Stationary Time Series Models Research Articles

Stationary count time series models

AbstractDuring the last 20–30 years, there was a remarkable growth in interest on approaches for stationary count time series. We consider popular classes of models for such time series, including thinning‐based models, conditional regression models, and Hidden‐Markov models. We review and compare important members of these model families, having regard to stochastic properties such as the dispersion and autocorrelation structure. Our survey covers univariate and multivariate count data, as well as unbounded and bounded counts. We also discuss an illustrative data example. Besides this critical presentation of the current state‐of‐the‐art, some existing challenges and opportunities for future research are identified.This article is categorized under: Statistical Models > Time Series Models Data: Types and Structure > Time Series, Stochastic Processes, and Functional Data Statistical Learning and Exploratory Methods of the Data Sciences > Modeling Methods Statistical and Graphical Methods of Data Analysis > Modeling Methods and Algorithms

Hybrid machine learning algorithm and statistical time series model for network-wide traffic forecast

We propose a novel approach for network-wide traffic state prediction where the statistical time series model ARIMA is used to postprocess the residuals out of the fundamental machine learning algorithm MLP. This approach is named as NN-ARIMA. Neural Network MLP is employed to capture network-scale co-movement pattern of all traffic flows, and ARIMA is used to further extract location-specific traffic features in the residual time series out of Neural Network. The experiment results show that the postprocessing the residuals of Neural Network by the ARIMA analysis helps to significantly improve accuracy of traffic state prediction by 8.9–13.4% in term of mean squared error reduction. In order to verify the efficiency of the ARIMA analysis in the postprocessing, Multidimensional Support Vector Regression (MSVR) model is also employed to replace the role of Neural Network in the comparative experiment. Two streams of comparisons, (1) NN vs. NN-ARIMA and (2) MSVR vs. MSVR-ARIMA, are performed and show consistent results. The proposed approach not only can capture network-wide co-movement pattern of traffic flows, but also seize location-specific traffic characteristics as well as sharp nonlinearity of macroscopic traffic variables. The case study indicates that the accuracy of prediction can be significantly improved when both network-scale traffic features and location-specific characteristics are taken into account.

Suggested Statistical Models for Analysis Non-stationary Time Series and Sudden Changes with Application on Stock Exchange Indices

This study evaluates the performance of a group of GARCH models under three different distributions in terms of their ability to estimate and forecasting the volatility of Egyptian Stock Exchange General Index (EGX30) in some horizon of forecasting using daily data for the period from January 2, 2000 to April 30, 2019, and tries to determine the best model according to some criteria. The primary purpose of the study is to investigate whether the two-regime MSW-GARCH model outperforms the uni-regime GARCH models in a very volatile time period during the global financial crisis. Hence, evaluating the predictive accuracy of the MSW-GARCH, and whether the MSW-GARCH assessed on the EGX30 would be successful. We explore and compare different possible sources of forecasts improvements: asymmetry in the conditional variance, fat-tailed distributions and regime-switching methodology. The results show that; there is an evidence that the EGX30 index has been affected by the crisis, and the TGARCH models are superior in predictive ability on EGX30 compared to the other tested models. Consequently, uni-regime GARCH models has priority in MSW-GARCH models in their forecasting performance. These models yield significantly better out-of-sample volatility forecasts.

COVID-19 prevalence estimation: Four most affected African countries.

The world at large has been confronted with several disease outbreak which has posed and still posing a serious menace to public health globally. Recently, COVID-19 a new kind of coronavirus emerge from Wuhan city in China and was declared a pandemic by the World Health Organization. There has been a reported case of about 8622985 with global death of 457,355 as of 15.05 GMT, June 19, 2020. South-Africa, Egypt, Nigeria and Ghana are the most affected African countries with this outbreak. Thus, there is a need to monitor and predict COVID-19 prevalence in this region for effective control and management. Different statistical tools and time series model such as the linear regression model and autoregressive integrated moving average (ARIMA) models have been applied for disease prevalence/incidence prediction in different diseases outbreak. However, in this study, we adopted the ARIMA model to forecast the trend of COVID-19 prevalence in the aforementioned African countries. The datasets examined in this analysis spanned from February 21, 2020, to June 16, 2020, and was extracted from the World Health Organization website. ARIMA models with minimum Akaike information criterion correction (AICc) and statistically significant parameters were selected as the best models. Accordingly, the ARIMA (0,2,3), ARIMA (0,1,1), ARIMA (3,1,0) and ARIMA (0,1,2) models were chosen as the best models for SA, Nigeria, and Ghana and Egypt, respectively. Forecasting was made based on the best models. It is noteworthy to claim that the ARIMA models are appropriate for predicting the prevalence of COVID-19. We noticed a form of exponential growth in the trend of this virus in Africa in the days to come. Thus, the government and health authorities should pay attention to the pattern of COVID-19 in Africa. Necessary plans and precautions should be put in place to curb this pandemic in Africa.

