in a eutrophic reservoir

Freshwater reservoirs play a significant role in the global carbon cycle by processing and storing large quantities of dissolved organic matter (DOM). Quantifying the magnitude of DOM fluctuations across multiple temporal scales can advance our understanding of how the controls on reservoir carbon cycling may vary. We monitored fluorescent DOM (fDOM) using an in situ epilimnetic sensor at a ten-minute resolution over one year in a eutrophic reservoir in southwestern Virginia, USA with low dissolved organic carbon concentrations (2–6 mg L−1). We determined the dominant time scales of variability and key environmental predictors of fDOM concentrations using continuous wavelet transforms and autoregressive time series modeling. Throughout the year, fDOM concentrations varied considerably, with maximum concentrations in the autumn (30.0 quinine sulfate units) and minimum concentrations in the spring (4.7 quinine sulfate units). The monthly time scale was the dominant time scale of variability, but the daily time scale was significant during the summer. Based on the autoregressive time series analysis, precipitation, water temperature, and shortwave radiation were important environmental predictors of fDOM on daily time scales, while water temperature alone best predicted monthly variability. Our study is one of the first to reveal substantial variability in fDOM concentrations during a full year, emphasizing the need for long-term, high-frequency in situ DOM monitoring to capture changes occurring on multiple time scales. By quantifying the variability and environmental predictors of fDOM on different time scales, we are able to better understand how and why DOM concentrations change throughout the year.

Parasympathetic-Sympathetic Causal Interactions Assessed by Time-Varying Multivariate Autoregressive Modeling of Electrodermal Activity and Heart-Rate-Variability.

Most of the bodily functions are regulated by multiple interactions between the parasympathetic (PNS) and sympathetic (SNS) nervous system. In this study, we propose a novel framework to quantify the causal flow of information between PNS and SNS through the analysis of heart rate variability (HRV) and electrodermal activity (EDA) signals. Our method is based on a time-varying (TV) multivariate autoregressive model of EDA and HRV time-series and incorporates physiologically inspired assumptions by estimating the Directed Coherence in a specific frequency range. The statistical significance of the observed interactions is assessed by a bootstrap procedure purposely developed to infer causalities in the presence of both TV model coefficients and TV model residuals (i.e., heteroskedasticity). We tested our method on two different experiments designed to trigger a sympathetic response, i.e., a hand-grip task (HG) and a mental-computation task (MC). Our results show a parasympathetic driven interaction in the resting state, which is consistent across different studies. The onset of the stressful stimulation triggers a cascade of events characterized by the presence or absence of the PNS-SNS interaction and changes in the directionality. Despite similarities between the results related to the two tasks, we reveal differences in the dynamics of the PNS-SNS interaction, which might reflect different regulatory mechanisms associated with different stressors. We estimate causal coupling between PNS and SNS through MVAR modeling of EDA and HRV time-series. Our results suggest promising future applicability to investigate more complex contexts such as affective and pathological scenarios.

A class of bootstrap tests on the tail index

This work proposes powerful tests using bootstrap methods for the tail index in the family of distribution functions with nondegenerate right tail. It is of interest to test whether the right tail of a distribution function is the same as or heavier than that of the Pareto distribution with index m 0 for some m 0, vs. alternatively the right tail is lighter. Based on the nonparametric tests of Jureckova and Picek (2001, A class of tests on the tail index, Extreme 4:2, 165–183) that use empirical distribution functions of sample maxima, the proposed bootstrap tests employ two-stage subsamplings: One is subsampling from the sample maxima to be applicable even to the heavy tailed index and the other is subsampling from collections of empirical distributions of the sample maxima. We show the first-order validity of the bootstrap for the nonparametric test and construct bootstrap test statistics. The limiting distribution of the bootstrap test statistics in the null hypothesis is established and the consistency of the bootstrap tests is verified. Applications of the proposed bootstrap tests are given to autoregressive time series models. A simulation study is conducted to see performance of the bootstrap tests and it illustrates that the proposed bootstrap tests outperform the existing ones. Real data of heavy tailed financial stock indices are applied to the proposed bootstrap tests.

Heavy Tailed Pareto Distribution: Properties and Applications

In this article, we introduce a class of distributions that have heavy tails as compared to Pareto distribution of third kind, which we termed as Heavy Tailed Pareto (HP) distribution. Various structural properties of the new distribution are derived. It is shown that HP distribution is in the domain of attraction of minimum of Weibull distribution. A representation of HP distribution in terms of Weibull random variable is obtained. Two characterizations of HP distribution are obtained. The method of maximum likelihood is used for estimation of model parameters and simulation results are presented to assess the performance of new model. Marshall-Olkin Heavy Tailed Pareto (MOHP) distribution is also introduced and some of its properties are studied. It is shown that MOHP distribution is geometric extreme stable. An autoregressive time series model with the new model as marginal distribution is developed and its properties are studied.

