Stationary Time Series Models Research Articles

Exponential tilted likelihood for stationary time series models

Depending on the asymptotical independence of periodograms, exponential tilted (ET) likelihood, as an effective nonparametric statistical method, is developed to deal with time series in this paper. Similar to empirical likelihood (EL), it still suffers from two drawbacks: the non-definition problem of the likelihood function and the under-coverage probability of confidence region. To overcome these two problems, we further proposed the adjusted ET (AET) likelihood. With a specific adjustment level, our simulation studies indicate that the AET method achieves a higher-order coverage precision than the unadjusted ET method. In addition, due to the good performance of ET under moment model misspecification [Schennach, S. M. (2007). Point estimation with exponentially tilted empirical likelihood. The Annals of Statistics, 35(2), 634–672. https://doi.org/10.1214/009053606000001208], we show that the one-order property of point estimate is preserved for the misspecified spectral estimating equations of the autoregressive coefficient of AR(1). The simulation results illustrate that the point estimates of the ET outperform those of the EL and their hybrid in terms of standard deviation. A real data set is analyzed for illustration purpose.

지수평활법과 ARIMA를 이용한 전남 김 위판가격 예측모형 비교

This study conducted a price forecast of major Purple laver production areas, Jeollanam-do, in South Korea. Based on the reasoning that price forecast of Purple laver production regions could assist in controlling supply and demand, through the Exponential smoothing technique(Single exponential smoothing, Holt-Winters Additive and Multiplicative, Exponential smoothing method) and Auto regressive integrated moving average model(ARIMA), Purple laver producer price of Jeollanam-do, the largest wet Purple laver producing area, has been predicted. Moreover, the accuracy and stability of the relevant forecasting model have been reviewed through the Historical simulation method. Concerning Jeollanam-do Purple laver producer price forecast results, among the total models adopted through the utilization of the Historical simulation method, the Simple exponential smoothing with DRIFT forecast model, which uses a DRIFT forecast, was ultimately selected after going through stationary Time series and forecast model accuracy tests.

SACF of the Errors of Stationary Time Series Models in the Presence of a Large Additive Outlier

In this paper, the limiting behaviour of the Sample Autocorrelation Function(SACF) of the errors {et} of First-Order Autoregressive (AR(1)), First-Order Moving Average (MA(1)) and First Order Autoregressive First-Order Moving Average (ARMA(1,1)) stationary time series models in the presence of a large Additive Outlier(AO) is discussed. It is found that the errors which are supposed to be uncorrelated due to either white noise process or normally distributed process are not so in the presence of a large additive outlier. The SACF of the errors follows a particular pattern based on the time series model. In the case of AR(1) model, at lag 1, the contaminated errors {et} are correlated, whereas at higher lags, they are uncorrelated. But in the MA(1) and ARMA(1,1) models, the contaminated errors {et} are correlated at all the lags. Furthermore it is observed that the intensity of correlations depends on the parameters of the respective models.

A parallel-series hybridization of seasonal intelligent based statistical model for demand forecasting

PurposeThe purpose of this paper, because of the complexity of demand time series and the need to construct a more accurate hybrid model that can model all relationships in data, is to propose a parallel-series hybridization of seasonal neural networks and statistical models for demand time series forecasting.Design/methodology/approachThe main idea of proposed model is centered around combining parallel and series hybrid methodologies to use the benefit of unique advantages of both hybrid strategies as well as intelligent and classic seasonal time series models simultaneously for achieving results that are more accurate for the first time. In the proposed model, in contrast of traditional parallel and series hybrid strategies, it can be generally shown that the performance of the proposed model will not be worse than components.FindingsEmpirical results of forecasting two well-known seasonal time series data sets, including the total production value of the Taiwan machinery industry and the sales volume of soft drinks, indicate that the proposed model can effectively improve the forecasting accuracy achieved by either of their components used in isolation. In addition, the proposed model can achieve more accurate results than parallel and series hybrid model with same components. Therefore, the proposed model can be used as an appropriate alternative model for seasonal time series forecasting, especially when higher forecasting accuracy is needed.Originality/valueTo the best of the authors’ knowledge, the proposed model, for first time and in contrast of traditional parallel and series hybrid strategies, is developed.

