Non-stationary Time Series Data Research Articles

Statistical inference of locally stationary functional coefficient models

In this paper, we propose a novel functional coefficient model, useful for direct modeling of nonstationary time series data without needing to detrend the original data. The proposed model could reveal the underlying dynamics and evolutionary nature of the data, and is easy to interpret. Through the local polynomial technique we investigate an estimation procedure for the proposed model and establish the asymptotic properties of the resulting estimator. In addition, we develop a test statistic to check time-invariance and derive the asymptotic distribution of the test statistic. An extensive simulation study is conducted to assess the finite-sample performances, and the proposed procedures work well and suggest the feasibleness and effectiveness. Two real time series applications in finance and epidemiology are provided.

Research on Short-term Ionospheric Prediction Combining with EOF and ARIMA Model Over Guangxi Area

Abstract. According to the empirical orthogonal function (EOF), the non-stationary time series data are decomposed into time function and space function, so this mathematical method can simplify the non-stationary time series and eliminate redundant information, thus it performs well in non-stationary time series analysis. The ionospheric Vertical Total Electron Content (VTEC) is a non-stationary time series, which has non-stationary and seasonal variation and the activity of VTEC is more active in low latitudes. Guangxi is located in the middle and low latitudes of the Northern Hemisphere with abundant sunshine in summer and autumn. The energy released by solar radiation makes the ionospheric activity in this region more complex than that in the high latitudes. However, no expert or scholar has used EOF analysis method to conduct a comprehensive study of the low latitudes. The International GNSS Service (IGS) provided by high precision Global Ionospheric Maps (GIM) center in Guangxi are used in the modeling data, the GIM data of the first 10 days of different seasons are decomposed by EOF, and then the time function is predicted by ARIMA model. VTEC values for the next five days are obtained through reconstruction, and relative accuracy and standard deviation are used as accuracy evaluation criteria. The results of EOF-ARIMA model are compared with those of ARIMA model, and the prediction accuracy of EOF-ARIMA model at the equatorial anomaly is analyzed in order to explore the reliability of the model in the more complex region of ionospheric activity. The results show that the average relative precision of EOF-ARIMA model is 84.0, the average standard deviation is 7.45TECu, the average relative precision of ARIMA model is 81.5, the average standard deviation is 8.29TECu, and the precision of EOF-ARIMA model is higher than that of ARIMA model.; There is no significant seasonal difference in the prediction accuracy of EOF-ARIMA model, and the prediction accuracy of ARIMA model in autumn is lower than that of other seasons, which indicates that the prediction results of EOF-ARIMA model are more reliable; The prediction accuracy of the EOF-ARIMA model at the equatorial anomaly is not affected, and it is consistent with the accuracy of the high latitude area in Guangxi. It is shown that the EOF-ARIMA model has high accuracy and stability in the short-term ionospheric prediction in Guangxi at low latitudes of China, and provides a new and reliable method for ionospheric prediction at low latitudes.

FDM based OA-ICOS for high accuracy 13C quantification in gaseous CO2

The wide-range applications of isotope analysis make isotope measurement approaches under attentive focus. Off-axis integrated cavity output spectroscopy technology (OA-ICOS) is the most advanced isotope analysis method; however, further studies are still needed to avoid signal noise and improve accuracy. Zero-phase low pass filtering multivariate Fourier Decomposition Method (FDM) was applied for data analysis in the present study, which has its unique advantage to fix up rapid but seasonal changes for nonlinear and non-stationary time series data. In the present study, δ13C content in gaseous CO2 sample were measured by OA-ICOS at ambient temperature. The experimental data treated by FDM showed less signal fluctuant and clearer value change tendency than what showed in raw data, whereas the data density kept same with that of raw data. In the meantime, the experimental results suggested that it is flexible to decide the variance explanation rate by simply change the order of an FDM filter. This approach meets up with the requirements of different practical application scenarios of isotope analysis, which enhances the feasibility for OA-ICOS application in real-time environmental monitoring field.