The Role of Bike Sharing in Promoting Transport Resilience

AbstractA resilient transport network, which is significant for urban sustainability and security, is characterized by its ability to recover from disruptions subject to natural and man-made disasters. Bike sharing could act as a viable alternative in the case of public transit disruptions given its flexibility and various social, environmental, and economic benefits. This study aims to estimate quantitatively the potential of bike sharing to promote transport resilience, by using autoregressive negative binomial time series model to investigate the effects of public transit closures on bike sharing demand in Washington, D.C. area during 2015–2017. We find that (1) bike sharing can act as a supplementary mode to enhance urban transport resilience in the case of complete transit closure; (2) the proximity of bike sharing docks to metro stations has a powerful effect on propensity to use a bike sharing program; and (3) extreme weather is one of major barriers to bicycling. Planners can enhance resilience of urban transport networks by fully considering the capacity and usage of bike sharing docks, as well as the coherence of metro stations and bike sharing docks, in distributing and rebalancing activities.

Scale-, time- and asset-dependence of Hawkes process estimates on high frequency price changes

The statistical estimate of the branching ratio η of the Hawkes model, when fitted to windows of mid-price changes, has been reported to approach criticality () as the fitting window becomes large. In this study – using price changes from the EUR/USD currency pair traded on the Electronic Broking Services (EBS) interbank trading platform and the S&P 500 E-mini futures contract traded at the Chicago Mercantile Exchange (CME) – it is shown that the estimated branching ratio depends little upon window size and is usually far from criticality. This is done by controlling for exogenous non-stationarities/heterogeneities at inter- and intraday scales, accomplished by using information criteria to select the degree of flexibility of the Hawkes immigration intensity, either piecewise constant or adaptive logspline, estimated using an expectation maximization (EM) algorithm. The (positive) bias incurred by keeping the immigration intensity constant is small for time scales up to two hours, but can become as high as 0.3 for windows spanning days. This emphasizes the importance of choosing an appropriate model for the immigration intensity in the application of Hawkes processes to financial data and elsewhere. The branching ratio is also found to have an intraday seasonality, where it appears to be higher during times where market activity is dominated by supposedly reflexive automated decisions and a lack of fundamental news and trading. The insights into the microstructure of the two considered markets derived from our Hawkes process fits suggest that equity futures exhibit more complex non-stationary features, are more endogenous, persistent and traded at higher speed than spot foreign exchange. We complement our point process study with EM-estimates of integer-valued autoregressive (INAR) time series models at even longer scales of months. Transferring our methodologies to the aggregate bin-count setting confirms that, even at these very long scales, criticality can be rejected.

How infomediaries on Twitter influence business outcomes of a bank

PurposeThe purpose of this paper is to empirically explore under which conditions Tweets of infomediaries (i.e. ordinary users having few or no followers on Twitter) might nevertheless promote a negative sentiment toward a corporation to the point of having a negative impact on the corporation's outcomes.Design/methodology/approachThe empirical study is based on a unique database that combines a sample of one year of Twitter conversations about an Italian bank and its daily business performances (i.e. number of closures and openings). The relationship between these two is analyzed using autoregressive time series models (VAR).FindingsFindings indicate that a tweet affects a bank’s outcomes only when embedded in a larger conversation about the bank, rather than simply repetitively shared. These findings contribute to two debates within bank marketing literature. First is the debate about the role of infomediaries in banks' outcomes, as it urges to reconsider the way banks' online reputation is conceptualized and measured. Second is the debate on opportunities and threats of social media for the banking industry, as it indicates that negative sentiment expressed by the general public influences not only stock markets but also directly banks' outcomes.Originality/valueThis study allows managers and corporations to understand what to do when conversations of unknown individuals become threatening for the company. To influence such situations, the company should identify not only the actors that are influencers but also the communications that have been popular in the past for their brand or the brand of their competitors and monitor the conversational volume and broadness.

Can the Baidu Index predict realized volatility in the Chinese stock market?

This paper incorporates the Baidu Index into various heterogeneous autoregressive type time series models and shows that the Baidu Index is a superior predictor of realized volatility in the SSE 50 Index. Furthermore, the predictability of the Baidu Index is found to rise as the forecasting horizon increases. We also find that continuous components enhance predictive power across all horizons, but that increases are only sustained in the short and medium terms, as the long-term impact on volatility is less persistent. Our findings should be expected to influence investors interested in constructing trading strategies based on realized volatility.