相关论文
2016 - Computational Intelligence and Neuroscience
Financial Time Series Prediction Using Elman Recurrent Random Neural Networks

In recent years, financial market dynamics forecasting has been a focus of economic research. To predict the price indices of stock markets, we developed an architecture which combined Elman recurrent neural networks with stochastic time effective function. By analyzing the proposed model with the linear regression, complexity invariant distance (CID), and multiscale CID (MCID) analysis methods and taking the model compared with different models such as the backpropagation neural network (BPNN), the stochastic time effective neural network (STNN), and the Elman recurrent neural network (ERNN), the empirical results show that the proposed neural network displays the best performance among these neural networks in financial time series forecasting. Further, the empirical research is performed in testing the predictive effects of SSE, TWSE, KOSPI, and Nikkei225 with the established model, and the corresponding statistical comparisons of the above market indices are also exhibited. The experimental results show that this approach gives good performance in predicting the values from the stock market indices.

2008 - EDBT '08
The TS-tree: efficient time series search and retrieval

Continuous growth in sensor data and other temporal data increases the importance of retrieval and similarity search in time series data. Efficient time series query processing is crucial for interactive applications. Existing multidimensional indexes like the R-tree provide efficient querying for only relatively few dimensions. Time series are typically long which corresponds to extremely high dimensional data in multidimensional indexes. Due to massive overlap of index descriptors, multidimensional indexes degenerate for high dimensions and access the entire data by random I/O. Consequently, the efficiency benefits of indexing are lost. In this paper, we propose the TS-tree (time series tree), an index structure for efficient time series retrieval and similarity search. Exploiting inherent properties of time series quantization and dimensionality reduction, the TS-tree indexes high-dimensional data in an overlap-free manner. During query processing, powerful pruning via quantized separator and meta data information greatly reduces the number of pages which have to be accessed, resulting in substantial speed-up. In thorough experiments on synthetic and real world time series data we demonstrate that our TS-tree outperforms existing approaches like the R*-tree or the quantized A-tree.

2014 - Isprs Journal of Photogrammetry and Remote Sensing
Improved maize cultivated area estimation over a large scale combining MODIS–EVI time series data and crop phenological information

Abstract The accurate and timely information of crop area is vital for crop production and food security. In this study, the Enhanced Vegetation Index (EVI) data from MODerate resolution Imaging Spectroradiometer (MODIS) integrated crop phenological information was used to estimate the maize cultivated area over a large scale in Northeast China. The fine spatial resolution China’s Environment Satellite (HJ-1 satellite) images and the support vector machine (SVM) algorithm were employed to discriminate distribution of maize in the reference area. The mean MODIS–EVI time series curve of maize was extracted in the reference area by using multiple periods MODIS–EVI data. By analysing the temporal shift of crop calendars from northern to southern parts in Northeast China, the lag value was derived from phenological data of twenty-one agro-meteorological stations; here integrating with the mean MODIS–EVI time series image of maize, a standard MODIS–EVI time series image of maize was obtained in the whole study area. By calculating mean absolute distances (MAD) map between standard MODIS–EVI image and mean MODIS–EVI time series images, and setting appropriate thresholds in three provinces, the maize cultivated area was extracted in Northeast China. The results showed that the overall classification accuracy of maize cultivated area was approximately 79%. At the county level, the MODIS-derived maize cultivated area and statistical data were well correlated ( R 2  = 0.82, RMSE = 283.98) over whole Northeast China. It demonstrated that MODIS–EVI time series data integrated with crop phenological information can be used to improve the extraction accuracy of crop cultivated area over a large scale.

1974 - Journal of Applied Probability
ON THE INVERSES OF SOME PATTERNED MATRICES ARISING IN THE THEORY OF STATIONARY TIME SERIES

Expressions are obtained for the determinant and inverse of the covariance matrix of a set of n consecutive observations on a mixed autoregressive moving average process. Explicit formulae for the inverse of this matrix are given for the general autoregressive process of order p (n ? p), and for the first order mixed autoregressive moving average process.

