Components Of Time Series Research Articles

Time Series Forecasting via Learning Convolutionally Low-Rank Models

Recently, Liu and Zhang studied the rather challenging problem of time series forecasting from the perspective of compressed sensing. They proposed a no-learning method, named Convolution Nuclear Norm Minimization (CNNM), and proved that CNNM can exactly recover the future part of a series from its observed part, provided that the series is convolutionally low-rank. While impressive, the convolutional low-rankness condition may not be satisfied whenever the series is far from being seasonal, and is in fact brittle to the presence of trends and dynamics. This paper tries to approach the issues by integrating a learnable, orthonormal transformation into CNNM, with the purpose for converting the series of involute structures into regular signals of convolutionally low-rank. We prove that the resultant model, termed Learning-Based CNNM (LbCNNM), strictly succeeds in identifying the future part of a series, as long as the transform of the series is convolutionally low-rank. To learn proper transformations that may meet the required success conditions, we devise an interpretable method based on Principal Component Pursuit (PCP). Equipped with this learning method and some elaborate data argumentation skills, LbCNNM not only can handle well the major components of time series (including trends, seasonality and dynamics), but also can make use of the forecasts provided by some other forecasting methods; this means LbCNNM can be used as a general tool for model combination. Extensive experiments on 100,452 real-world time series from Time Series Data Library (TSDL) and M4 Competition (M4) demonstrate the superior performance of LbCNNM.

Regional fire occurrence in Southern Africa using BFAST iterative break detection in seasonal and trend components of a MODIS time series

ABSTRACT Fire is an integral part of southern African savannas, but despite being well-studied, complex relationships among fire, humans, climate and ecological systems remain poorly understood across much of the region. Analyses that provide information on fire trends in diverse regional contexts are essential for informing fire management and monitoring change. Harmonic seasonal patterns, linear time-series trends and breakpoints in fire occurrence (BFAST) were analysed for 2001–2018 in Botswana using remotely sensed fire occurrence measurements. Regional classification schemes were organized by human land-use, annual precipitation zones and vegetation communities. At the regional scale, mean annual precipitation, land-use and vegetation type influenced fire occurrence magnitude. Seasonality and variability were most clearly organized according to mean annual precipitation. Variability in seasonal and long-term fire trends were observed across the different classification schemes apart from mean annual precipitation zones above 600 mm. The methodology used effectively identified key differences in fire variability across regional classification schemes. However, the spatial resolution and classification scheme may be less effective for human land use and small fires. Overall, MODIS fire data analysed with BFAST is a promising and accessible method for analysing regional savanna fire regimes.

Finite Mixture Model: Prediction of Time Series Data Using Bayesian Method

The aim of this study is to measure the number of components that exhibits from the variables' series. The number of components can be affected by the time series components including trend, seasonal adjustment, and irregular changes. By using a finite mixture model, the number of components can be identifies and thereafter we can formulate a Bayesian regression equation to predict the relationship between exchange rate and international tourism expenditure in Malaysia. Identification of the number of components is an important step to weigh the probability density function for a time series data. The weight of the probability density function is then used for prediction. Besides, a Bayesian method is also used in this study to fit with the finite mixture model due to its consistency characteristic. The Bayesian parameter estimates are close to the predictive distributions because it will integrate the prior distribution with the likelihood function to produce posterior distribution. The results show that there is a two-component normal mixture model exists for the time series data. In addition, a prediction equation is obtained from the analysis.

ROTATED EMPIRICAL ORTHOGONAL FUNCTION ANALYSIS FOR SPATIO-TEMPORAL DATA ANALYSIS

Given any space-time field, Empirical orthogonal function (EOF) analysis finds a set of orthogonal spatial patterns along with a set of associated uncorrelated time series or principal components (PCs). Spatial orthogonality and temporal uncorrelation of EOFs and PCs respectively impose limits on the physical interpretability of EOF patterns. This is because physical processes are not independent, and therefore physical modes are expected in general to be non-orthogonal. Rotated empirical orthogonal functions (REOF) were introduced to generate general localized structures by compromising some of the EOF properties such as orthogonality. EOF and REOF analysis are carried out for the significant wave height (SWH) data for the Bay of Bengal (BOB) region for the period 1958 to 2001. Separate experiments were conducted for all the months together and also for July and December representing the southwest and northeast monsoon periods. The first eigenmodes account for 84%, 68%, and 59% of the total variability for the above three cases respectively. The REOF proved to be more effective than EOF for the above region.