Analisis Indeks Harga Saham Gabungan (IHSG) Menggunakan Metode Wavelet Thresholding

Stock is one type of long-term investment in the capital market. The stock movement indicator that is most often used in analysis by investors is the Indonesia Composite Index (ICI). ICI data is a variety of time series data, so it can be analyzed using forecasting. One forecasting method that can be used is the wavelet thresholding method. The wavelet threshold can analyze stationary, non-stationary, and nonlinear time series data by producing smooth estimates. The wavelet threshold has a wavelet filter and threshold parameters and threshold functions that can be used in analyzing. In this study MSE was assessed from several wavelet filters namely haar, daubechies, and coiflets filters at levels 1 to 7 with the thresholding function namely soft thresholding and thresholding parameters, namely minimax thresholding and sure thresholding. The data used is IHGS data in 2018 totaling 240 data. Based on the data analysis performed, MSE was obtained which means that the best filter provided in order 2 wavelet coiflet filter at level 2 and thresholding parameter is sure of thresholding with MSE value of 0.0094

Characterization of Fluidization Regimes and Their Transition in Gas–Solid Fluidization by Hilbert–Huang Transform

It is common to characterize fluidized bed dynamics using spectral analysis and nonlinear methods such as correlation entropy (Kolmogorov entropy). In this paper, an alternative method, the Hilbert–Huang transform (HHT), a nonlinear and nonstationary time series data analysis method, is applied to experimental data from two independent setups from the literature: circulating fluidized bed (CFB) and bubbling fluidized bed (BFB). Characterization of four representative regimes for the CFB is realized with the Hilbert spectral analysis, HSA. It is also shown in this work that an entropy based on the HHT is capable of reproducing the flow regime boundaries previously identified using other methods. Linear relationships are observed between the HHT entropy, power spectral density (PSD), and average cycle frequency. Likewise for the BFB, the HHT entropy captured the regime change from slugging to turbulent fluidization.

Benchmarking company performance from economic and environmental perspectives

Purpose The purpose of this paper is to develop an approach to measuring the performance of motor vehicle manufacturers (MVMs) from economic and environmental (E&E) perspectives. Design/methodology/approach Eight measures are identified for benchmarking the performance from E&E perspectives. A new company performance index IMVM is constructed to quantitatively generate the historical data of MVMs’ company performance. Autoregressive integrated moving average (ARIMA) models are built to generate the forecast data of the IMVM. The minimum Akaike information criteria value is used to identify the model of the best fit. Forecast accuracy of the ARIMA models is tested by the mean absolute percentage error. Findings The construction of the index IMVM is benchmarked against three frameworks by six benchmark metrics. The IMVM satisfies all of its applicable metrics while the three frameworks are incapable to satisfy their applicable metrics. Out of 15, 4 MVMs are excluded for benchmarking future performance due to their non-stationary time series data. Based on the forecast IMVM data, GM is the best performer among the 15 samples in the FY2018. Originality/value This research highlights the environmental perspective during vehicles’ production. The development of this approach is based on publicly available data and transparent about the methods it used. The data out of the approach can benefit stakeholders with insights by benchmarking the historical performance of MVMs as well as their future performance.

An Interval Type 2 Fuzzy Logic Framework for Faster Evolutionary Design

In this paper, a fast processing and efficient framework has been proposed to get an optimum output from a noisy data set of a system by using interval type-2 fuzzy logic system. Further, the concept of GPGPU (General Purpose Computing on Graphics Processing Unit) is used for fast execution of the fuzzy rule base on Graphics Processing Unit (GPU). Application of Whale Optimization Algorithm (WOA) is used to ascertain optimum output from noisy data set. Which is further integrated with Interval Type-2 (IT2) fuzzy logic system and executed on Graphics Processing Unit for faster execution. The proposed framework is also designed for parallel execution using GPU and the results are compared with the serial program execution. Further, it is clearly observed that the parallel execution rule base evolved provide better accuracy in less time. The proposed framework (IT2FLS) has been validated with classical bench mark problem of Mackey Glass Time Series. For non-stationary time-series data with additive gaussian noise has been implemented with proposed framework and with T1 FLS. Further, it is observed that IT2 FLS provides better rule base for noisy data set.