1984 - Journal of Business & Economic Statistics
Forecasting Contemporaneously Aggregated Vector ARMA Processes

Given a multiple time series that is generated by a multivariate ARMA process and assuming the objective is to forecast a weighted sum of the individual variables, then under a mean squared error measure of forecasting precision, it is preferable to forecast the disaggregated multiple time series and aggregate the forecasts, rather than forecast the aggregated series directly, if the involved processes are known. This result fails to hold if the processes used for forecasting are estimated from a given set of time series data. The implications of these results for empirical research are investigated using different sets of economic data.

2012 - 2012 IEEE 12th International Conference on Data Mining
Clustering Time Series Using Unsupervised-Shapelets

Time series clustering has become an increasingly important research topic over the past decade. Most existing methods for time series clustering rely on distances calculated from the entire raw data using the Euclidean distance or Dynamic Time Warping distance as the distance measure. However, the presence of significant noise, dropouts, or extraneous data can greatly limit the accuracy of clustering in this domain. Moreover, for most real world problems, we cannot expect objects from the same class to be equal in length. As a consequence, most work on time series clustering only considers the clustering of individual time series "behaviors," e.g., individual heart beats or individual gait cycles, and contrives the time series in some way to make them all equal in length. However, contriving the data in such a way is often a harder problem than the clustering itself. In this work, we show that by using only some local patterns and deliberately ignoring the rest of the data, we can mitigate the above problems and cluster time series of different lengths, i.e., cluster one heartbeat with multiple heartbeats. To achieve this we exploit and extend a recently introduced concept in time series data mining called shapelets. Unlike existing work, our work demonstrates for the first time the unintuitive fact that shapelets can be learned from unlabeled time series. We show, with extensive empirical evaluation in diverse domains, that our method is more accurate than existing methods. Moreover, in addition to accurate clustering results, we show that our work also has the potential to give insights into the domains to which it is applied.

2008 - Expert Syst. Appl.
Financial time series prediction using polynomial pipelined neural networks

This paper proposes a novel type of higher-order pipelined neural network: the polynomial pipelined neural network. The proposed network is constructed from a number of higher-order neural networks concatenated with each other to predict highly nonlinear and nonstationary signals based on the engineering concept of divide and conquer. The polynomial pipelined neural network is used to predict the exchange rate between the US dollar and three other currencies. In this application, two sets of experiments are carried out. In the first set, the input data are pre-processed between 0 and 1 and passed to the neural networks as nonstationary data. In the second set of experiments, the nonstationary input signals are transformed into one step relative increase in price. The network demonstrates more accurate forecasting and an improvement in the signal to noise ratio over a number of benchmarked neural networks.

2009 - BMC Systems Biology
Identification of neutral biochemical network models from time series data

BackgroundThe major difficulty in modeling biological systems from multivariate time series is the identification of parameter sets that endow a model with dynamical behaviors sufficiently similar to the experimental data. Directly related to this parameter estimation issue is the task of identifying the structure and regulation of ill-characterized systems. Both tasks are simplified if the mathematical model is canonical, i.e., if it is constructed according to strict guidelines.ResultsIn this report, we propose a method for the identification of admissible parameter sets of canonical S-systems from biological time series. The method is based on a Monte Carlo process that is combined with an improved version of our previous parameter optimization algorithm. The method maps the parameter space into the network space, which characterizes the connectivity among components, by creating an ensemble of decoupled S-system models that imitate the dynamical behavior of the time series with sufficient accuracy. The concept of sloppiness is revisited in the context of these S-system models with an exploration not only of different parameter sets that produce similar dynamical behaviors but also different network topologies that yield dynamical similarity.ConclusionThe proposed parameter estimation methodology was applied to actual time series data from the glycolytic pathway of the bacterium Lactococcus lactis and led to ensembles of models with different network topologies. In parallel, the parameter optimization algorithm was applied to the same dynamical data upon imposing a pre-specified network topology derived from prior biological knowledge, and the results from both strategies were compared. The results suggest that the proposed method may serve as a powerful exploration tool for testing hypotheses and the design of new experiments.

