Autoregressive Time Series Models Research Articles

Trends in methamphetamine use, markets and harms in Australia, 2003-2019.

To describe trends in methamphetamine use, markets and harms in Australia from 2003 to 2019. Data comprised patterns of use and price from sentinel samples of people who inject drugs and who use MDMA/other illicit stimulants and population-level amphetamine-related police seizures, arrests, hospitalisations, treatment episodes and deaths from approximately 2003 to 2019. Bayesian autoregressive time-series models were analysed for: no change; constant rate of change; and change over time differing in rate after one to three changepoints. Related indicators were analysed post hoc with identical changepoints. The percentage of people who inject drugs reporting weekly use increased from 2010 to 2013 onwards, while use among samples of people who regularly use ecstasy and other illicit stimulants decreased. Seizures and arrests rose steeply from around 2009/10 to 2014/15 and subsequently plateaued. Price increased ($15.9 [95% credible interval, CrI $9.9, $28.9] per point of crystal per year) from around 2009 to 2011, plateauing and then declining from around 2017. Hospitalisation rates increased steeply from around 2009/10 until 2015/16, with a small subsequent decline. Treatment also increased (19.8 episodes [95% CrI 13.2, 27.6] with amphetamines as the principal drug of concern per 100 000 persons per year) from 2010/11 onwards. Deaths involving amphetamines increased (0.285 per 100 000 persons per year) from 2012 until 2016. These findings suggest that problematic methamphetamine use and harms escalated from 2010 to 2012 onwards in Australia, with continued demand and a sustained market for methamphetamine. [Correction added on 30 May 2022, after first online publication: In the Abstract under 'Discussion and Conclusions' 'onwards' has been added after … 2010 to 2012].

Trends in Performance of Anti-Incontinence Treatment at the Time of Pelvic Organ Prolapse Repair From 2011 to 2019.

There are no publications on national trends in performance of concomitant stress urinary incontinence (SUI) treatment with pelvic organ prolapse surgery over the past decade. The objective of this study was to describe trends in the performance and type of concomitant SUI treatment from 2011 to 2019. Surgical procedures for pelvic organ prolapse and coding for prolapse repair were identified from the American College of Surgeons National Surgical Quality Improvement Program database. An autoregressive interrupted time series model estimated temporal trends in concomitant SUI treatment associated with 3 consequential events: U.S. Food and Drug Administration's (FDA) requirement for postmarketing studies from mesh manufacturers (January 2012), publication of the Outcomes following Vaginal Prolapse Repair and Midurethral Sling (OPUS) trial (June 2012), and the FDA's reclassification of vaginal mesh as a high-risk device (January 2016). There were 43,370 cases identified. The rate of concomitant SUI treatment decreased from 46.1% to 35.7% across the analysis period. No significant trend before postmarketing studies (-0.2%; 95% confidence interval [CI], -0.8 to 1.1) was observed. After postmarketing studies, there was a downward deflection of -2.0% per quarter (95% CI, -3.6 to -0.4). After OPUS, we observed a flattening of the trend to -0.2% (95% CI, -0.8 to 0.4) that persisted after FDA reclassification. Sling procedures remained predominant (96.2% of SUI procedures) and performance of urethropexy decreased across the analysis period (-0.1%; 95% CI, -0.08 to -0.2). After the FDA's order for postmarketing studies, rates of concomitant SUI treatment significantly decreased. Rates stabilized after the OPUS trial at around 35% and did not subsequently change. Rates of nonmesh concomitant SUI treatment decreased during the analysis period.

SARS-CoV-2 Dissemination Using a Network of the US Counties

During 2020 and 2021, severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) transmission has been increasing among the world’s population at an alarming rate. Reducing the spread of SARS-CoV-2 and other diseases that are spread in similar manners is paramount for public health officials as they seek to effectively manage resources and potential population control measures such as social distancing and quarantines. By analyzing the US county network structure, one can model and interdict potential higher infection areas. County officials can provide targeted information, preparedness training, and increase testing the researchers conclude that traditional the researchers conclude that traditional in these areas. While these approaches may provide adequate countermeasures for localized areas, they are inadequate for the holistic USA. We solve this problem by collecting coronavirus disease 2019 (COVID-19) infections and deaths from the Center for Disease Control and Prevention, and adjacency between all counties obtained from the United States Census Bureau. Generalized network autoregressive (GNAR) time series models have been proposed as an efficient learning algorithm for networked datasets. This work fuses network science and operations research techniques to univariately model COVID-19 cases, deaths, and current survivors across the US county network structure.