Aplicação de métodos estatísticos com suavização exponencial dupla e tripla para previsão de demanda na gestão de estoques

Os métodos estatísticos com suavização exponencial dupla e tripla amplamente utilizados para modelar tendências significativas em dados não estacionários por séries temporais são aplicados neste trabalho para obter em curto prazo, previsões para o planejamento da demanda do processo produtivo em uma indústria metalúrgica do norte de Santa Catarina. O objetivo principal da aplicação de tais métodos é estabelecer a previsão de demanda com o propósito de antecipar cenários futuros de vendas em duas categorias de produtos e obter o melhor aproveitamento da capacidade produtiva através de uma gestão de estoques adequada para a redução de riscos no processo de tomada de decisões gerenciais dessa indústria. Os resultados obtidos com a seleção apropriada dos métodos preditivos com suavização exponencial, objeto de estudo deste trabalho, foram fundamentais para o analista do sistema de previsão de demanda direcionar especial atenção ao grau de acurácia que integrado a uma política de gerenciamento de estoques eficiente foi responsável por minimizar os efeitos de variabilidade e custos operacionais, além contribuir na melhoria dos níveis de serviço e no consequente aumento da rentabilidade da indústria envolvida.

부의 효과의 분위 추정: 분위 정준 공적분회귀를 중심으로 (Wealth Effects Revisited: Quantile Canonical Cointegrating Regression Approach)

Korean Abstract: 본고는 소비함수에 대한 부의 효과와 가계부채가 민간소비에 미치는 영향을 소비의 분위별로 분석해 보았다. 본고는 이와 같은 분석을 위해 시계열 자료에 적용되는 통상적인 분위회귀와 시계열에 대한 공적분회귀모형을 결합함으로써 불안정 변수로 구성된 방정식에 대해 분위별 공적분 회귀추정이 가능하게 해주는 분위 정준 공적분회귀(Quantile Canonical Cointegrating Regression) 기법을 제안하였다. 추정 결과에 의하면, 가처분소득은 분위에 상관없이 양(+)의 효과를 지니는 것으로 나타나 기존 연구의 결과와 부합하였다. 둘째, 주가지수로 본금융자산은 소비에 양(+)의 영향을 미쳐 기존 연구를 뒷받침하나, 주택가격지수로 본 실물자산은 소비에 음(-)의 부의 효과를 보여 기존 연구와는 다른 결과를 나타냈다. 가계대출은 전체적으로 소비를 확대하는 것으로 추정되었으나, 동 대출은 소비에 미치는 영향의 방향이 서로 다른 주택담보대출과 기타대출의 합으로 구성되므로 가계대출의 소비확대 효과는 작거나 통계적으로 유의하지 않을 가능성이 있다. English Abstract: This paper analyzes the effects of wealth and household debt on household consumption expenditure using macro time series data by quantile regression. For this purpose, we propose the QCCRE(Quantile Canonical Cointegrating Regression Estimator). The QCCRE provides an estimation method for quantile regression with non-stationary time series data. The estimator is a solution to the Koenker and Bassetts (1978)’s minimization problem, and its asymptotic distribution follows a mixed normal distribution. The estimation results show that disposible income has a positive effect which confirms previous research. Financial assets (stock price index) have a positive wealth effect, however, household’s real assets (house price index) have a negative wealth effect which is different from previous research. Household debt has a positive effect on household consumption. However, the net effects of household debt may be smaller or even insignificant because household debt is sum of martgage loan and non-martgage loans that have opposite effects on household consumption.

An improved framework to predict river flow time series data.

