CSAR: the cross-sectional autoregression model for short and long-range forecasting

Forecasting time series data is an integral component for management, planning and decision making. Following the Big Data trend, large amounts of time series data are available from many heterogeneous data sources in more and more applications domains. The highly dynamic and often fluctuating character of these domains in combination with the logistic problems of collecting such data from a variety of sources, imposes new challenges to forecasting. Traditional approaches heavily rely on extensive and complete historical data to build time series models and are thus no longer applicable if time series are short or, even more important, intermittent. In addition, large numbers of time series have to be forecasted on different aggregation levels with preferably low latency, while forecast accuracy should remain high. This is almost impossible, when keeping the traditional focus on creating one forecast model for each individual time series. In this paper we tackle these challenges by presenting a novel forecasting approach called cross-sectional forecasting. This method is especially designed for Big Data sets with a multitude of time series. Our approach breaks with existing concepts by creating only one model for a whole set of time series and requiring only a fraction of the available data to provide accurate forecasts. By utilizing available data from all time series of a data set, missing values can be compensated and accurate forecasting results can be calculated quickly on arbitrary aggregation levels.

Time series data are collected based on certain periods which have constants value (e.g. daily, weekly or monthly), it can be used to forecast or predict future circumstance. Prediction is one of the objectives of the time series analysis by identifying the model from previous data and assuming the current information will also occur in the future. In Big Data trend, huge amount of time series data come from different heterogeneous sources and multiple application domains. This present a new challenge for time series forecasting. Time series modelling has been widely applied and proposed in various fields to improve its accuracy and efficiency of forecasting. This paper discusses time series forecasting for electricity consumption using kernel principal component analysis (KPCA) and Support Vector Machine (SVM). This research will be measured with Mean Absolute Error and Mean Squared Error.

Time series analysis is a key technique for extracting and predicting events in domains as diverse as epidemiology, genomics, neuroscience, environmental sciences, economics, and more. Matrix profile, the state-of-the-art algorithm to perform time series analysis, computes the most similar subsequence for a given query subsequence within a sliced time series. Matrix profile has low arithmetic intensity, but it typically operates on large amounts of time series data. In current computing systems, this data needs to be moved between the off-chip memory units and the on-chip computation units for performing matrix profile. This causes a major performance bottleneck as data movement is extremely costly in terms of both execution time and energy. In this work, we present NATSA, the first Near-Data Processing accelerator for time series analysis. The key idea is to exploit modern 3D-stacked High Bandwidth Memory (HBM) to enable efficient and fast specialized matrix profile computation near memory, where time series data resides. NATSA provides three key benefits: 1) quickly computing the matrix profile for a wide range of applications by building specialized energy-efficient floating-point arithmetic processing units close to HBM, 2) improving the energy efficiency and execution time by reducing the need for data movement over slow and energy-hungry buses between the computation units and the memory units, and 3) analyzing time series data at scale by exploiting low-latency, high-bandwidth, and energy-efficient memory access provided by HBM. Our experimental evaluation shows that NATSA improves performance by up to 14.2× (9.9× on average) and reduces energy by up to 27.2 × (19.4 × on average), over the state-of-the-art multi-core implementation. NATSA also improves performance by 6.3 × and reduces energy by 10.2 × over a general-purpose NDP platform with 64 in-order cores.

Sequences constitute a large portion of data stored in databases. Data mining applications require the ability to process similarity queries over a large amount of time series data. The query processing performance is an important factor that needs to be taken into consideration. This article proposes a similarity retrieval algorithm for time series. The proposed approach utilizes wavelet transformation in order to reduce the dimensionality of the time series. The transformed series are indexed using X-Trees, which is a spatial indexing technique able to efficiently index high-dimensional data. The article proves that this technique outperforms the usage of the Fourier transformation, since the wavelet transformation provides better approximation of the time series. Through the experiments, it can be concluded that the optimum performance is obtained using 16 to 20 wavelet coefficients. Furthermore, a novel mechanism for reducing the complexity of the calculation for the false alarms removal is proposed. Storing the approximation coefficients of the penultimate level of the decomposition tree, the Euclidean distance between the two sequences is calculated, thus reducing further the number of false alarms before calculating the actual Euclidean distance using the complete time series. The article concludes with a detailed performance evaluation of the proposed similarity retrieval algorithm using data from the Greek stock market and the temperature measurements from Athens. The comparison is done with techniques that use the Haar transform and the R*-Tree, and the proposed algorithm is shown to outperform them.