2018 - 2018 17th IEEE International Conference on Machine Learning and Applications (ICMLA)
Unsupervised Anomaly Detection in Energy Time Series Data Using Variational Recurrent Autoencoders with Attention

In the age of big data, time series are being generated in massive amounts. In the energy field, smart grids are enabling a unprecedented data acquisition with the integration of sensors and smart devices. In the context of renewable energies, there has been an increasing interest in solar photovoltaic energy generation. These installations are often integrated with smart sensors that measure the energy production. Such amount of data collected makes the quest for developing smart monitoring systems that can detect anomalous behaviour in these systems, trigger alerts and enable maintenance operations. In this paper, we propose a generic, unsupervised and scalable framework for anomaly detection in time series data, based on a variational recurrent autoencoder. Furthermore, we introduce attention in the model, by means of a variational self-attention mechanism (VSAM), to improve the performance of the encoding-decoding process. Afterwards, we perform anomaly detection based on the probabilistic reconstruction scores provided by our model. Our results on solar energy generation time series show the ability of the proposed approach to detect anomalous behaviour in time series data, while providing structured and expressive representations. Since it does not need labels to be trained, our methodology enables new applications for anomaly detection in energy time series data and beyond.

1996 - Econometric Reviews
Recent developments in bootstrapping time series

In recent years, several new parametric and nonparametric bootstrap methods have been proposed for time series data. Which of these methods should applied researchers use? We provide evidence that for many applications in time series econometrics parametric methods are more accurate, and we identify directions for future research on improving nonparametric methods. We explicitly address the important, but often neglected issue of model selection in bootstrapping. In particular, we emphasize the advantages of the AIC over other lag order selection criteria and the need to account for lag order uncertainty in resampling. We also show that the block size plays an important role in determining the success of the block bootstrap, and we propose a data-based block size selection procedure.

2014 - Journal of Econometrics
Spillover Dynamics for Systemic Risk Measurement Using Spatial Financial Time Series Models

We extend the well-known static spatial Durbin model by introducing a time-varying spatial dependence parameter. The updating steps for this model are functions of past data and have information theoretic optimality properties. The static parameters are conveniently estimated by maximum likelihood. We establish the theoretical properties of the model and show that the maximum likelihood estimators of the static parameters are consistent and asymptotically normal. Using spatial weights based on cross-border lending data and European sovereign CDS spread data over the period 2009–2014, we find evidence of contagion in terms of high, time-varying spatial spillovers in the perceived credit riskiness of European sovereigns during the sovereign debt crisis. We find a particular downturn in spatial dependence in the second half of 2012 after the outright monetary transactions policy measures taken by the European Central Bank. Earlier non-standard monetary operations by the ECB did not induce such changes. The findings are robust to a wide range of alternative model specifications.

2010 - Renewable Energy
Wind speed forecasting in three different regions of Mexico, using a hybrid ARIMA–ANN model

In this paper the wind speed forecasting in the Isla de Cedros in Baja California, in the Cerro de la Virgen in Zacatecas and in Holbox in Quintana Roo is presented. The time series utilized are average hourly wind speed data obtained directly from the measurements realized in the different sites during about one month. In order to do wind speed forecasting Hybrid models consisting of Autoregressive Integrated Moving Average (ARIMA) models and Artificial Neural Network (ANN) models were developed. The ARIMA models were first used to do the wind speed forecasting of the time series and then with the obtained errors ANN were built taking into account the nonlinear tendencies that the ARIMA technique could not identify, reducing with this the final errors. Once the Hybrid models were developed 48 data out of sample for each one of the sites were used to do the wind speed forecasting and the results were compared with the ARIMA and the ANN models working separately. Statistical error measures such as the mean error (ME), the mean square error (MSE) and the mean absolute error (MAE) were calculated to compare the three methods. The results showed that the Hybrid models predict the wind velocities with a higher accuracy than the ARIMA and ANN models in the three examined sites.

