Time Series Problems Research Articles

Devising Hourly Forecasting Solutions Regarding Electricity Consumption in the Case of Commercial Center Type Consumers

This paper focuses on an important issue regarding the forecasting of the hourly energy consumption in the case of large electricity non-household consumers that account for a significant percentage of the whole electricity consumption, the accurate forecasting being a key-factor in achieving energy efficiency. In order to devise the forecasting solutions, we have developed a series of dynamic neural networks for solving nonlinear time series problems, based on the non-linear autoregressive (NAR) and non-linear autoregressive with exogenous inputs (NARX) models. In both cases, we have used large datasets comprising the hourly energy consumption recorded by the smart metering device from a commercial center type of consumer (a large hypermarket), while in the NARX case we have used supplementary temperature and time stamps datasets. Of particular interest was to research and obtain an optimal mix between the training algorithm (Levenberg-Marquardt, Bayesian Regularization, Scaled Conjugate Gradient), the hidden number of neurons and the delay parameter. Using performance metrics and forecasting scenarios, we have obtained results that highlight an increased accuracy of the developed forecasting solutions. The developed hourly consumption forecasting solutions can bring significant benefits to both the consumers and electricity suppliers.

Estimation of rainfall and stream flow missing data for Terengganu, Malaysia by using interpolation technique methods

Missing data is a serious problem in many climatological time series. Daily rainfall and stream flow datasets with no missing values are required for efficient estimation for application purposes. In order to estimate any missing observations in data, interpolation techniques are often used. This study focuses on comparing a few selected methods in the estimation of missing rainfall and stream flow data. The interpolation techniques studied were the Arithmetic Average (AA) method, Normal Ratio (NR) method, Inverse Distance (ID) method and Coefficient of Correlation (CC) method. However, in the case when there is no information from neighboring stations, the mean on the same day and month but at different years is taken as estimation of the missing value on that particular date. Twenty years of daily rainfall and stream flow data at 12 stations located at Terengganu were used for this study. In testing to verify which method is the best in evaluating missing values at the target station using information from the nearby stations (in the radius range of 10 km to 50 km), several percentages of missing values were considered. The validation of the best estimation methods is done based on the estimation error; with tests such as Root Mean Square Error (RMSE), Mean Absolute Error (MAE) and Correlation Coefficient (R) tests.

A Moment-Based Notion of Time Dependence for Functional Time Series

This paper addresses the fundamental topic of time dependence for time series when data points are given as functions. We construct a notion of time dependence through the scores of the principal components, which allows us to adapt various scalar time series techniques to the functional data context. In particular, we define dependence based on the autocovariances and cumulants of the scores, covering short and long memory scenarios. This notion naturally applies to linear processes. To justify this moment based approach we investigate the asymptotic properties of the estimator of the functional principal components and show its consistency under short and long memory. Finally, the applicability of our notion is illustrated through several statistical problems in functional time series: estimation of the functional autoregressive model, estimation of the long-run covariance function and testing for short memory against the long memory alternative.

FAKTOR-FAKTOR YANG MEMPENGARUHI NILAI TUKAR RUPIAH TERHADAP DOLAR AMERIKA DENGAN MODEL KOREKSI KESALAHAN ENGLE-GRANGER (PENDEKATAN MONETER)

Exchange rate measures the value of a certain foreign exchange from other foreign exchange's perspective. As the condition of economic changes, the exchange rate ma change substantially. The decrease of the value of a foreign exchange is called depreciation and the increase value of a foreign exchange is called appreciation.The equilibrium exchange rate will change along with the change of demand and supply. Factors causing the change of demand and supply curve among others are the amount of money supply, relative gross domestic product (GDP) and the level of relative interest rate.The research is aimed to analyze the influence of variables of Indonesian money supply, American money supply, Indonesian real Gross Domestic Product, American real Gross Domestic Product, deposits interest rate and LIBOR (London Interbank Offer Rates on SDR Deposit) both in short and long terms.One of the ways to analyze the influence of short term and long term is by developing the dynamic model. In this research, the analyzes of dynamic model was conducted with ENGEL-GRANGER ERROR CORRECTION MODEL approach which was developed by ENGEL-GRANGER (1987) based on GRANGER REPRESENTATION THEOREM.The ECM analyzes was chosen not only because of its ability to solve the problem of time series which is not stationer, and spurious regression and spurious correlation in the economic analyses but also its ability to discuss the consistence of empiric model with economic theory. Beside, ECM concept is also thought to be more realistic in observing the development of economics variables from the result of the analyzes during the time of observation. It was known that long-term exchange rate is influenced by Indonesia real Gross Domestic Product and the number of Indonesian money supply. The variable of Indonesian real Gross Domestic showed the significant result and the signal test was convenient with the theory. The variable which influence" short term exchange rate are the amount of Indonesian money supply, Indonesian real Gross Domestic Product, and Indonesian deposit interest rate. The three variables showed the significant result and the signal test was convenient with the theory.