Forecasting of Tomato Yields Using Attention-Based LSTM Network and ARMA Model

Nonlinear autoregressive exogenous (NARX), autoregressive integrated moving average (ARIMA) and multi-layer perceptron (MLP) networks have been widely used to predict the appearance value of future points for time series data. However, in recent years, new approaches to predict time series data based on various networks of deep learning have been proposed. In this paper, we tried to predict how various environmental factors with time series information affect the yields of tomatoes by combining a traditional statistical time series model and a deep learning model. In the first half of the proposed model, we used an encoding attention-based long short-term memory (LSTM) network to identify environmental variables that affect the time series data for tomatoes yields. In the second half of the proposed model, we used the ARMA model as a statistical time series analysis model to improve the difference between the actual yields and the predicted yields given by the attention-based LSTM network at the first half of the proposed model. Next, we predicted the yields of tomatoes in the future based on the measured values of environmental variables given during the observed period using a model built by integrating the two models. Finally, the proposed model was applied to determine which environmental factors affect tomato production, and at the same time, an experiment was conducted to investigate how well the yields of tomatoes could be predicted. From the results of the experiments, it was found that the proposed method predicts the response value using exogenous variables more efficiently and better than the existing models. In addition, we found that the environmental factors that greatly affect the yields of tomatoes are internal temperature, internal humidity, and CO2 level.

A decision integration strategy for short-term demand forecasting and ordering for red blood cell components

Blood transfusion is one of the most crucial and commonly administered therapeutics worldwide. The need for more accurate and efficient ways to manage blood demand and supply is an increasing concern. Building a technology-based, robust blood demand and supply chain that can achieve the goals of reducing ordering frequency, inventory level, wastage and shortage, while maintaining the safety of blood usage, is essential in modern healthcare systems. In this study, we summarize the key challenges in current demand and supply management for red blood cells (RBCs). We combine ideas from statistical time series modeling, machine learning, and operations research in developing an ordering decision strategy for RBCs, through integrating a hybrid demand forecasting model using clinical predictors and a data-driven multi-period inventory problem considering inventory and reorder constraints. We have applied the integrated ordering strategy to the blood inventory management system in Hamilton, Ontario using a large clinical database from 2008 to 2018. The proposed hybrid demand forecasting model provides robust and accurate predictions, and identifies important clinical predictors for short-term RBC demand forecasting. Compared with the actual historical data, our integrated ordering strategy reduces the inventory level by 40% and decreases the ordering frequency by 60%, with low incidence of shortages and wastage due to expiration. If implemented successfully, our proposed strategy can achieve significant cost savings for healthcare systems and blood suppliers. The proposed ordering strategy is generalizable to other blood products or even other perishable products.

Integer-valued Bilinear Model with Dependent Counting Series

The present work proposes a new stationary integer-valued bilinear time series model with dependent counting series. The model will enable one to tackle the presence of some correlation between underlying events. The various probabilistic and statistical properties of the model are discussed, unknown parameters are estimated by several methods. Moreover, the performance of the estimation methods is illustrated through a simulation study and an empirical application to two data sets.

Sequential change point test in the presence of outliers: the density power divergence based approach

In this study, we consider a problem of monitoring parameter changes particularly in the presence of outliers. To propose a sequential procedure that is robust against outliers, we use the density power divergence to derive a detector and stopping time that make up our procedure. We first investigate the asymptotic properties of our sequential procedure for i.i.d. sequences and then extend the proposed procedure to stationary time series models, where we provide a set of sufficient conditions under which the proposed procedure has an asymptotically controlled size and consistency in power. As an application, our procedure is applied to the GARCH models. We demonstrate the validity and robustness of the proposed procedure through a simulation study. Finally, two real data analyses are provided to illustrate the usefulness of the proposed sequential procedure.

Flood Extent Mapping in the Caprivi Floodplain Using Sentinel-1 Time Series

Deployment of Sentinel-1 (S1) satellite constellation carrying a C-band synthetic aperture radar (SAR) enables regular and timely monitoring of floods from their onset until returning to nonflooded (NF) conditions. The major constraint on using SAR for near-real-time (NRT) flood mapping has been the inability to rapidly process the obtained imagery into reliable flood maps. This study evaluates the efficacy of S1 time series for quantifying and characterizing inundation extents in vegetated environments. A novel algorithm based on statistical time-series modeling of flooded (F) and NF pixels is proposed for NRT flood monitoring. For each new available S1 image, the probability of temporarily F conditions is tested against that of NF conditions by means of likelihood ratio tests. The likelihoods for the two conditions are derived from early acquisitions in the time series. The algorithm calibration consists of adjusting two likelihood ratio thresholds to match the reference F area extent during a single flood season. The proposed algorithm is applied to the Caprivi region, the resulting maps were compared to cloud-free Landsat-8 (LS8) derived maps captured during two flood events. A good spatial agreement (85-87%) between LS8 and S1 flood maps was observed during the flood peak in both 2017 and 2018 seasons. Significant discrepancies were noted during the flood expansion and recession phases, mainly due to different sensitivities of the data sources to the emerging vegetation. Overall, the analysis shows that S1 can stand as an effective standalone or gap-filling alternative to optical imagery during a flood event.