Does bootstrapping the remainder component of seasonal time series improve forecasting using SARIMA model? An application to rainfall data

Does bootstrapping the remainder component of seasonal time series improve forecasting using SARIMA model? An application to rainfall data

Trend triplet based data clustering for eliminating nonlinear trend components of wind time series to improve the performance of statistical forecasting models

Trend triplet based data clustering for eliminating nonlinear trend components of wind time series to improve the performance of statistical forecasting models

Seasonal Lead Release into Drinking Water and the Effect of Aluminum.

Monitoring lead in drinking water is important for public health, but seasonality in lead concentrations can bias monitoring programs if it is not understood and accounted for. Here, we describe an apparent seasonal pattern in lead release into orthophosphate-treated drinking water, identified through point-of-use sampling at sites in Halifax, Canada, with various sources of lead. Using a generalized additive model, we extracted the seasonally varying components of time series representing a suite of water quality parameters and we identified aluminum as a correlate of lead. To investigate aluminum’s role in lead release, we modeled the effect of variscite (AlPO4·2H2O) precipitation on lead solubility, and we evaluated the effects of aluminum, temperature, and orthophosphate concentration on lead release from new lead coupons. At environmentally relevant aluminum and orthophosphate concentrations, variscite precipitation increased predicted lead solubility by decreasing available orthophosphate. Increasing the aluminum concentration from 20 to 500 μg L–1 increased lead release from coupons by 41% and modified the effect of orthophosphate, rendering it less effective. We attributed this to a decrease in the concentration of soluble (<0.45 μm) phosphorus with increasing aluminum and an accompanying increase in particulate lead and phosphorus (>0.45 μm).

Impacts of Climate Oscillation on Offshore Wind Resources in China Seas

The long-term stability and sustainability of offshore wind energy resources are very important for wind energy exploration. In this study, the Cyclostationary Empirical Orthogonal Function (CSEOF) method, which can determine the time varying spatial distributions and long-term fluctuations in the cyclostationary geophysical process, was adopted to investigate the geographical and temporal variability of offshore wind resources in China Seas. The CSEOF analysis was performed on wind speeds at 70 m height above the sea surface from a validated combined Quick Scatterometer (QuikSCAT) and Advanced Scatterometer (ASCAT) wind product (2000–2016) with high spatial resolution of 12.5 km, and Climate Forecast System Reanalysis (CFSR) wind data (1979–2016) with a grid size of 0.5° × 0.5°. The decomposition results of the two datasets indicate that the first CSEOF mode represents the variability of wind annual cycle signal and contributes 77.7% and 76.5% to the wind energy variability, respectively. The principal component time series (PCTS) shows an interannual variability of annual wind cycle with a period of 3–4 years. The second mode accounts for 4.3% and 4.7% of total wind speed variability, respectively, and captures the spatiotemporal contribution of El Niño Southern Oscillation (ENSO) on regional wind energy variability. The correlations between the mode-2 PCTS of scatterometer or CFSR winds and the Southern Oscillation Index (SOI) are greater than 0.7, illustrating that ENSO has a significant impact on China’s offshore wind resources. Moreover, the mode-1 or mode-2 spatial pattern of CFSR winds is basically consistent with that of scatterometer data, but CFSR underestimates the temporal variability of annual wind speed cycle and the spatial changes of wind speed related to ENSO. Compared with reanalysis data, scatterometer winds always demonstrate a finer structure of wind energy variability due to their higher spatial resolution. For ENSO events with different intensities, the impact of ENSO on regional wind resources varies with time and space. In general, El Niño has reduced wind energy in most regions of China Seas except for the Bohai Sea and Beibu Bay, while La Niña has strengthened the winds in most areas except for the Bohai Sea and southern South China Sea.