SUPERPOSITIONED STATIONARY COUNT TIME SERIES

AbstractThis paper probabilistically explores a class of stationary count time series models built by superpositioning (or otherwise combining) independent copies of a binary stationary sequence of zeroes and ones. Superpositioning methods have proven useful in devising stationary count time series having prespecified marginal distributions. Here, basic properties of this model class are established and the idea is further developed. Specifically, stationary series with binomial, Poisson, negative binomial, discrete uniform, and multinomial marginal distributions are constructed; other marginal distributions are possible. Our primary goal is to derive the autocovariance function of the resulting series.

High-frequency measurements explain quantity and quality of dissolved organic carbon mobilization in a headwater catchment

Abstract. Increasing dissolved organic carbon (DOC) concentrations and exports from headwater catchments impact the quality of downstream waters and pose challenges to water supply. The importance of riparian zones for DOC export from catchments in humid, temperate climates has generally been acknowledged, but the hydrological controls and biogeochemical factors that govern mobilization of DOC from riparian zones remain elusive. A high-frequency dataset (15 min resolution for over 1 year) from a headwater catchment in the Harz Mountains (Germany) was analyzed for dominant patterns in DOC concentration (CDOC) and optical DOC quality parameters SUVA254 and S275−295 (spectral slope between 275 and 295 nm) on event and seasonal scales. Quality parameters and CDOC systematically changed with increasing fractions of high-frequency quick flow (Qhf) and antecedent hydroclimatic conditions, defined by the following metrics: aridity index (AI60) of the preceding 60 d and the quotient of mean temperature (T30) and mean discharge (Q30) of the preceding 30 d, which we refer to as discharge-normalized temperature (DNT30). Selected statistical multiple linear regression models for the complete time series (R2=0.72, 0.64 and 0.65 for CDOC, SUVA254 and S275−295, resp.) captured DOC dynamics based on event (Qhf and baseflow) and seasonal-scale predictors (AI60, DNT30). The relative importance of seasonal-scale predictors allowed for the separation of three hydroclimatic states (warm and dry, cold and wet, and intermediate). The specific DOC quality for each state indicates a shift in the activated source zones and highlights the importance of antecedent conditions and their impact on DOC accumulation and mobilization in the riparian zone. The warm and dry state results in high DOC concentrations during events and low concentrations between events and thus can be seen as mobilization limited, whereas the cold and wet state results in low concentration between and during events due to limited DOC accumulation in the riparian zone. The study demonstrates the considerable value of continuous high-frequency measurements of DOC quality and quantity and its (hydroclimatic) key controlling variables in quantitatively unraveling DOC mobilization in the riparian zone. These variables can be linked to DOC source activation by discharge events and the more seasonal control of DOC production in riparian soils.

An Adaptive Intrusion Detection Scheme for Cloud Computing

To provide dynamic resource management, live virtual machine migration is used to move a virtual machine from one host to another. However, virtual machine migration poses challenges to cloud intrusion detection systems because movement of VMs from one host to another makes it difficult to create a consistent normal profile for anomaly detection. Hence, there is a need to provide an adaptive anomaly detection system capable of adapting to changes that occur in the cloud data during VM migration. To achieve this, the authors proposed a scheme for adaptive IDS for Cloud computing. The proposed adaptive scheme is comprised of four components: an ant colony optimization-based feature selection component, a statistical time series change point detection component, adaptive classification, and model update component, and a detection component. The proposed adaptive scheme was evaluated using simulated datasets collected from vSphere and performance comparison shows improved performance over existing techniques.

Forecasting methods in engineering

Forecasting in engineering is one of the most important topics when it comes to optimisation, which is related to energy savings, material savings, increasing efficiency, and appropriate and correct decisions at the level of a company, institution, city, or region. Moreover, forecasting is indirectly related to cost savings and the sustainable development of society and environment. In the energy industry (electricity, natural gas, heat load), there are requirements to balance the supply and demand. Markets are very dynamic, and for this reason forecasting is more challenging. Forecasting errors are usually penalized drastically. However, a well-developed forecasting approach represents a competitive advantage, and so a company may significantly reduce expenditure and increase profits. Many publications on forecasting have been published during recent years. Long-term forecasting methods offer many opportunities for strategic planning and optimal scheduling, whereas a short-term forecasting approach would help attain optimal daily operations and the maximum utilisation of the company’s resources. Although different forecasting techniques can be used, the major conclusions are that exponential smoothing methods are the simplest and the least expensive. Distinguished by their simplicity, their forecasts are comparable to forecasts of more complex statistical time series models. In this paper, the forecasting performance of Additive, Multiplicative, and Extended Holt-Winters methods were analysed. We also analyse whether the data format influences the choice of the forecasting method: is the most accurate method for monthly data also the best method for quarterly data?