Testing the equality of several independent stationary and non-stationary time series models with fractional Brownian motion errors

This work is devoted to apply the parametric and nonparametric techniques to construct test of hypothesis about the equality of the probabilistic behaviors of several time series models with fractional Brownian motion errors fitted on several independent datasets. The accuracy and power of the introduced method are studied using the simulated and real datasets. The results indicate that the introduced approach is more powerful than other alternative approaches, in non-stationary cases.

On Edgeworth models for count time series

Inspired by the Edgeworth–Portnoy model for Gaussian time series, a family of randomized moving window (RMW) and randomized moving sum (RMS) models for stationary count time series is proposed. For the RMW process, we derive Markov properties which, in turn, allow to conclude on a connection of the RMS model to the Hidden-Markov model. This connection is used to develop an efficient scheme for maximum likelihood estimation. Then, we derive marginal and serial moment properties of the RMS process. It commonly exhibits an autoregressive autocorrelation structure, but also forms of a long memory are possible. The latter holds in particular for the proposed extended RMS model, which also satisfies certain Markov properties.

Ability Assessment of the Stationary and Cyclostationary Time Series Models to Predict Drought Indices

Drought forecasting and monitoring play a significant role in reducing the negative effects of global meteorological droughts caused by different intensities at different temporal and spatial scales in different regions, especially in regions with high dependency on rainwater. The present study tries to compare the accuracy of stationary time series (ST) models including autoregressive moving average (ARMA), moving average (MA) and autoregressive (AR) and cyclostationary time series (CT) models including periodic autoregressive moving average (PARMA), periodic moving average (PMA) and periodic autoregressive (PAR) to predict drought index (i.e. monthly reconnaissance drought index (RDI)) in periodic data series considering that CT models are more powerful and efficient than ST models by using data series of 8 synoptic stations with different climate conditions in Iran from 1967 to 2017. According to the results the monthly RDI was significantly periodic in all selected stations. The PAR (25) model was the best fitted CT model in data series at all stations and on the other hand, the following models were the best-fitted ST models in data series: the AR models at Babolsar and Rasht AR (25) and at Gorgan AR (24) and ARMA models at Tehran ARMA (2, 3), at Zahedan and Shiraz ARMA (2, 4) and at Esfahan and Shahre Kord ARMA (2, 5). Based on the best fitted CT and ST models, the results showed that the correlation coefficients (R) between observed and simulated RDI vary from 0.882 to 0.946 and from 0.693 to 0.874, respectively from January 1967 to December 2017. According to the best fitted CT and ST models, the validation test of the best fitted models indicated that the R between observed and simulated RDI vary from 0.634 to 0.883 and 0.585 to 0.847, respectively from January 2012 to December 2017. In total, it can be concluded that that the accuracy and capability of CT models in predicting the RDI were more than those of the ST models at all stations and the hypothesis of the study was confirmed.

Operational control algorithm of parameters of high-pressure sodium lamps based on a statistical time series model

The developed operational control algorithm parameters of a high pressure sodium lamp is considered in this work. We used a mathematical model to develop the algorithm. An analytical method was used to describe the operation of a sodium lamp based on differential equations as well as an algorithm for evaluating time series. The mathematical expectation and dispersion were also evaluated. The described models for quality control of sodium lamps have been tested in production. The obtained simulation results coincide with the results of the experiment. Using a series of tests based on the proposed control method we confirmed the adequacy of the developed model.

Deterministic and Interval Wind Speed Prediction Method in Offshore Wind Farm Considering the Randomness of Wind