Empirical Mode Decomposition and Fourier analysis of Caspian Sea level's time series

The present study described Caspian Sea's water level changes by using the recorded data in three ports namely Anzali, Nowshahr, and Amirabad. The data are the mean values of daily records within a three-year period. Primary determinations revealed that the water level drops to the lowest amount in the winter but then starts to increase towards the spring. Afterwards, the water level peaks in the summer and again it decreases in the autumn. It was also detected that water level decreased 22 cm annually in the given period. Fourier Transform and Empirical Mode Decomposition (EMD) were adopted for the decomposition of time series. Fourier analysis indicated that the dominant sinusoidal component possessed a period and amplitude of 294 days and 0.148 m, respectively. EMD yielded six Intrinsic Mode Functions (IMFs) and one residual mode. The average period of each IMF was calculated through zero-down crossing method. Afterwards, the spectrum of each IMF and their summit characteristics were extracted. A maximum value of 0.127 m was observed at the frequency of 0.0034 cycle/day in the IMF6 spectrum, which perfectly corresponds to the dominant sinusoidal component in time series.

Causality in Control Systems Based on Data-Driven Oscillation Identification

This paper addresses the subject of causality analysis using simulation data and data collected from a real control system. Simulated data includes Gaussian and Cauchy noise signals. Real-time series include various, mostly unknown distortions, like trends, oscillations, and noises. Presented research focuses on the oscillatory component in data and its propagation in multi-loop control systems. Oscillation identification is based on a deep decomposition process for control error time series. Identified periodic signals are used for further causality processing. The analysis uses the Transfer Entropy approach. This method belongs to the group of model-free methods. The determination of information pathways is conducted without any model or a priori process knowledge. The research investigates the impact of the oscillation time-series component on the Transfer Entropy causality analysis. The summary shows the observations obtained for given simulated datasets and those collected from real processes. The obtained results show that simulated analysis works properly. On the contrary, the direct application of the oscillation decomposition in real industrial cases may be misleading. Large datasets demand modification in the methodology. Different variants are tested. They show that oscillation propagation is biased in real systems and, therefore, the decomposition should be applied with caution. Furthermore, it is important to remember that the algorithm transition from simulated data to real industrial ones is demanding and should be done with the utmost care.

Data-based model with EMD and a new model selection criterion for dam health monitoring

Data-based models are extensively applied in concrete dam health monitoring. In this paper, the Empirical Mode Decomposition (EMD) is adopted to extract and visualize the irreversible component of deformation monitoring sequence. Consequently proper mathematical formulation of the irreversible component of deformation monitoring model for concrete dams can be established, and the problem of improperly assuming the mathematical form of irreversible component when constructing data-based models is well addressed. The periodic component of the deformation time series is modelled by regression and three machine learning algorithms (i.e., Extreme learning machine, Support Vector Machine based on Grid search and Cross-Verification, and Back Propagation Neural Networks optimized by Genetic Algorithm and Simulated Annealing) respectively. The data-based models with the EMD are able to effectively improve the performance of formulating irreversible component of concrete dam deformation and decrease the over-fitting levels. A new model selection criterion, namely Over-fitting coefficient, is proposed for evaluating and selecting the optimum model among candidate monitoring models. The Over-fitting coefficient can better reflect over-fitting levels of individual monitoring models compared to traditional model selection criteria. As a case study, the displacement and strain monitoring data from the YL gravity dam are modeled by data-based models with the EMD and machine learning algorithms. It is shown that data-based models with the EMD are of higher prediction accuracy and lower rate of false alarm in deformation monitoring than traditional models. The Over-fitting coefficient can better reflect over-fitting levels of monitoring models compared to the error measurement criteria and information criteria. The case study highlights the merits of the proposed data-based models and the model selection criterion for health monitoring of concrete dams.

A RIC&amp;lt;sub&amp;gt;p&amp;lt;/sub&amp;gt; criterion for periodicity analysis of hydrological time series