In the big data era, large amounts of time series data have been collected from scientific experiments and business operations. With the fast growth of data volume, significant challenges in pattern recognition has emerged in diverse time series analysis systems. Since existing methods are inefficient and not applicable to large-scale and especially incremental time series, this paper proposes a novel and efficient pattern recognition method named MDLits for large-scale and incremental time series. It eliminates most redundant computation in the related works, and re-uses existing information by exploiting the correlation between existing data and newly-arrived ones. A Hadoop platform is implemented for clinical electrocardiography classification. The experiments on practical healthcare data show that our method outperforms the related arts in processing time, precision and recall. Moreover, it can scale to a large size and fit to incremental time series, which demonstrates the effectiveness and scalability of our method and system.

In this paper, we propose a method for creating a reduced-order model (ROM) for temperature prediction that can be applied to nonlinear time-variant systems. Our nonlinear time-variant ROM is an extension of sparse identification of nonlinear dynamical systems, first proposed in 2016. Three machine learning methods are developed for automatically deriving a thermal network model from time series data. Link relationships between temperature nodes and parameter settings, such as thermal resistance and heat capacity, are automatically inferred by machine learning. Because the proposed model targets phenomena that can be represented as a thermal network model, it can deal with forced convection with velocity as a variable. The model can also handle natural convection and radiation, where thermal resistance is a function of temperature. The model can be created using a very small amount of time series data. Unlike black-box AI, the proposed model is easy to interpret; in other words, it enables us to understand the heat transfer process. Furthermore, because it is based on a physical model, it has high prediction accuracy when extrapolated. The effectiveness of the proposed method is demonstrated using the results of thermo-fluid analysis for an air-cooled power module. In addition, because the proposed method can be created using a very small amount of time series data, has high extrapolation accuracy, and is easy to interpret, it is expected not only that design parameters can be fine-tuned and actual loads can be taken into account, but also that condition-based maintenance can be realized through real-time simulation.

Large amount of time series data generated by sensors and Web users is great source of contextual information. Detecting outliers with unusually high values in time series data is crucial for inferring about any events in the real world. In this work, we describe an infinite Poisson mixture model to detect events by identifying outliers in time series of count data. This unsupervised technique estimates the probability densities of count data which have an unknown Poisson mixture while it simultaneously detects outliers in the data. The advantage of our model is that outliers are mapped to mixture components discovered by infinite mixture model and thus inference can be drawn on the different 'types' of outliers and their proportions in the data. This lets us identify and categorize events based on magnitude of outlier data. We have analysed the performance of our model against a well known event detection technique based on Markov Modulated Poisson Process (MMPP) using synthetic and real world data. Results show that our approach to detecting events is more appropriate in analysing periodic count data as compared to the MMPP baseline. The experiments demonstrate that the presented model provides robust, detailed, and interpretable results for the analysis of outliers to detect events.

Continuation processes in chemical and/or biotechnical plants always generate a large amount of time series data. However, since conventional process models are described as a set of control models, it is difficult to explain the complicated and active plant behaviors. Based on the background, this research proposes a novel method to develop a process response model from continuous time-series data.