In order to improve the prediction accuracy of wind speed, this paper proposes a hybrid wind speed prediction (WSP) method considering the fluctuation, randomness and nonlinear of wind, which can be applied to short-term deterministic and interval prediction. Variational mode decomposition (VMD) decomposes wind speed time series into nonlinear series Intrinsic mode function 1 (IMF1), stationary time series IMF2 and error sreies (ER). Principal component analysis-Radial basis function (PCA-RBF) model is used to model the nonlinear series IMF1, where PCA is applied to reduce the redundant information. Long short-term memory (LSTM) is used to establish a stationary time series model for IMF2, which can better describe the fluctuation trend of wind speed; mixture Gaussian process regression (MGPR) is used to predict ER to obtain deterministic and interval prediction results simultaneously. Finally, above methods are reconstructed to form VMD-PRBF-LSTM-MGPR which is the abbreviation of hybrid model to obtain the final results of WSP, which can better reflect the volatility of wind speed. Nine comparison models are built to verify the availability of the hybrid model. The mean absolute percentage error (MAE) and mean square error (MSE) of deterministic WSP of the proposed model are only 0.0713 and 0.3158 respectively, which are significantly smaller than the prediction results of comparison models. In addition, confidence intervals (CIs) and prediction interval (PIs) are compared in this paper. The experimental results show that both of them can quantify and represent forecast uncertainty and the PIs is wider than the corresponding CIs.

Complexity in psychological self-ratings: implications for research and practice

BackgroundPsychopathology research is changing focus from group-based “disease models” to a personalized approach inspired by complex systems theories. This approach, which has already produced novel and valuable insights into the complex nature of psychopathology, often relies on repeated self-ratings of individual patients. So far, it has been unknown whether such self-ratings, the presumed observables of the individual patient as a complex system, actually display complex dynamics. We examine this basic assumption of a complex systems approach to psychopathology by testing repeated self-ratings for three markers of complexity: memory, the presence of (time-varying) short- and long-range temporal correlations; regime shifts, transitions between different dynamic regimes; and sensitive dependence on initial conditions, also known as the “butterfly effect,” the divergence of initially similar trajectories.MethodsWe analyzed repeated self-ratings (1476 time points) from a single patient for the three markers of complexity using Bartels rank test, (partial) autocorrelation functions, time-varying autoregression, a non-stationarity test, change point analysis, and the Sugihara-May algorithm.ResultsSelf-ratings concerning psychological states (e.g., the item “I feel down”) exhibited all complexity markers: time-varying short- and long-term memory, multiple regime shifts, and sensitive dependence on initial conditions. Unexpectedly, self-ratings concerning physical sensations (e.g., the item “I am hungry”) exhibited less complex dynamics and their behavior was more similar to random variables.ConclusionsPsychological self-ratings display complex dynamics. The presence of complexity in repeated self-ratings means that we have to acknowledge that (1) repeated self-ratings yield a complex pattern of data and not a set of (nearly) independent data points, (2) humans are “moving targets” whose self-ratings display non-stationary change processes including regime shifts, and (3) long-term prediction of individual trajectories may be fundamentally impossible. These findings point to a limitation of popular statistical time series models whose assumptions are violated by the presence of these complexity markers. We conclude that a complex systems approach to mental health should appreciate complexity as a fundamental aspect of psychopathology research by adopting the models and methods of complexity science. Promising first steps in this direction, such as research on real-time process monitoring, short-term prediction, and just-in-time interventions, are discussed.

Measures of Cross‐Dependence for Bidimensional Periodic AR(1) Model with α‐Stable Distribution

Discrete‐time models with periodic behavior are useful for the description of different phenomenon. The most popular time series taking into consideration the periodicity of the real data is the periodic autoregressive moving average (PARMA) model. The PARMA models were considered in the literature from a theoretical and practical point of view. Most of the considerations related to the PARMA models are based on the assumption of the Gaussian (or finite‐variance) distribution of the noise. However, in many applications, the Gaussian distribution seems to be inappropriate. Thus, generalized models are considered. The natural extension of the Gaussian distribution is the ‐stable one which is a perfect distribution for the modeling of real data with large observations. However, for the ‐stable‐based models the classical methods adequate to Gaussian‐based systems cannot be used. The main problem comes from the fact that, in general, for the ‐stable based models the covariance cannot be applied as a measure of dependence. Thus, alternative measures are used. In this article, we consider the generalization of the classical PARMA models and take into consideration the ‐stable PAR system. Moreover, we analyze the bidimensional version of the univariate model and examine its structure of cross‐dependence in the language of the alternative cross‐dependence measures appropriate for the infinite‐variance systems. As the main result, we prove that the ratio of two considered alternative cross‐dependence measures tends to the stability index of the noise distribution. This result is the continuation of the authors' previous research where a similar study was performed for one‐dimensional models based on the ‐stable distribution. Moreover, in the authors' recent papers the stationary bidimensional time series models were considered in the same direction. Finally, we propose a possible application of the introduced methodology.

Forecasting Global Fire Emissions on Subseasonal to Seasonal (S2S) Time Scales.