2012 - Knowledge and Information Systems
Early classification on time series

In this paper, we formulate the problem of early classification of time series data, which is important in some time-sensitive applications such as health informatics. We introduce a novel concept of MPL (minimum prediction length) and develop ECTS (early classification on time series), an effective 1-nearest neighbor classification method. ECTS makes early predictions and at the same time retains the accuracy comparable with that of a 1NN classifier using the full-length time series. Our empirical study using benchmark time series data sets shows that ECTS works well on the real data sets where 1NN classification is effective.

1997 - Review of Economics and Statistics
Estimating the Density Tail Index for Financial Time Series

Abstract The tail index of a density has been widely used as an indicator of the probability of getting a large deviation in a random variable. Most of the theory underlying popular estimators of it assume that the data are independently and identically distributed (i.i.d.). However, many recent applications of the estimator have been to financial data, and such data tend to exhibit long-range dependence. We show, via Monte Carlo simulations, that conventional measures of the precision of the estimator, which are based on the i.i.d. assumption, are greatly exaggerated when such dependent data are used. This conclusion also has implications for estimates of the likelihood of getting some extreme values, and we illustrate the changed conclusions one would get using equity return data.

2017 - Journal of Systems Engineering and Electronics
Convolutional neural networks for time series classification

Time series classification is an important task in time series data mining, and has attracted great interests and tremendous efforts during last decades. However, it remains a challenging problem due to the nature of time series data: high dimensionality, large in data size and updating continuously. The deep learning techniques are explored to improve the performance of traditional feature-based approaches. Specifically, a novel convolutional neural network (CNN) framework is proposed for time series classification. Different from other feature-based classification approaches, CNN can discover and extract the suitable internal structure to generate deep features of the input time series automatically by using convolution and pooling operations. Two groups of experiments are conducted on simulated data sets and eight groups of experiments are conducted on real-world data sets from different application domains. The final experimental results show that the proposed method outperforms state-of-the-art methods for time series classification in terms of the classification accuracy and noise tolerance.

2000 - Journal of the American Statistical Association
Transitional Regression Models, with Application to Environmental Time Series

Abstract Environmental epidemiologists often encounter time series data in the form of discrete or other nonnormal outcomes; for example, in modeling the relationship between air pollution and hospital admissions or mortality rates. We present a case study examining the association between pollen counts and meteorologic covariates. Although such time series data are inadequately described by standard methods for Gaussian time series, they are often autocorrelated, and warrant an analysis beyond those provided by ordinary generalized linear models (GLMs). Transitional regression models (TRMs), signifying nonlinear regression models expressed in terms of conditional means and variances given past observations, provide a unifying framework for two mainstream approaches to extending the GLM for autocorrelated data. The first approach models current outcomes with a GLM that incorporates past outcomes as covariates, whereas the second models individual outcomes with marginal GLMs and then couples the error terms with an autoregressive covariance matrix. Although the two approaches coincide for the Gaussian GLM, which serves as a helpful introductory example, in general they yield fundamentally different models. We analyze the pollen study using TRM's of both types and present parameter estimates together with asymptotic and bootstrap standard errors. In several cases we find evidence of residual autocorrelation; however, when we relax the TRM to allow for a nonparametric smooth trend, the autocorrelation disappears. This kind of trade-off between autocorrelation and flexibility is to be expected, and has a natural interpretation in terms of the covariance function for a nonparametric smoother. We provide an algorithm for fitting these flexible TRM's that is relatively easy to program with the generalized additive model software in S-PLUS.