Due to non-stationary and noise characteristics of river flow time series data, some pre-processing methods are adopted to address the multi-scale and noise complexity. In this paper, we proposed an improved framework comprising Complete Ensemble Empirical Mode Decomposition with Adaptive Noise-Empirical Bayesian Threshold (CEEMDAN-EBT). The CEEMDAN-EBT is employed to decompose non-stationary river flow time series data into Intrinsic Mode Functions (IMFs). The derived IMFs are divided into two parts; noise-dominant IMFs and noise-free IMFs. Firstly, the noise-dominant IMFs are denoised using empirical Bayesian threshold to integrate the noises and sparsities of IMFs. Secondly, the denoised IMF’s and noise free IMF’s are further used as inputs in data-driven and simple stochastic models respectively to predict the river flow time series data. Finally, the predicted IMF’s are aggregated to get the final prediction. The proposed framework is illustrated by using four rivers of the Indus Basin System. The prediction performance is compared with Mean Square Error, Mean Absolute Error (MAE) and Mean Absolute Percentage Error (MAPE). Our proposed method, CEEMDAN-EBT-MM, produced the smallest MAPE for all four case studies as compared with other methods. This suggests that our proposed hybrid model can be used as an efficient tool for providing the reliable prediction of non-stationary and noisy time series data to policymakers such as for planning power generation and water resource management.

A hybrid Elman recurrent neural network, group search optimization, and refined VMD-based framework for multi-step ahead electricity price forecasting

This paper presents a synergy of three methods for training the Elman recurrent neural network to forecast the multi-step-ahead electricity price in an electric power system. Electricity prices are characterized as non-stationary time series data that entail vigorous learning model for predicting the future electricity price from past data. To accomplish this, an enhanced hybrid framework that integrates the refined variational mode decomposition method and the group search optimization algorithm is proposed for training the Elman recurrent neural network. The variational mode decomposition method is optimized using a complement particle swarm optimization method so as to decompose the non-stationary pricing data into optimum number of intrinsic mode functions. Subsequently, based on the power values of intrinsic mode, functions are further filtered and used as the input data to train the Elman neural network. The group search optimization algorithm is used to optimize the weights of the Elman neural network. Three real-time time series non-stationary data for multi-step ahead price prediction are adopted from Australian, British, and Indian power markets and experimented using the proposed forecasting model.

A better way to define and describe Morlet wavelets for time-frequency analysis

Complex Morlet wavelets are frequently used for time-frequency analysis of non-stationary time series data, such as neuroelectrical signals recorded from the brain. The crucial parameter of Morlet wavelets is the width of the Gaussian that tapers the sine wave. This width parameter controls the trade-off between temporal precision and spectral precision. It is typically defined as the “number of cycles,” but this parameter is opaque, and often leads to uncertainty and suboptimal analysis choices, as well as being difficult to interpret and evaluate. The purpose of this paper is to present alternative formulations of Morlet wavelets in time and in frequency that allow parameterizing the wavelets directly in terms of the desired temporal and spectral smoothing (expressed as full-width at half-maximum). This formulation provides clarity on an important data analysis parameter, and can facilitate proper analyses, reporting, and interpretation of results. MATLAB code and sample data are provided.

Over-Differencing and Forecasting with Non-Stationary Time Series Data

In time series analysis, over-differencing is a common phenomenon to make the data to be stationary. However, it is not always a good idea to take over-differencing in order to ensure the stationarity of time series data. In this paper, the effect of over-differencing has been investigated via a simulation study to observe how far or how close the fitted model from the true one. Simulation results show that the fitted model is found to be different and very far from the true model because of over-differencing in most of the scenarios considered in this study. In practice, it may be worthy to consider differencing as well as suitable transformation of the time series data to make it stationary. Both transformation and differencing are used for a non-stationary time series data on average monthly house prices to ensure it to be stationary. We then analyse the data and make prediction for the future values.
 Dhaka Univ. J. Sci. 67(1): 21-26, 2019 (January)