Forecasting the Main Indicators of Food Security of Russia

In the context of current geopolitical events, accurate and correct forecasting of food security and provision becomes highly relevant for solving managerial tasks and making management decisions under modern conditions. This article reviews the main trends in the field of food security, forecasts its key indicators, and identifies the main problems and directions for the development of food security in the Russian Federation. Indicators in the field of food independence, production, and consumption are analyzed. Forecasts of gross collection of vegetables and melons, cultivated areas, imports of food and agricultural raw materials, and consumer price index for food products are presented. The theoretical and methodological basis of the research includes both general and specific scientific methods for assessing the level of food security, as well as methods of economic and statistical analysis, extrapolation methods, modeling and forecasting of time series, adaptive forecasting methods, and factorial analysis. The main problems and threats to food security are identified, including the low level of real income of the population, low share of highly processed products in exports, continuing effect of Western sanctions, low level of innovation and technological development of the agro-industrial sector, etc.. The following measures to improve state regulation of food security have been determined: to increase the economic and physical access to food, to develop the capacity of the agro-industrial complex in the production and scientific and technical fields, to introduce modifications to the Food Security Doctrine, to implement innovative technologies in crop production and to increase its efficiency, to increase the share of companies engaged in organic farming, etc.

An integer-valued bilinear time series model via two random operators

ABSTRACTThis paper presents a new stationary integer-valued bilinear time series model of the first order by mixing the thinning and Pegram operators. Some statistical properties of the model are obtained, involving the conditional moments, autocovariance and spectral density function. Estimation of the model parameters is discussed using the Yule-Walker and conditional least squares methods with a simulation study for evaluating the performance of those estimators. Applicability of the process is investigated using a practical count data set with comparing the model to a competitive bilinear model using some marginal distributions of innovations. Issue of forecasting data is discussed under the proposed model.

Research on real-time network\xa0data mining technology for big data

The data distribution in big data environment is very different, and it is difficult to mine the data because of the strong interference of redundant data and frequent items. The traditional data mining algorithm uses closed frequent item feature extraction algorithm. Due to the uneven distribution of web data in big data environment, the mining accuracy of closed frequent item feature extraction is not high. A real-time web data mining model is proposed based on high order spectral feature fuzzy neural network learning in big data environment. The transmission channel model and statistical time series model of web data under big data environment are constructed, and the redundant information flow is removed and reprocessed, and the web data after redundant filtering is analyzed by fusion clustering. The feature of high order spectrum is extracted, and the optimal mining of web data is realized by using fuzzy neural network learning classification method. The simulation results show that this web data mining method has good timeliness, high mining precision, and superior performance.

Minute-Scale Forecasting of Wind Power—Results from the Collaborative Workshop of IEA Wind Task 32 and 36

The demand for minute-scale forecasts of wind power is continuously increasing with the growing penetration of renewable energy into the power grid, as grid operators need to ensure grid stability in the presence of variable power generation. For this reason, IEA Wind Tasks 32 and 36 together organized a workshop on “Very Short-Term Forecasting of Wind Power” in 2018 to discuss different approaches for the implementation of minute-scale forecasts into the power industry. IEA Wind is an international platform for the research community and industry. Task 32 tries to identify and mitigate barriers to the use of lidars in wind energy applications, while IEA Wind Task 36 focuses on improving the value of wind energy forecasts to the wind energy industry. The workshop identified three applications that need minute-scale forecasts: (1) wind turbine and wind farm control, (2) power grid balancing, (3) energy trading and ancillary services. The forecasting horizons for these applications range from around 1 s for turbine control to 60 min for energy market and grid control applications. The methods that can be applied to generate minute-scale forecasts rely on upstream data from remote sensing devices such as scanning lidars or radars, or are based on point measurements from met masts, turbines or profiling remote sensing devices. Upstream data needs to be propagated with advection models and point measurements can either be used in statistical time series models or assimilated into physical models. All methods have advantages but also shortcomings. The workshop’s main conclusions were that there is a need for further investigations into the minute-scale forecasting methods for different use cases, and a cross-disciplinary exchange of different method experts should be established. Additionally, more efforts should be directed towards enhancing quality and reliability of the input measurement data.