Fire emissions of gases and aerosols alter atmospheric composition and have substantial impacts on climate, ecosystem function, and human health. Warming climate and human expansion in fire‐prone landscapes exacerbate fire impacts and call for more effective management tools. Here we developed a global fire forecasting system that predicts monthly emissions using past fire data and climate variables for lead times of 1 to 6 months. Using monthly fire emissions from the Global Fire Emissions Database (GFED) as the prediction target, we fit a statistical time series model, the Autoregressive Integrated Moving Average model with eXogenous variables (ARIMAX), in over 1,300 different fire regions. Optimized parameters were then used to forecast future emissions. The forecast system took into account information about region‐specific seasonality, long‐term trends, recent fire observations, and climate drivers representing both large‐scale climate variability and local fire weather. We cross‐validated the forecast skill of the system with different combinations of predictors and forecast lead times. The reference model, which combined endogenous and exogenous predictors with a 1 month forecast lead time, explained 52% of the variability in the global fire emissions anomaly, considerably exceeding the performance of a reference model that assumed persistent emissions during the forecast period. The system also successfully resolved detailed spatial patterns of fire emissions anomalies in regions with significant fire activity. This study bridges the gap between the efforts of near‐real‐time fire forecasts and seasonal fire outlooks and represents a step toward establishing an operational global fire, smoke, and carbon cycle forecasting system.

Estimating multiple breaks in nonstationary autoregressive models

Chong (1995) and Bai (1997) proposed a sample-splitting method to estimate a multiple-break model. However, their studies focused on stationary time series models, in which the identification of the first break depends on the magnitude and the duration of the break, and a testing procedure is needed to assist the estimation of the remaining breaks in subsamples split by the break points found earlier. In this paper, we focus on nonstationary multiple-break autoregressive models. Unlike the stationary case, we show that the duration of a break does not affect whether it will be identified first. Rather, it depends on the stochastic order of magnitude of signal strength of the break under the case of constant break magnitude and also the square of the magnitude of the break under the case of shrinking break magnitude. Since the subsamples usually have different stochastic orders in nonstationary autoregressive models with breaks, one can therefore determine which break will be identified first. We apply this finding to the models proposed in Phillips and Yu (2011) and Phillips et al. (2011, 2015a, 2015b). We propose an estimation procedure as well as the asymptotic theory for the model. Some extensions to more general models are provided, and the hypothesis test with the null hypothesis being the unit root model is examined. Results of numerical simulations and an empirical study are given to illustrate the finite-sample performance.

A review study of functional autoregressive models with application to energy forecasting

AbstractIn this data‐rich era, it is essential to develop advanced techniques to analyze and understand large amounts of data and extract the underlying information in a flexible way. We provide a review study on the state‐of‐the‐art statistical time series models for univariate and multivariate functional data with serial dependence. In particular, we review functional autoregressive (FAR) models and their variations under different scenarios. The models include the classic FAR model under stationarity; the FARX and pFAR model dealing with multiple exogenous functional variables and large‐scale mixed‐type exogenous variables; the vector FAR model and common functional principal component technique to handle multiple dimensional functional time series; and the warping FAR, varying coefficient‐FAR and adaptive FAR models to handle seasonal variations, slow varying effects and the more challenging cases of structural changes or breaks respectively. We present the models’ setup and detail the estimation procedure. We discuss the models’ applicability and illustrate the numerical performance using real‐world data of high‐resolution natural gas flows in the high‐pressure gas pipeline network of Germany. We conduct 1‐day and 14‐days‐ahead out‐of‐sample forecasts of the daily gas flow curves. We observe that the functional time series models generally produce stable out‐of‐sample forecast accuracy.This article is categorized under: Statistical Models > Semiparametric Models Data: Types and Structure > Time Series, Stochastic Processes, and Functional Data

Discontinuities in Wintertime Warming in Northern Europe during 1951–2016

Although there is a general consensus about the trends of current climate change, the North Atlantic region deserves special attention, as it is the key region for many climate processes. The aim of this study is to assess the climatic changes in this region for the period 1951–2016, based on the analysis of surface air temperature (SAT) observations from weather stations, and the North Atlantic Oscillation (NAO). Statistical modeling of time series for January, February and March shows a stepwise increase of SAT in Northern Europe in 1987–1989, with the stationarity increasing towards spring. The divided trends of the NAO and SAT indicate a good coherence at the level of climate tendencies. This research reveals the discontinuity of the present-day wintertime warming in Northern Europe, with a warming of about 2 °C after the stepwise jump of the SAT.