Time Series Prediction Based on Adaptive Weight Online Sequential Extreme Learning Machine

A novel adaptive weight online sequential extreme learning machine (AWOS-ELM) is proposed for predicting time series problems based on an online sequential extreme learning machine (OS-ELM) in this paper. In real-world online applications, the sequentially coming data chunk usually possesses varying confidence coefficients, and the data chunk with a low confidence coefficient tends to mislead the subsequent training process. The proposed AWOS-ELM can improve the training process by accessing the confidence coefficient adaptively and determining the training weight accordingly. Experiments on six time series prediction data sets have verified that the AWOS-ELM algorithm performs better in generalization performance, stability, and prediction ability than the OS-ELM algorithm. In addition, a real-world mechanical system identification problem is considered to test the feasibility and efficacy of the AWOS-ELM algorithm.

Co-evolutionary multi-task learning with predictive recurrence for multi-step chaotic time series prediction

Multi-task learning employs a shared representation of knowledge for learning several instances of the same problem. Multi-step time series problem is one of the most challenging problems for machine learning methods. The performance of a prediction model face challenges for higher prediction horizons due to the accumulation of errors. Cooperative coevolution employs in a divide and conquer approach for training neural networks and has been very promising for single step ahead time series prediction. Recently, co-evolutionary multi-task learning has been proposed for dynamic time series prediction. In this paper, we adapt co-evolutionary multi-task learning for multi-step prediction where predictive recurrence is developed to feature knowledge from previous states for future prediction horizon. The goal of the paper is to present a network architecture with predictive recurrence which is capable of multi-step prediction through a form of multi-task learning. We employ cooperative neuro-evolution and an evolutionary algorithm as baselines for comparison. The results show that the proposed method provides the best generalization performance in most cases. Comparison of results with the literature has shown to be promising which motivates further application of the approach for related real-world problems.

Interpretation of numerically detected rank defects in GNSS data analysis problems in terms of deficiencies in reference system definition

New tools in the form of angular deficiency indices are developed for the physical interpretation of numerically detected rank deficiencies or weaknesses, in terms of defects or weaknesses in the definition of the reference system characteristics (origin, orientation and scale) to which coordinates and other unknown parameters refer. Within a least squares estimation procedure, the numerical detection is based on the subspace of the parameter space spanned by eigenvectors of the coefficient matrix of the normal equations, which correspond to zero or very small eigenvalues. The physical interpretation is based on the well-known theoretically derived basis of the null space of the design matrix, provided by the columns of the matrix appearing in the so-called inner constraints. This null space basis is elaborated for single-epoch (weekly) solutions of GNSS networks, for deformable networks with constant station velocities, as well as for the stacking problem of coordinate time series. The applicability of these new tools and their implementation strategy are demonstrated by simple numerical examples.

Sensor Fault Diagnosis for Aero Engine Based on Online Sequential Extreme Learning Machine with Memory Principle

The on-board sensor fault detection and isolation (FDI) system is essential to guarantee the reliability and safety of an aero engine. In this paper, a novel online sequential extreme learning machine with memory principle (MOS-ELM) is proposed for detecting, isolating, and reconstructing the fault sensor signal of aero engines. In many practical online applications, the sequentially coming data chunk usually possesses a characteristic of timeliness, and the overdue training data may mislead the subsequent learning process. The proposed MOS-ELM can improve the training process by introducing the concept of memory principle into the online sequential extreme learning machine (OS-ELM) to tackle the timeliness of the data chunk. Simulations on some time series problems and some benchmark databases show that MOS-ELM performs better in generalization performance, stability, and prediction accuracy than OS-ELM. The experiment results of the MOS-ELM-based sensor fault diagnosis system also verify the excellent generalization performance of MOS-ELM and indicate the effectiveness and feasibility of the developed diagnosis system.