Data-driven monitoring of the gearbox using multifractal analysis and machine learning methods

Data-driven diagnostic methods allow to obtain a statistical model of time series and to identify deviations of recorded data from the pattern of the monitored system. Statistical analysis of time series of mechanical vibrations creates a new quality in the monitoring of rotating machines. Most real vibration signals exhibit nonlinear properties well described by scaling exponents. Multifractal analysis, which relies mainly on assessing local singularity exponents, has become a popular tool for statistical analysis of empirical data. There are many methods to study time series in terms of their fractality. Comparing computational complexity, a wavelet leaders algorithm was chosen. Using Wavelet Leaders Multifractal Formalism, multifractal parameters were estimated, taking them as diagnostic features in the pattern recognition procedure, using machine learning methods. The classification was performed using neural network, k-nearest neighbours’ algorithm and support vector machine. The article presents the results of vibration acceleration tests in a demonstration transmission system that allows simulations of assembly errors and teeth wear.

Predictive, finite-sample model choice for time series under stationarity and non-stationarity

In statistical research there usually exists a choice between structurally simpler or more complex models. We argue that, even if a more complex, locally stationary time series model were true, then a simple, stationary time series model may be advantageous to work with under parameter uncertainty. We present a new model choice methodology, where one of two competing approaches is chosen based on its empirical, finite-sample performance with respect to prediction, in a manner that ensures interpretability. A rigorous, theoretical analysis of the procedure is provided. As an important side result we prove, for possibly diverging model order, that the localised Yule-Walker estimator is strongly, uniformly consistent under local stationarity. An R package, forecastSNSTS, is provided and used to apply the methodology to financial and meteorological data in empirical examples. We further provide an extensive simulation study and discuss when it is preferable to base forecasts on the more volatile time-varying estimates and when it is advantageous to forecast as if the data were from a stationary process, even though they might not be.

Prediction intervals and regions for multivariate time series models with sieve bootstrap

In the paper, the construction of unconditional bootstrap prediction intervals and regions for some class of second order stationary multivariate linear time series models is considered. Our approach uses the sieve bootstrap procedure introduced by Kreiss 1992 and Bühlmann 1997. Basic theoretical results concerning consistency of the bootstrap replications and the bootstrap prediction regions are proved. We present a simulation study comparing the proposed bootstrap methods with the Box–Jenkins approach.

An approximate fractional Gaussian noise model with $$\mathcal {O}(n)$$ O ( n ) computational cost

Fractional Gaussian noise (fGn) is a stationary time series model with long-memory properties applied in various fields like econometrics, hydrology and climatology. The computational cost in fitting an fGn model of length n using a likelihood-based approach is $${{\mathcal {O}}}(n^{2})$$ , exploiting the Toeplitz structure of the covariance matrix. In most realistic cases, we do not observe the fGn process directly but only through indirect Gaussian observations, so the Toeplitz structure is easily lost and the computational cost increases to $${{\mathcal {O}}}(n^{3})$$ . This paper presents an approximate fGn model of $${{\mathcal {O}}}(n)$$ computational cost, both with direct and indirect Gaussian observations, with or without conditioning. This is achieved by approximating fGn with a weighted sum of independent first-order autoregressive (AR) processes, fitting the parameters of the approximation to match the autocorrelation function of the fGn model. The resulting approximation is stationary despite being Markov and gives a remarkably accurate fit using only four AR components. Specifically, the given approximate fGn model is incorporated within the class of latent Gaussian models in which Bayesian inference is obtained using the methodology of integrated nested Laplace approximation. The performance of the approximate fGn model is demonstrated in simulations and two real data examples.

Forecasting pulmonary air leak duration following lung surgery using transpleural airflow data from a digital pleural drainage device.

Prolonged air leak (PAL) is often the limiting factor for hospital discharge after lung surgery. Our goal was to develop a statistical model that reliably predicts pulmonary air leak resolution by applying statistical time series modeling and forecasting techniques to digital drainage data. Autoregressive Integrated Moving Average (ARIMA) modeling was used to forecast air leak flow from transplural air flow data. The results from ARIMA were retrospectively internally validated with a group of 100 patients who underwent lung resection between December 2012 and March 2017, for whom digital pleural drainage data was available for analysis and a persistent air leak was the limiting factor for chest tube removal. The ARIMA model correctly identified 82% (82/100) of patients as to whether or not the last chest tube removal was appropriate. The performance characteristics of the model in properly identifying patients whose air leak would resolve and who would therefore be candidates for safe chest tube removal were: sensitivity 80% (95% CI, 69-88%), specificity 88% (95% CI, 68-97%), positive predictive value 95% (95% CI, 86-99%), and negative predictive value 59% (95% CI, 42-79%). The false positive and false negative rate was 12% (95% CI, 12-31%) and 20% (95% CI, 12-31%). We were able to validate a statistical model that that reliably predicted resolution of pulmonary air leak resolution over a 24-hour period. This information may improve the care of patients with chest tube by optimizing duration of pleural drainage.