Tracking Poisson Parameter for Non-Stationary Discontinuous Time Series with Taylor’s Abnormal Fluctuation Scaling

We propose a parameter estimation method for non-stationary Poisson time series with the abnormal fluctuation scaling, known as Taylor’s law. By introducing the effect of Taylor’s fluctuation scaling into the State Space Model with the Particle Filter, the underlying Poisson parameter’s time evolution is estimated correctly from given non-stationary time series data with abnormally large fluctuations. We also developed a discontinuity detection method which enables tracking the Poisson parameter even for time series including sudden discontinuous jumps. As an example of application of this new general method, we analyzed Point-of-Sales data in convenience stores to estimate change of probability of purchase of commodities under fluctuating number of potential customers. The effectiveness of our method for Poisson time series with non-stationarity, large discontinuities and Taylor’s fluctuation scaling is verified by artificial and actual time series.

Multi-View Temporal Ensemble for Classification of Non-Stationary Signals

In the classification of non-stationary time series data such as sounds, it is often tedious and expensive to get a training set that is representative of the target concept. To alleviate this problem, the proposed method treats the outputs of a number of deep learning sub-models as the views of the same target concept that can be linearly combined according to their complementarity. It is proposed that the view's complementarity be the contribution of the view to the global view, chosen in this paper to be the Laplacian eigenmap of the combined data. Complementarity is computed by alternate optimization, a process that involves the cost function of the Laplacian eigenmap and the weights of the linear combination. By blending the views in this way, a more complete view of the underlying phenomenon can be made available to the final classifier. Better generalization is obtained, as the consensus between the views reduces the variance while the increase in the discriminatory information reduces the bias. The data experiment with artificial views of environment sounds formed by deep learning structures of different configurations shows that the proposed method can improve the classification performance.

Improving forecasting accuracy for stock market data using EMD-HW bagging.

Many researchers documented that the stock market data are nonstationary and nonlinear time series data. In this study, we use EMD-HW bagging method for nonstationary and nonlinear time series forecasting. The EMD-HW bagging method is based on the empirical mode decomposition (EMD), the moving block bootstrap and the Holt-Winter. The stock market time series of six countries are used to compare EMD-HW bagging method. This comparison is based on five forecasting error measurements. The comparison shows that the forecasting results of EMD-HW bagging are more accurate than the forecasting results of the fourteen selected methods.

A Smoother State Space Multitaper Spectrogram.

A recent work (Kim et al. 2018) has reported a novel statistical modeling framework, the State-Space Multitaper (SSMT) method, to estimate time-varying spectral representation of non-stationary time series data. It combines the strengths of the multitaper spectral (MT) analysis paradigm with that of state-space (SS) models. In this current work, we explore a variant of the original SSMT framework by imposing a smoothness promoting SS model to generate smoother estimates of power spectral densities for non-stationary data. Specifically, we assume that the continuous processes giving rise to observations in the frequencies of interest follow multiple independent Integrated Wiener Processes (IWP). We use both synthetic data and electroencephalography (EEG) data collected from a human subject under anesthesia to compare the IWP- SSMT with the SSMT method and demonstrate the former's utility in yielding smoother descriptions of underlying processes. The original SSMT and IWP-SSMT can co-exist as a part of a model selection toolkit for nonstationary time series data.

Variational mode decomposition based low rank robust kernel extreme learning machine for solar irradiation forecasting