The interannual trend and preliminary quantitative estimation of the oceans condition in the Bohai Sea area

After different frequency observed temperature data of Bohai sea marine observation stations was analyzed, results showed that daily average sea surface temperature value obtained from 3-hour-observations (08h, 14h, 20h) which was slightly lower than that from 24-hour-observations. The general gap was within 0.10°, while the value was 0.05° for the monthly mean temperature. Daily average sea surface temperature values of 3-hour-observations have a little effect both in statistical properties and the accuracy of statistical data, which does not affect the representativeness of the data. It can be used in studying long time series problems. Analyzing the trend of the SST data changes in 1960-2012 and the SAT data changes in 1965-2012 by using the linear tendency estimate and cumulative distance square method, it can prove that SST annual variation rate was 0.010°/a, with a total increase of 0.53° in last 53 years; and SAT annual variation rate was 0.043°/a, with a total increase of 2.06° in last 48 years. Although the long-term trend of these two factors is significantly increased, but there was a significant mutation around 1987. From 1960 to 1987, it had a downward trend, after 1987 it began to grow, the upward trend has not diminished until 2009.

基于ARIMA模型的河南省全社会固定资产投资预测分析

ARIMA模型能较好的解决非平稳时间序列的建模问题，并且在时间序列模型的短期预测方面有很好的应用时间，文章通过搜集从1989年~2014年的数据，结合EVIEWS软件，建立河南省全社会固定资产投资总额自回归移动平均模型ARIMA (p, d, q)的时间序列模型并进行检验，最后将ARIMA模型应用于河南省全社会固定资产投的资总额分析及预测。结果表明，该模型能较好的解决河南省全社会固定资产投资的估计和预测问题，预测精度较高。从而为政府提供固定资产投资比例和投资金额提供可靠的参考依据，促进经济的健康发展。 ARIMA model can solve the modeling problem of non-stationary time series well, and it has a good application time in the short-term prediction of time series model. By collecting the data from 1989 to 2014, combined with EVIEWS software, finally, the ARIMA model is applied to the analysis and forecast of the total investment of fixed assets in Henan province. The results show that the ARIMA model can be used to analyze the total assets of Henan province. The results show that the model can solve the problem of estimating and forecasting the investment of fixed assets in Henan province, and the prediction accuracy is high so as to provide the government with a fixed asset investment ratio and the amount of investment to provide a reliable reference to promote the healthy development of the economy.

Univariate Time-Series Analysis of Second-Hand Car Importation in Zambia

Zambia largely depends on the international second-hand car (SHC) market for their motor vehicle supply. The importation of Second hand Cars in Zambia presents a time series problem. The data used in this paper is monthly data on SHC importation from 1st January, 2014 to 31st December, 2016. Data was analyzed using Exponential Smoothing (ES) and Autoregressive Integrated Moving Average (ARIMA) models. The results showed that ARIMA (2, 1, 2) was the best fit for the SHC importation since its errors were smaller than those of the SES, DES and TES. The four error measures used were Root-mean-square error (RMSE), Mean absolute error (MAE), Mean percentage error (MPE) and Mean absolute percentage error (MAPE). The forecasts were also produced using the ARIMA (2, 1, 2) model for the next 18 months from January 2017. Although there is percentage increase of 90.6% from November 2015 to December 2016, the SHC importation generally is on the decrease in Zambia with percentage change of 59.5% from January 2014 to December 2016. The forecasts also show a gradual percentage decrease of 1.12% by June 2018. These results are more useful to policy and decision makers of Government departments such as Zambia Revenue Authority (ZRA) and Road Development Agency (RDA) in a bid to plan and execute their duties effectively.

Processing Uncertainties in Modeling Nonstationary Time Series Using Decision Support Systems

Background . Forecasting of nonlinear nonstationary time series (NNTS) is important problem in economics, marketing, industry, ecology and many other branches of science and practical activities. Successful solution of the problem requires development of modern computer based decision support systems (DSS) capable to generate reliable estimates of forecasts in conditions of uncertainty of various type and origin. Objective . The purpose of the research is as follows: development of requirements to the modern DSS and their formal representation; analysis of uncertainty types characteristic for model building and forecasting; selection of techniques for taking into consideration of the uncertainties; and illustration of the system application to solving the problem of forecasts estimation for heteroscedastic NNTS using statistical data. Methods . To reach the objectives stated the following methods were used: systemic approach to statistical data analysis; statistical approach to identification and taking into consideration of possible uncertainties; Kalman filtering techniques; Bayesian programming approach and statistical criteria of model adequacy and quality of forecasts. Results . Formal description of the DSS is provided, and requirements to its development are given; the classes of mathematical methods necessary for DSS implementation are proposed; some approaches to formal taking into consideration of probabilistic, statistical and parametric uncertainties are discussed; and illustrating example of the DSS application is considered. Conclusions . Systemic approach to DSS constructing for solving the problem of nonlinear nonstationary time series forecasting turned out to be very fruitful. Using the system proposed it is possible to take into consideration various uncertainties of probabilistic, statistical and parametric type, and to compute high quality estimates of short and medium term forecasts for NNTS. The approach proposed has good perspectives for the future improvements and enhancement.