Modelling Palaeoecological Time Series Using Generalised Additive Models

In the absence of annual laminations, time series generated from lake sediments or other similar stratigraphic sequences are irregularly spaced in time, which complicates formal analysis using classical statistical time series models. In lieu, statistical analyses of trends in palaeoenvironmental time series, if done at all, have typically used simpler linear regressions or (non-) parametric correlations with little regard for the violation of assumptions that almost surely occurs due to temporal dependencies in the data or that correlations do not provide estimates of the magnitude of change, just whether or not there is a linear or monotonic trend. Alternative approaches have used LOESS-estimated trends to justify data interpretations or test hypotheses as to the causal factors without considering the inherent subjectivity of the choice of parameters used to achieve the LOESS fit (e.g. span width, degree of polynomial). Generalized additive models (GAMs) are statistical models that can be used to estimate trends as smooth functions of time. Unlike LOESS, GAMs use automatic smoothness selection methods to objectively determine the complexity of the fitted trend, and as formal statistical models, GAMs, allow for potentially complex, non-linear trends, a proper accounting of model uncertainty, and the identification of periods of significant temporal change. Here, I present a consistent and modern approach to the estimation of trends in palaeoenvironmental time series using GAMs, illustrating features of the methodology with two example time series of contrasting complexity; a 150-year bulk organic matter δ15N time series from Small Water, UK, and a 3000-year alkenone record from Braya-So, Greenland. I discuss the underlying mechanics of GAMs that allow them to learn the shape of the trend from the data themselves and how simultaneous confidence intervals and the first derivatives of the trend are used to properly account for model uncertainty and identify periods of change. It is hoped that by using GAMs greater attention is paid to the statistical estimation of trends in palaeoenvironmental time series leading to more a robust and reproducible palaeoscience.

A Time Series Model Comparison for Monitoring and Forecasting Water Quality Variables

The monitoring and prediction of water quality parameters are important tasks in the management of water resources. In this work, the performances of time series statistical models were evaluated to predict and forecast the dissolved oxygen (DO) concentration in several monitoring sites located along the main river Vouga, in Portugal, during the period from January 2002 to May 2015. The models being compared are a regression model with correlated errors and a state-space model, which can be seen as a calibration model. Both models allow the incorporation of water quality variables, such as time correlation or seasonality. Results show that, for the DO variable, the calibration model outperforms the regression model for sample modeling, that is, for a short-term forecast, while the regression model with correlated errors has a better performance for the forecasting h-steps ahead framework. So, the calibration model is more useful for water monitoring using an online or real-time procedure, while the regression model with correlated errors can be applied in order to forecast over a longer period of time.

A procedure to increase the power of Granger-causal analysis through temporal smoothing

BackgroundHow the human brain coordinates network activity to support cognition and behavior remains poorly understood. New high-resolution recording modalities facilitate a more detailed understanding of the human brain network. Several approaches have been proposed to infer functional networks, indicating the transient coordination of activity between brain regions, from neural time series. One category of approach is based on statistical modeling of time series recorded from multiple sensors (e.g., multivariate Granger causality). However, fitting such models remains computationally challenging as the history structure may be long in neural activity, requiring many model parameters to fully capture the dynamics. New MethodWe develop a method based on Granger causality that makes the assumption that the history dependence varies smoothly. We fit multivariate autoregressive models such that the coefficients of the lagged history terms are smooth functions. We do so by modelling the history terms with a lower dimensional spline basis, which requires many fewer parameters than the standard approach and increases the statistical power of the model. ResultsWe show that this procedure allows accurate estimation of brain dynamics and functional networks in simulations and examples of brain voltage activity recorded from a patient with pharmacoresistant epilepsy. Comparison with Existing MethodThe proposed method has more statistical power than the Granger method for networks of signals that exhibit extended and smooth history dependencies. ConclusionsThe proposed tool permits conditional inference of functional networks from many brain regions with extended history dependence, furthering the applicability of Granger causality to brain network science.