NTreeClus: A tree-based sequence encoder for clustering categorical series

The overwhelming presence of categorical/sequential data in diverse domains emphasizes the importance of sequence mining. The challenging nature of sequences proves the need for continuing research to find a more accurate and faster approach providing a better understanding of their (dis) similarities. This paper proposes a new Model-based approach for clustering sequence data, namely nTreeClus. The proposed method deploys Tree-based Learners, k-mers, and autoregressive models for categorical time series, culminating with a novel numerical representation of the categorical sequences. Adopting this new representation, we cluster sequences, considering the inherent patterns in categorical time series. Accordingly, the model showed robustness to its parameter. Under different simulated scenarios, nTreeClus improved the baseline methods for various internal and external cluster validation metrics for up to 10.7% and 2.7%, respectively. The empirical evaluation using synthetic and real datasets, protein sequences, and categorical time series showed that nTreeClus is competitive or superior to most state-of-the-art algorithms.

Modelling Clusters of Corporate Defaults: Regime-Switching Models Significantly Reduce the Contagion Source

Abstract In this paper, we report robust evidence that the process of corporate defaults is time-dependent and can be modelled by extending an autoregressive count time series model class via the introduction of regime-switching. That is, some of the parameters of the model depend on the regime of an unobserved Markov chain, capturing the model changes during clusters observed for count time series in corporate defaults. Thus, the process of corporate defaults is more dynamic than previously believed. Moreover, the contagion effect—that current defaults affect the probability of other firms defaulting in the future—is reduced compared to models without regime-switching, and is only present in one regime. A two-regime model drives the counts of monthly corporate defaults in the United States. To estimate the model, we introduce a novel quasi-maximum likelihood estimator by adapting the extended Hamilton–Gray algorithm for the Poisson autoregressive model.

A Bayesian detection of structural changes in autoregressive time series models

A Bayesian detection of structural changes in autoregressive time series models

Shock trace prediction by reduced models for a viscous stochastic Burgers equation.

Viscous shocks are a particular type of extreme event in nonlinear multiscale systems, and their representation requires small scales. Model reduction can thus play an essential role in reducing the computational cost for the prediction of shocks. Yet, reduced models typically aim to approximate large-scale dominating dynamics, which do not resolve the small scales by design. To resolve this representation barrier, we introduce a new qualitative characterization of the space-time locations of shocks, named the "shock trace," via a space-time indicator function based on an empirical resolution-adaptive threshold. Unlike exact shocks, the shock traces can be captured within the representation capacity of the large scales, thus facilitating the forecast of the timing and locations of the shocks utilizing reduced models. Within the context of a viscous stochastic Burgers equation, we show that a data-driven reduced model, in the form of nonlinear autoregression (NAR) time series models, can accurately predict the random shock traces, with relatively low rates of false predictions. Furthermore, the NAR model, which includes nonlinear closure terms to approximate the feedback from the small scales, significantly outperforms the corresponding Galerkin truncated model in the scenario of either noiseless or noisy observations. The results illustrate the importance of the data-driven closure terms in the NAR model, which account for the effects of the unresolved dynamics brought by nonlinear interactions.

Autoregressive mixture models for clustering time series

Clustering time series into similar groups can improve models by combining information across like time series. While there is a well developed body of literature for clustering of time series, these approaches tend to generate clusters independently of model training, which can lead to poor model fit. We propose a novel distributed approach that simultaneously clusters and fits autoregression models for groups of similar individuals. We apply a Wishart mixture model so as to cluster individuals while modelling the corresponding autocovariance matrices at the same time. The fitted Wishart scale matrices map to cluster‐level autoregressive coefficients through the Yule–Walker equations, fitting robust parsimonious autoregressive mixture models. This approach is able to discern differences in underlying autocorrelation variation of time series in settings with large heterogeneous datasets. We prove consistency of our cluster membership estimator, asymptotic distributions of coefficients and compare our approach against competing methods through simulation as well as by fitting a COVID‐19 forecast model.