<p indent="0mm">Identification of periodicity in hydrological time series is important for understanding the complex variability of hydrological processes. Previous studies mainly focused on the comparison, improvement and development of different methods for the identification of periodicity. However, these methods have big subjectivity in the selection of significance levels, which may lead to pseudo-periodic components in the identification results. In this article, a new criterion called RIC_p<italic> </italic>(R for correlation coefficient, IC for information criterion, and subscript p for periodicity) is proposed to accurately identify periodic components in hydrological time series and evaluate their statistical significance. The RIC_p is based on the idea of Akaike information criterion, and it is established by consisting of a fitting accuracy index and an uncertainty measurement. The fitting accuracy index is based on the correlation coefficient, and the uncertainty measurement is based on the form of information entropy. Different synthetic time series, which are composed of multiple periodic components and Pearson-III noise data, are used to verify the superiority of the RIC_p method. The performance of RIC_p is compared with the moving correlation coefficient-based method for periodicity identification (MCCP), harmonic analysis method (HAM), and maximum entropy spectral analysis (MESA), by checking the accuracy and reliability of the identification results. The results suggest that in HAM and MCCP methods, more pseudo-periodic components are identified compared to other methods. Differently, the number of periodic components identified by MESA is less than the true value, as some significant periodic components can be missed. By comparison, the RIC_p performs the best among these four methods. The advantage of RIC_p is that it can describe the periodicity and also evaluate its statistical significance level. The RIC_p method is further applied to analyze the surface water resource time series in six secondary water resource regions in Southwest Rivers basin, by comparing with HAM and MESA. Results further verified the advantages of the RIC_p method developed. It also indicates that the runoff in the basin generally has a 9-year periodic pattern; the precipitation has the same periodicity as the runoff except Lancang River region, which can be attributed to the 11-year periodic cycle of the Indian Ocean monsoon.

Health Hazard

Health of every living being is dependent on level of pollutant in the environment, weather condition, etc, which are interrelated and influencing each other. Presence of pollution particles in high percentage such as particulate matter of size 10 and 2.5 (PM10, PM25) microns in creates higher risk in lung functionality, respiratory disease and reduces cardio functionality; also affects the quality of water sources. Rainfall, technically known as precipitation, occur at non season also create health hazards, seasonal diseases. In our previous work, the relationship between precipitation and pollution were analysed; it is observed that pollution attribute particulate matter, PM2.5, influences precipitation. Pollution data as well as numerical weather data are time series data in nature. This research work analyses the time series data (day wise observations) of pollution and weather, recorded at Chennai city at the year 2017. ARIMA model is constructed after applying required transformations on underlying data. Trend and seasonality found in underlying time series data set are unique since time series components are data-dependent and autocorrelated with previous day observations. Improved forecasting of PM2.5 and precipitation are obtained through ARIMA modelling.

Evaluation of Technology for the Analysis and Forecasting of Precipitation Using Cyclostationary EOF and Regression Method

Precipitation time series exhibit complex fluctuations and statistical changes. Existing research stops short of a simple and feasible model for precipitation forecasting. In this article, the authors investigate and forecast precipitation variations in South Korea from 1973 to 2021 using cyclostationary empirical orthogonal function (CSEOF) and regression methods. First, empirical orthogonal function (EOF) and CSEOF analyses are used to examine the periodic changes in the precipitation data. Then, the autoregressive integrated moving average (ARIMA) method is applied to the principal component (PC) time series derived from the EOF and CSEOF precipitation analyses. The fifteen leading EOF and CSEOF modes and their corresponding PC time series clearly reflect the spatial distribution and temporal evolution characteristics of the precipitation data. Based on the PC forecasts of the EOF and CSEOF models, the EOF–ARIMA composite model and CSEOF–ARIMA composite model are used to obtain quantitative precipitation forecasts. The comparison results show that both composite models have good performance and similar accuracy. However, the performance of the CSEOF–ARIMA model is better than that of the EOF–ARIMA model under various measurements. Therefore, the CSEOF–ARIMA composite forecast model can be considered an efficient and feasible technology representing an analytical approach for precipitation forecasting in South Korea.

DIC-ST: A Hybrid Prediction Framework Based on Causal Structure Learning for Cellular Traffic and Its Application in Urban Computing

The development of technology has strongly affected regional urbanization. With development of mobile communication technology, intelligent devices have become increasingly widely used in people’s lives. The application of big data in urban computing is multidimensional; it has been involved in different fields, such as urban planning, network optimization, intelligent transportation, energy consumption and so on. Data analysis becomes particularly important for wireless networks. In this paper, a method for analyzing cellular traffic data was proposed. Firstly, a method to extract trend components, periodic components and essential components from complex traffic time series was proposed. Secondly, we introduced causality data mining. Different from traditional time series causality analysis, the depth of causal mining was increased. We conducted causality verification on different components of time series and the results showed that the causal relationship between base stations is different in trend component, periodic component and essential component in urban wireless network. This is crucial for urban planning and network management. Thirdly, DIC-ST: a spatial temporal time series prediction based on decomposition and integration system with causal structure learning was proposed by combining GCN. Final results showed that the proposed method significantly improves the accuracy of cellular traffic prediction. At the same time, this method can play a crucial role for urban computing in network management, intelligent transportation, base station siting and energy consumption when combined with remote sensing map information.