Evaluation of co-evolutionary neural network architectures for time series prediction with mobile application in finance

The fusion of soft computing methods such as neural networks and evolutionary algorithms have given a very promising performance for time series prediction problems. In order to fully harness their strengths for wider impact, effective real-world implementation of prediction systems must incorporate the use of innovative technologies such as mobile computing. Recently, co-evolutionary algorithms have shown to be very promising for training neural networks for time series prediction. Cooperative coevolution decomposes a problem into subcomponents that are evolved in isolation and cooperation typically involves fitness evaluation. The challenge has been in developing effective subcomponent decomposition methods for different neural network architectures. In this paper, we evaluate the performance of two problem decomposition methods for training feedforward and recurrent neural networks for chaotic time series problems. We further apply them for financial prediction problems selected from the NASDAQ stock exchange. We highlight the challenges in real-time implementation and present a mobile application framework for financial time series prediction. The results, in general, show that recurrent neural networks have better generalisation ability when compared to feedforward networks for real-world time series problems.

Collusion-Tolerable and Efficient Privacy-Preserving Time-Series Data Aggregation Protocol

Many miraculous ideas have been proposed to deal with the privacy-preserving time-series data aggregation problem in pervasive computing applications, such as mobile cloud computing. The main challenge consists in computing the global statistics of individual inputs that are protected by some confidentiality mechanism. However, those works either suffer from collusive attack or require time-consuming initialization at every aggregation request. In this paper, we proposed an efficient aggregation protocol which tolerates up to k passive adversaries that do not try to tamper the computation. The proposed protocol does not require a trusted key dealer and needs only one initialization during the whole time-series data aggregation. We formally analyzed the security of our protocol and results showed that the protocol is secure if the Computational Diffie-Hellman (CDH) problem is intractable. Furthermore, the implementation showed that the proposed protocol can be efficient for the time-series data aggregation.

Designing fuzzy expert methods of numeric evaluation of an object for the problems of forecasting

The research is devoted to the models and methods of determining the numeric evaluation of the object. A fuzzy model of the problem was built that allows presenting the results of experts surveys as the intervals of change in the numeric evaluation including determining the degrees of the confidence of the experts in their opinions. Heuristics were proposed to determine those experts from an expert group, the degrees of confidence of who have certain features in their assessments. The application of such mechanism allows excluding the experts who are not confident in their opinions or who display equal confidence in all the values of the intervals, determined by them. Rules of determining collective numeric evaluation of objects in the fuzzy problem of the numeric evaluation have been developed that are based on the simultaneous consideration of competence degrees of the experts as well as the degrees of their confidence in their assessments. A forecasting model of time series was constructed, based on the fuzzy methods of determining collective numeric object assessment that provides a possibility to consider non-systematic and poor formalized external factors. The method of simultaneous usage of classic methods of forecasting and an “expert block” was designed to solve the problem of time series forecasting that provides a possibility to include the external factors to the forecasting value which have a high impact on the forecasting value but which have not systematic character or cannot be formalized. The efficiency and expedience of application of the proposed approaches to solving the practical problems of time series forecasting were proven, on the example of the task of forecasting quantitative characteristics of HIV–infected people, registered officially in the region.

Time series forecasting for building energy consumption using weighted Support Vector Regression with differential evolution optimization technique

Electricity load forecasting is crucial for effective operation and management of buildings. Support Vector Regression (SVR) have been successfully used in solving nonlinear regression and time series problems related to building energy consumption forecasting. As the performance of SVR heavily depends on the selection of its parameters, differential evolution (DE) algorithm is employed in this study to solve this problem. The forecasting model is developed using weighted SVR models with nu-SVR and epsilon-SVR. The DE algorithm is again used to determine the weights corresponding to each model. A case of time series energy consumption data from an institutional building in Singapore is used to elucidate the performance of the proposed model. The proposed model can be used to forecast both, half-hourly and daily electricity consumption time series data for the same building. The results show that for half-hourly data, the model exhibits higher weight for nu-SVR, whereas for daily data, a higher weight for epsilon-SVR is observed. The mean absolute percentage error (MAPE) for daily energy consumption data is 5.843 and that for half-hourly energy consumption is 3.767 respectively. A detailed comparison with other evolutionary algorithms show that the proposed model yields higher accuracy for building energy consumption forecasting.