Improving forecasting accuracy of time series data using a new ARIMA-ANN hybrid method and empirical mode decomposition

Evaluation of hybrid forecasting approaches for wind speed and power generation time series

Fuzzy time series is widely used in forecasting time series data in linguistic forms. Implementing the intuitionistic fuzzy sets (IFS) in fuzzy time series can better handle uncertainties and vagueness in the time series data. However, the time series data always fluctuate randomly and cause drastic changes. In this study, the 4253HT smoother is integrated with the intuitionistic fuzzy time series forecasting model to improve the forecasting accuracy. The proposed model is implemented in predicting the Malaysian crude palm oil prices. The data are firstly smoothed, and followed with the fuzzification process. Next are the transformation of fuzzy sets into IFS and the de-i-fuzzification via equal distribution of hesitancy. The forecasted data are calculated based on the defuzzified values considering the new membership degrees of the IFS after de-i-fuzzification. The results show that the integrated model produces a better forecasting performance compared to the common intuitionistic fuzzy time series forecasting model. In the future, the integration of the data smoothing should be considered before the forecasting of data using fuzzy time series could be performed.

SummaryTo quantify the major environmental drivers of stream bacterial population dynamics, we modelled temporal differences in stream bacterial communities to quantify community shifts, including those relating to cyclical seasonal variation and more sporadic bloom events. We applied Illumina MiSeq 16S rRNA bacterial gene sequencing of 892 stream biofilm samples, collected monthly for 36‐months from six streams. The streams were located a maximum of 118 km apart and drained three different catchment types (forest, urban and rural land uses). We identified repeatable seasonal patterns among bacterial taxa, allowing their separation into three ecological groupings, those following linear, bloom/trough and repeated, seasonal trends. Various physicochemical parameters (light, water and air temperature, pH, dissolved oxygen, nutrients) were linked to temporal community changes. Our models indicate that bloom events and seasonal episodes modify biofilm bacterial populations, suggesting that distinct microbial taxa thrive during these events including non‐cyanobacterial community members. These models could aid in determining how temporal environmental changes affect community assembly and guide the selection of appropriate statistical models to capture future community responses to environmental change.

Granular modelling of signals: A framework of Granular Computing

Deep learning methods such as recurrent neural network and long short-term memory have recently drawn a lot of attentions in many fields such as computer vision, natural language processing and finance. Long short-term memory is a type of recurrent neural network capable of predicting future values of sequential data by learning observed data over time. Many real-world time series in business, finance, weather forecasting and engineering science have periodic property like daily, monthly, quarterly or yearly period and need efficient tools to forecast their future events and values. The forecasting study and tools in these fields are therefore essential and important. In this paper, we present a deep learning technique, called bidirectional long short-term memory, in forecasting time series data. The bidirectional long short-term memory model is evaluated based on the benchmark periodic time series dataset. The model performs well on the macro and industry categories and achieves average mean absolute percentage errors less than 9%. It is shown that the bidirectional architecture obtains the better results than the baseline models. We also test the model by tuning the time step parameter to evaluate how the time step length impacts on forecasting performance of the model.

The k-nearest neighbour (k-NN) algorithm is one of the most widely used benchmark algorithms in classification, supported by its simplicity and intuitiveness in finding similar instances in multivariate and large-dimensional feature spaces of arbitrary attribute scales. In contrast, only few scientific studies of k-NN exist in forecasting time series data, which have mainly assessed various distance metrics to identify similar univariate time series motifs in past data. In electricity load forecasting, k-NN studies are limited to identifying past motifs of the same dependent variable to match future realisations, in a non-causal approach to forecasting. However, causal information in the form of deterministic calendar information is readily available on past and future time series motifs, allowing the distinction between load profiles of working days, weekends and bank-holidays to be encoded as binary dummy variables, and to be efficiently included in the search for similar neighbours. In this paper, we propose a multivariate k-NN regression method for forecasting the electricity demand in the UK market which utilises binary dummy variables as a second feature to categorise the day being forecasted as a working day or a non-working day. We assess the efficacy of this approach in a robust empirical evaluation using UK electricity load data. The approach shows improvements beyond conventional k-NN approaches and accuracy beyond that of simple statistical benchmark methods.