The Importance of Noise Colour in Simulations of Evolutionary Systems.

Simulations of evolutionary dynamics often employ white noise as a model of stochastic environmental variation. Whilst white noise has the advantages of being simply generated and analytically tractable, empirical analyses demonstrate that most real environmental time series have power spectral densities consistent with pink or red noise, in which lower frequencies contribute proportionally greater amplitudes than higher frequencies. Simulated white noise environments may therefore fail to capture key components of real environmental time series, leading to erroneous results. To explore the effects of different noise colours on evolving populations, a simple evolutionary model of the interaction between life-history and the specialism-generalism axis was developed. Simulations were conducted using a range of noise colours as the environments to which agents adapted. Results demonstrate complex interactions between noise colour, reproductive rate, and the degree of evolved generalism; importantly, contradictory conclusions arise from simulations using white as opposed to red noise, suggesting that noise colour plays a fundamental role in generating adaptive responses. These results are discussed in the context of previous research on evolutionary responses to fluctuating environments, and it is suggested that Artificial Life as a field should embrace a wider spectrum of coloured noise models to ensure that results are truly representative of environmental and evolutionary dynamics.

Combining autoregressive integrated moving average with Long Short-Term Memory neural network and optimisation algorithms for predicting ground water level

The groundwater resources are the essential sources for irrigation and agriculture management. Forecasting groundwater levels (GWL) for the current and future periods is an essential topic of watershed management. The prediction of GWL helps prevent overexploitation. The Auto-Regressive Integrated Moving Average model (ARIMA) is a widely known linear statistical model. One of the drawbacks of the ARIMA models is that they may not capture all existing patterns, such as non-linear parts of time series. This article introduces a new hybrid model, namely the ARIMA-Long Short-Term Memory (LSTM) neural network, to capture the linear and non-linear components of a GWL time series in the Yazd-Ardekn Plain in Iran. This study applied the ARIMA-LSTM in forecasting three-, six-, and nine-month-ahead GWL. To determine the hyperparameters of the LSTM algorithm, the Salp Swarm Algorithm (SSA), sine cosine optimisation algorithm (SCOA), particle swarm optimisation algorithm (PSOA), and genetic algorithm (GA) were coupled with the LSTM model. Two different scenarios were devised to introduce new input combinations. In the first scenario, the residual values of the ARIMA model and the lagged GWL data were inserted into hybrid and standalone LSTM models for forecasting the GWL. In the second scenario, the summation of the outputs of the ARIMA and LSTM models gave the final outputs. In terms of the content of three-month-ahead GWL predictions for the second scenario, the ARIMA-LSTM-SSA produced better results than the ARIMA-LSTM-SCOA, ARIMA-LSTM-PSOA, ARIMA-LSTM-GA, ATIMA-LSTM, LSTM, and ARIMA algorithms, which had lower mean absolute error values (MAE) of 5%, 9.4%, 15%, 38%, 42%, and 47%, respectively. However, the general results indicated that an increased forecasting horizon reduced the accuracy of the models. The new hybrid ARIMA-LSTM- SSA model was highly capable of forecasting other hydrological variables for capturing non-linear and linear elements of the time series.

Interannual Variability and Trends of Sea Surface Temperature Around Southern South America