First-order random coefficient mixed-thinning integer-valued autoregressive model

The paper develops a first-order random coefficient mixed-thinning integer-valued autoregressive time series model (RCMTINAR(1)) to deal with the data related to the counting of elements of variable character. Moments and autocovariance functions for this model are studied as the distribution of the innovation sequence is unknown. The conditional least squares and modified quasi-likelihood are adopted to estimate the model parameters. Asymptotic properties of the obtained estimators are established. The performances of these estimators are investigated and compared with false modified quasi-likelihood via simulations. Finally, the practical relevance of the model is illustrated by using two applications to a SIMpass data set and a burglary data set with a comparison with relevant models that exist so far in the literature.

Comparative assessment of methods for short-term forecasts of COVID-19 hospital admissions in England at the local level

BackgroundForecasting healthcare demand is essential in epidemic settings, both to inform situational awareness and facilitate resource planning. Ideally, forecasts should be robust across time and locations. During the COVID-19 pandemic in England, it is an ongoing concern that demand for hospital care for COVID-19 patients in England will exceed available resources.MethodsWe made weekly forecasts of daily COVID-19 hospital admissions for National Health Service (NHS) Trusts in England between August 2020 and April 2021 using three disease-agnostic forecasting models: a mean ensemble of autoregressive time series models, a linear regression model with 7-day-lagged local cases as a predictor, and a scaled convolution of local cases and a delay distribution. We compared their point and probabilistic accuracy to a mean-ensemble of them all and to a simple baseline model of no change from the last day of admissions. We measured predictive performance using the weighted interval score (WIS) and considered how this changed in different scenarios (the length of the predictive horizon, the date on which the forecast was made, and by location), as well as how much admissions forecasts improved when future cases were known.ResultsAll models outperformed the baseline in the majority of scenarios. Forecasting accuracy varied by forecast date and location, depending on the trajectory of the outbreak, and all individual models had instances where they were the top- or bottom-ranked model. Forecasts produced by the mean-ensemble were both the most accurate and most consistently accurate forecasts amongst all the models considered. Forecasting accuracy was improved when using future observed, rather than forecast, cases, especially at longer forecast horizons.ConclusionsAssuming no change in current admissions is rarely better than including at least a trend. Using confirmed COVID-19 cases as a predictor can improve admissions forecasts in some scenarios, but this is variable and depends on the ability to make consistently good case forecasts. However, ensemble forecasts can make forecasts that make consistently more accurate forecasts across time and locations. Given minimal requirements on data and computation, our admissions forecasting ensemble could be used to anticipate healthcare needs in future epidemic or pandemic settings.

Trend decomposition aids forecasts of air particulate matter (PM2.5) assisted by machine and deep learning without recourse to exogenous data

A near-past, trend-attribute extraction technique is proposed for short-term hourly particulate matter (PM2.5) forecasting. Multiple attributes are extracted from the univariate PM2.5 time-series data for the prior 12 h to forecast PM2.5 for the next 12 h with the aid of machine/deep learning (ML/DL) algorithms. The method avoids the uncertainties of using a selection of exogeneous variables to forecast PM2.5 trends that tend to be highly volatile with erratically spaced peaks. Fifteen trend-decomposed attributes are extracted for each hourly data record of a 2016 to 2020 dataset for Nottingham Centre (a city in the United Kingdom). The 41979 data records are evaluated by sixteen ML/DL forecasting models. Each model is trained and validated with two datasets (2016–2018 and 2016–2019) that are then used to forecast 5 h-ahead periods (t0, t+1, t+3, t+6 and t+12) for 2019 and 2020, respectively. ML models outperform DL models in forecasting PM2.5 for 2019 and 2020, because the DL models are adversely impacted by suboptimal convergence and/or overfitting. The best performing models are multiple linear regression (MLR) and support vector regression (SVR) that outperform traditional timeseries autoregressive models which estimate a parametric autocorrelation parameter, substantially so for time periods beyond t+1. The transparent MLR model reveals that all the trend-attribute variables considered influence the forecasts of the trained models, but their relative contribution varies according to the time period being forecast. Enabling the models to allocate different weights to each variable for different time period forecasts adds a useful dimension of flexibility to this method compared to autoregressive models.