In this paper a new hybrid method has been implemented by combining Variational Mode Decomposition (VMD) and a new low rank robust kernel based Extreme Learning Machine (RKELM) for solar irradiation forecasting. This hybrid model presents an efficient and effective short term solar irradiation prediction approach using the historical solar irradiation data. The original non-stationary time series data is decomposed into various modes using VMD approach. The proposed VMD-RMWK (VMD based reduced Morlet Wavelet Kernel extreme learning machine) method is used to predict the solar irradiation of an experimental 1 MW solar power plant in Odisha, India. Different time intervals of 15 min, 1 h and 1 day ahead in different weather conditions are considered for forecasting purpose. The VMD technique decomposes the original nonlinear irradiation into a set of Variational Mode Functions (VMFs), and the extracted VMFs are used to train the kernel based robust ELM. Comparison with empirical mode decomposition (EMD) based low rank kernel is also presented in this paper. As a new contribution to the previously performed literature survey this paper presents a more accurate solar irradiation prediction paradigm for distinctive weather conditions, and different time intervals varying from very short duration of 15 min to one day ahead. Also to improve the reliability of the KELM and to make it robust under noisy conditions and the presence of outliers in the data, a weight loss matrix has been derived using a non-parametric kernel density estimation method and incorporated in the new formulation (RKELM). A typical solar power experimental solar power station in India has been taken for detailed study showing clearly the accuracy and robustness of the proposed approach. For cross validation of the proposed model, solar irradiation data from a solar power plant located in the state of Florida has been implemented.

GSTARI model of BPR assets in West Java, Central Java, and East Java

Bank Perkreditan Rakyat (BPR) is a financial institution in Indonesia dealing with Micro, Small, and Medium Enterprises (MSMEs). Though limited to MSMEs, the development of the BPR industry continues to increase. West Java, Central Java, and East Java have high BPR asset development are suspected to be interconnected because of their economic activities as a neighboring provincies. BPR assets are nonstationary time series data that follow the uptrend pattern. Therefore, the suitable model with the data is generalized space time autoregressive integrated (GSTARI) which considers the spatial and time interrelationships. GSTARI model used spatial order 1 and the autoregressive order is obtained of optimal lag which has the smallest value of Akaike information criterion corrected. The correlation test results showed that the location used in this study had a close relationship. Based on the results of model identification, the best model obtained is GSTAR(31)-I(1). The parameter estimation used the ordinary least squares with the selection of significant variables used the stepwise method and the normalization cross correlation weighting. The residual model fulfilled the assumption of white noise and normal multivariate, so the model was appropriate. The average RMSE and MAPE values of the model were 498.75 and 2.48%.

Hierarchical symbolic dynamic filtering of streaming non-stationary time series data

Abstract This paper proposes a hierarchical feature extractor for non-stationary streaming time series based on the concept of switching observable Markov chain models. The slow time-scale non-stationary behaviors are considered to be a mixture of quasi-stationary fast time-scale segments that are exhibited by complex dynamical systems. The key idea is to model each unique stationary characteristics without apriori knowledge (e.g., number of possible unique characteristics) at a lower logical level, and capture the transitions from one low-level model to another at a higher level. In this context, the concepts in the recently developed Symbolic Dynamic Filtering is extended, to build an online algorithm suited for handling quasi-stationary data at a lower level and a non-stationary behavior at a higher level without apriori knowledge. A key observation made in this study is that the rate of change of data likelihood seems to be a better indicator of change in data characteristics compared to the traditional methods that mostly consider data likelihood for change detection. Thus, an adaptive Chinese Restaurant Process (CRP) distribution is formulated to accommodate the rate of change of data likelihood in the learning algorithm. The algorithm also aims to minimize model complexity while capturing data characteristics (likelihood). Efficacy demonstration and comparative evaluation of the proposed algorithm are performed using time series data both from a simulated system that exhibit nonlinear dynamics as well as a real residential electrical energy disaggregation case study using the publicly available reference energy disaggregation dataset (REDD). We discuss results that show that the proposed hierarchical symbolic dynamic filtering (HSDF) algorithm can identify underlying features with significantly high degree of accuracy, even under very noisy conditions. Based on our validation experiments, we demonstrate better performance of the proposed fast algorithm compared to the baseline Hierarchical Dirichlet Process-Hidden Markov Models (HDP-HMM). The proposed algorithm’s low computational complexity also makes it suitable for on-board, real time operations.