On prediction and filtering problem of long-run stationary time series

Suppose by the irregularity of the reflectivity of the earth a seismic signal is not always stationary in usual sense, but only long-run stationary (see [6,7]). Then there arises a question: ‘why is wiener filter, which is as well known is used in prediction and filtering of ergodic stationary time series, also applicable in processing seismic signals? In this paper we try to give answer to this question.

Understanding Water Level Residuals in Malacca Strait Using Genetic Programming

Hydrodynamics are highly complex in Malacca Strait as it is where tides from Indian Ocean and South China Sea interact. Highly varying topography and geometry, river discharges from land and seasonal monsoon climate contribute further complication to the local flow dynamics and usually requires numerical model to resolve. However, no matter how well the numerical model is calibrated, residual will exist due to imperfect description of underlying physics and lack of high quality input data. Numerous studies have applied data-driven methods to correct numerical model prediction by forecasting the residuals, and shown that these methods are undeniably effective and efficient and being great value to more traditional modelling approaches. However, in complex hydrodynamic system of Malacca Strait, instead of simply treating numerical model residual as a numerical mismatch and addressing it as a time series problem by local correction, in this paper a more interesting and meaningful effort to uncover the underlying dynamics is attempted. This paper explores the ability of genetic programming to unearth the embedded components or dependencies of the numerical model residual in Malacca Strait.

Сравнительный анализ мер сходства, основанных на преобразовании скользящих аппроксимаций, в задачах классификации временных рядов

One of the major issues dealing with time-series classification problem is the choice of similarity measure. This article presents a comparative analysis of the similarity measure for time series based on moving approximations transform (MAP transforms) with other two most useful measures: Algorithm Dynamic Transformation and Euclidean distance for classification task. In addition, algorithm, that improves the precision of the measure for time series, that have similar values, but shifted relative to each other on the axis X, where coordinate on the X axis represents the time unit, is proposed.

Blind source separation problem in GPS time series

A critical point in the analysis of ground displacement time series, as those recorded by space geodetic techniques, is the development of data-driven methods that allow the different sources of deformation to be discerned and characterized in the space and time domains. Multivariate statistic includes several approaches that can be considered as a part of data-driven methods. A widely used technique is the principal component analysis (PCA), which allows us to reduce the dimensionality of the data space while maintaining most of the variance of the dataset explained. However, PCA does not perform well in finding the solution to the so-called blind source separation (BSS) problem, i.e., in recovering and separating the original sources that generate the observed data. This is mainly due to the fact that PCA minimizes the misfit calculated using an $$L_{2}$$ norm ( $$\chi ^{2})$$ , looking for a new Euclidean space where the projected data are uncorrelated. The independent component analysis (ICA) is a popular technique adopted to approach the BSS problem. However, the independence condition is not easy to impose, and it is often necessary to introduce some approximations. To work around this problem, we test the use of a modified variational Bayesian ICA (vbICA) method to recover the multiple sources of ground deformation even in the presence of missing data. The vbICA method models the probability density function (pdf) of each source signal using a mix of Gaussian distributions, allowing for more flexibility in the description of the pdf of the sources with respect to standard ICA, and giving a more reliable estimate of them. Here we present its application to synthetic global positioning system (GPS) position time series, generated by simulating deformation near an active fault, including inter-seismic, co-seismic, and post-seismic signals, plus seasonal signals and noise, and an additional time-dependent volcanic source. We evaluate the ability of the PCA and ICA decomposition techniques in explaining the data and in recovering the original (known) sources. Using the same number of components, we find that the vbICA method fits the data almost as well as a PCA method, since the $$\chi ^{2}$$ increase is less than 10 % the value calculated using a PCA decomposition. Unlike PCA, the vbICA algorithm is found to correctly separate the sources if the correlation of the dataset is low ( $$<$$ 0.67) and the geodetic network is sufficiently dense (ten continuous GPS stations within a box of side equal to two times the locking depth of a fault where an earthquake of $$M_\mathrm{{w}} >6$$ occurred). We also provide a cookbook for the use of the vbICA algorithm in analyses of position time series for tectonic and non-tectonic applications.