Wind and Sea Breeze Characteristics for the Offshore Wind Farms in the Central Coastal Area of Taiwan

Renewable energy is crucial for achieving net zero emissions. Taiwan has abundant wind resources and most major wind farms are offshore over the Taiwan Strait due to a lack of space on land. A thorough study that includes time series modeling of wind speed and sea breeze identification and evaluation for Taiwan’s offshore wind farms was conducted. The time series modeling identified two periodic (annual and diurnal) components and an autoregressive model for multiple-year wind speed time series. A new method for sea breeze type identification and magnitude evaluation is proposed. The method (named as EACH) utilizes a vector and an ellipse to represent the wind condition of a day. Verification of the type identification determined by the new method in two cases of different seasons has been conducted by using surface weather charts and wind data measured by lidar. It is a concise, effective, and programmable way to filter a number of dates for type identification and speed change precursor of sea breeze. We found that the typical daily wind power production of corkscrew sea breeze in Central Taiwan is more than 33 times that of pure sea breeze and more than 9 times that of backdoor sea breeze, which highlights the impact of sea breeze types on wind power.

Joint Parameter and Time-Delay Estimation for a Class of Nonlinear Time-Series Models

Nonlinear time-series modeling is fundamental to a wide variety of control and prediction problems. This letter focuses on the joint parameter and time-delay estimation for an extended version of the nonlinear exponential autoregressive (ExpAR) time-series model. To address the difficulties posed by the unknown time-delay and improve the estimation accuracy, we first employ the redundant rule to transform the ExpAR model into an augmented identification model. Then we invoke the multi-innovation theory to enhance data utilization and propose a new algorithm that combines stochastic gradient descent with discrete search for estimating the unknown model parameters and time-delay. The simulation results show that by properly adjusting the innovation length, the estimation accuracy of the proposed multi-innovation algorithm can significantly exceed that of the single-innovation algorithm.

Penalized estimation of threshold auto-regressive models with many components and thresholds.

Thanks to their simplicity and interpretable structure, autoregressive processes are widely used to model time series data. However, many real time series data sets exhibit non-linear patterns, requiring nonlinear modeling. The threshold Auto-Regressive (TAR) process provides a family of non-linear auto-regressive time series models in which the process dynamics are specific step functions of a thresholding variable. While estimation and inference for low-dimensional TAR models have been investigated, high-dimensional TAR models have received less attention. In this article, we develop a new framework for estimating high-dimensional TAR models, and propose two different sparsity-inducing penalties. The first penalty corresponds to a natural extension of classical TAR model to high-dimensional settings, where the same threshold is enforced for all model parameters. Our second penalty develops a more flexible TAR model, where different thresholds are allowed for different auto-regressive coefficients. We show that both penalized estimation strategies can be utilized in a three-step procedure that consistently learns both the thresholds and the corresponding auto-regressive coefficients. However, our theoretical and empirical investigations show that the direct extension of the TAR model is not appropriate for high-dimensional settings and is better suited for moderate dimensions. In contrast, the more flexible extension of the TAR model leads to consistent estimation and superior empirical performance in high dimensions.