The interannual variability and trends of sea surface temperature (SST) around southern South America are studied from 1982 to 2017 using monthly values of the Optimally Interpolation SST version 2 gridded database. Mid-latitude (30°–50°S) regions in the eastern South Pacific and western South Atlantic present moderate to intense warming (~0.4°C decade−1), while south of 50°S the region around southern South America presents moderate cooling (~ −0.3°C decade−1). Two areas of statistically significant trends of SST anomalies (SSTa) with opposite sign are found on the Patagonian Shelf over the southwest South Atlantic: a warming area delimited between 42 and 45°S (Northern Patagonian Shelf; NPS), and a cooling area between 49 and 52°S (Southern Patagonian Shelf; SPS). Between 1982 and 2017 the warming rate has been 0.15 ± 0.01°C decade−1 representing an increase of 0.52°C at NPS, and the cooling rate has been –0.12 ± 0.01°C decade−1 representing a decrease of 0.42°C at SPS. On both regions, the largest trends are observed during 2008–2017 (0.35 ± 0.02°C decade−1 at NPS and –0.27 ± 0.03°C decade−1 at SPS), while the trends in 1982–2007 are non-significant, indicating the record-length SSTa trends are mostly associated with the variability observed during the past 10 years of the record. The spectra of the records present significant variance at interannual time scales, centered at about 80 months (~6 years). The observed variability of SSTa is studied in connection with atmospheric forcing (zonal and meridional wind components, wind speed, wind stress curl and surface heat fluxes). During 1982–2007, the local meridional wind explains 25–30% of the total variance at NPS and SPS on interannual time scales. During 2008–2017, the SSTa at NPS is significantly anticorrelated with the local zonal wind (r = –0.85), while at SPS it is significantly anticorrelated with the meridional wind (r = –0.61). Our results show that a substantial fraction of the interannual variability of SSTa around southern South America can be described by the first three empirical orthogonal function (EOF) modes which explain 28, 16, and 12% of the variance, respectively. The variability of the three EOF principal components time series is associated with the combined variability of El Niño–Southern Oscillation, the Interdecadal Pacific Oscillation and the Southern Annular Mode.

Copula Modelling to Analyse Financial Data

Copula modelling is a popular tool in analysing the dependencies between variables. Copula modelling allows the investigation of tail dependencies, which is of particular interest in risk and survival applications. Copula modelling is also of specific interest to economic and financial modelling as it can help in the prediction of financial contagion and periods of “boom” or “bust”. Bivariate copula modelling has a rich variety of copulas that may be chosen to represent the modelled dataset dependencies and possible extreme events that may lie within the dataset tails. Financial copula modelling tends to diverge as this richness of copula types within the literature may not be well realised with the two different types of modelling, one being non-time-series and the other being time-series, being undertaken differently. This paper investigates standard copula modelling and financial copula modelling and shows why the modelling strategies in using time-series and non-time-series copula modelling is undertaken using different methods. This difference, apart from the issues surrounding the time-series component, is mostly due to standard copula modelling having the ability to use empirical CDFs for the probability integral transformation. Financial time-series copula modelling uses pseudo-CDFs due to the standardized time-series residuals being centred around zero. The standardized residuals inhibit the estimation of the possible distributions required for constructing the copula model in the usual manner.

Data driven approach to forecast the next day aggregate production of scattered small rooftop solar photovoltaic systems without meteorological parameters

Photovoltaic (PV) power has became an attractive research subject, despite the variability and uncertainty of the phenomenon, PV power forecasting is considered as a promising solution for successful PV power integration, and also an important decision making information for both, grid operators and energy traders. Forecasting the aggregated PV power in different spatiotemporal scales is very relevant for grid operators, but unfortunately, in the state of the art, few works deal with this subject. In the aim to forecast directly the next day aggregate photovoltaic power of scattered small rooftop installations based only on historical production data, we propose in this paper a hybrid nonlinear autoregressive regression model, composed from a combination of empirical mode decomposition (EMD), stepwise regression (SWR) and least square support vector regression (LsSVR) techniques. To address the lack of meteorological parameters, we propose a different data preprocessing strategy, this strategy will also allow capturing the diurnal component of the PV power time series in an efficient way. An in depth analysis of the proposed approach using publicly available database was conducted. We compared the results of the proposed approach with three other models, two nonlinear autoregressive models based on LsSVR (AR-LsSVR) and FFNN (AR-FFNN), and the third one is a persistent forecaster. Three accuracy metrics were adopted to compare the different models, the nMAE, nMBE and nMRSE. In general good results were obtained in clear and partially cloudy days, but there are few days characterized by sudden change in the time series pattern that the model cant handle. But still competitive results are obtained, the hybrid model gives an nMAE = 4.12% compared to 4.94%, 4.95% and 164.98% for AR-LsSVR, AR-FFNN and the persistent forecaster respectively. The projection of the obtained results on five recently developed models shows the effectiveness of the proposed approach.