Modelling and forecasting of potato sales prices in Ukraine

Purpose. Under the background of the climate change and other crises, the world food system is becoming increasingly vulnerable to price fluctuations. This highlights the need to consider and better manage the risks associated with price volatility in accordance with the principles of a market economy and simultaneously protecting the most vulnerable groups of population. Responding to these challenges, in this study we aim to determine the main parameters of time series of potato sales prices in agricultural enterprises in Ukraine, to build an appropriate model, and to form a short-term (one-year) forecast.
 Methodology / approach. We used in the research the data from the State Statistics Service of Ukraine on average monthly sales prices of potatoes in agricultural enterprises from December 2012 to July 2021 (104 observations) adjusted for the price index of crop products sold by enterprises for the month (with December 2012 base period). Decomposition was used to determine the characteristics of the time series; exponential smoothing methods (Holt-Winters and State Space Framework – ETS) and autoregressive-moving average were used to find the model that fits the actual data the best and has high prognostic quality. We applied the Rstudio forecast package to model and to forecast the time series. 
 Results. The time series of potato sales prices in enterprises is characterized by seasonality (mainly related to seasonal production) with the lowest prices in November, and the highest – in June; although, other periods of price growth were identified during the year: in January and April. The ARMA (2, 2) (1,0)12 with a non-zero mean was found to be the best model for forecasting potatoes sales prices. ARMA (2, 2) (1,0)12, compared to the state-space exponential smoothing model with additive errors – ETS (A), better fits the observed data and provides more accurate forecasting model (with lower errors). Forecast made with ARMA (2, 2) (1,0)12 shows that potato sale prices in agricultural enterprises in November 2021 (months with the lowest price) will range from 2154.76 UAH/t to 7414.57 UAH/t, in June 2022 – from 3016.72 UAH/t to 14051.63 UAH/t (prices of July 2021) with a probability of 95%. The forecast’s mean absolute percentage error is 14.87%.
 Originality / scientific novelty. This research deepens the methodological basis for food prices modelling and forecasting, thus contributing to the agricultural economics science development. The obtained results confirm the previous research findings on the better quality of food prices forecasts made with autoregressive models (for univariate time series) compared with exponential smoothing. Additionally, the study reveals advantages of the state space framework for exponential smoothing (ETS) compared to Holt-Winters methods in case of time series with seasonality: although the ETS model overlaps with the observed (train) data, it is better in terms of information criteria and forecasting (for the test data).
 Practical value / implications. The obtained results can serve as an information basis for decision-making on potato production and sales by producers, on more efficient use of resources by the population, on more effective measures to support industrial potato growing, to implement social programs and food security policy by the government.

Modeling serially correlated heavy-tailed data with some missing response values using stochastic EM algorithm

The linear regression model is a popular tool used by almost all in different areas of research. The model relies mainly on the assumption of uncorrelated errors from a Gaussian distribution. However, many datasets in practice violate this basic assumption, making inference in such cases invalid. Therefore, the linear regression model with structured errors driven by heavy-tailed innovations are preferred in practice. Another issue that occur frequently with real-life data is missing values, due to some reasons such as system breakdown and labor unrest. Despite the challenge these two issues pose to practitioners, there is scarcity of literature where they have jointly been studied. Hence, this article considers these two issues jointly, for the first time, and develops an efficient parameter estimation procedure for Student’s-t autoregressive regression model for time series with missing values of the response variable. The procedure is based on a stochastic approximation expectation–maximization algorithm coupled with a Markov chain Monte Carlo technique. The procedure gives efficient closed-form expressions for the parameters of the model, which are very easy to compute. Simulations and real-life data analysis show that the method is efficient for use with incomplete time series data.

On the impact of deep learning-based time-series forecasts on multistage stochastic programming policies

Multistage stochastic programming provides a modeling framework for sequential decision-making problems that involve uncertainty. One typically overlooked aspect of this methodology is how uncertainty is incorporated into modeling. Traditionally, statistical forecasting techniques with simple forms, e.g. (first-order) autoregressive time-series models, are used to extract scenarios to be added to optimization models to represent the uncertain future. However, often times, the performance of these forecasting models are not thoroughly assessed. Motivated by the advances in probabilistic forecasting, we incorporate a deep learning-based time-series forecasting method into multistage stochastic programming framework, and compare it with the cases where a traditional forecasting method is employed to model the uncertainty. We assess the impact of more accurate forecasts on the quality of two commonly used look-ahead policies, a deterministic one and a two-stage one, in a rolling-horizon framework on a practical problem. Our results illustrate that more accurate forecasts contribute substantially to the model performance, and enable obtaining high-quality solutions even from computationally cheap heuristics. They also show that the probabilistic forecasting capabilities of deep learning-based methods can be especially beneficial when used as a (conditional) sampling tool for scenario-based models, and to predict the worst-case scenario for risk-averse models.

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.