2002 - Proceedings of the eighth ACM SIGKDD international conference on Knowledge discovery and data mining
A unifying framework for detecting outliers and change points from non-stationary time series data

We are concerned with the issues of outlier detection and change point detection from a data stream. In the area of data mining, there have been increased interest in these issues since the former is related to fraud detection, rare event discovery, etc., while the latter is related to event/trend by change detection, activity monitoring, etc. Specifically, it is important to consider the situation where the data source is non-stationary, since the nature of data source may change over time in real applications. Although in most previous work outlier detection and change point detection have not been related explicitly, this paper presents a unifying framework for dealing with both of them on the basis of the theory of on-line learning of non-stationary time series. In this framework a probabilistic model of the data source is incrementally learned using an on-line discounting learning algorithm, which can track the changing data source adaptively by forgetting the effect of past data gradually. Then the score for any given data is calculated to measure its deviation from the learned model, with a higher score indicating a high possibility of being an outlier. Further change points in a data stream are detected by applying this scoring method into a time series of moving averaged losses for prediction using the learned model. Specifically we develop an efficient algorithms for on-line discounting learning of auto-regression models from time series data, and demonstrate the validity of our framework through simulation and experimental applications to stock market data analysis.

1990
Forecasting, Structural Time Series Models and the Kalman Filter

In this book, Andrew Harvey sets out to provide a unified and comprehensive theory of structural time series models. Unlike the traditional ARIMA models, structural time series models consist explicitly of unobserved components, such as trends and seasonals, which have a direct interpretation. As a result the model selection methodology associated with structural models is much closer to econometric methodology. The link with econometrics is made even closer by the natural way in which the models can be extended to include explanatory variables and to cope with multivariate time series. From the technical point of view, state space models and the Kalman filter play a key role in the statistical treatment of structural time series models. The book includes a detailed treatment of the Kalman filter. This technique was originally developed in control engineering, but is becoming increasingly important in fields such as economics and operations research. This book is concerned primarily with modelling economic and social time series, and with addressing the special problems which the treatment of such series poses. The properties of the models and the methodological techniques used to select them are illustrated with various applications. These range from the modellling of trends and cycles in US macroeconomic time series to to an evaluation of the effects of seat belt legislation in the UK.

2010
Statistical Analysis of Time Series

Chapter 31 contains formulas relevant for time series analysis: 31.1. Predictions in Time Series, 31.2. Decomposition of (Economic) Time Series, 31.3. Estimation of Correlation and Spectral Characteristics, 31.4. Linear Time Series, 31.5 Nonlinear and Financial Time Series, 31.6 Multivariate Time Series, 31.7. Kalman Filter.

2006 - Data Mining and Knowledge Discovery
Characteristic-Based Clustering for Time Series Data

AbstractWith the growing importance of time series clustering research, particularly for similarity searches amongst long time series such as those arising in medicine or finance, it is critical for us to find a way to resolve the outstanding problems that make most clustering methods impractical under certain circumstances. When the time series is very long, some clustering algorithms may fail because the very notation of similarity is dubious in high dimension space; many methods cannot handle missing data when the clustering is based on a distance metric.This paper proposes a method for clustering of time series based on their structural characteristics. Unlike other alternatives, this method does not cluster point values using a distance metric, rather it clusters based on global features extracted from the time series. The feature measures are obtained from each individual series and can be fed into arbitrary clustering algorithms, including an unsupervised neural network algorithm, self-organizing map, or hierarchal clustering algorithm.Global measures describing the time series are obtained by applying statistical operations that best capture the underlying characteristics: trend, seasonality, periodicity, serial correlation, skewness, kurtosis, chaos, nonlinearity, and self-similarity. Since the method clusters using extracted global measures, it reduces the dimensionality of the time series and is much less sensitive to missing or noisy data. We further provide a search mechanism to find the best selection from the feature set that should be used as the clustering inputs.The proposed technique has been tested using benchmark time series datasets previously reported for time series clustering and a set of time series datasets with known characteristics. The empirical results show that our approach is able to yield meaningful clusters. The resulting clusters are similar to those produced by other methods, but with some promising and interesting variations that can be intuitively explained with knowledge of the global characteristics of the time series.

Forecasting Economics and Financial Time Series: ARIMA vs. LSTM

Akbar Siami Namin
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Sima Siami-Namini
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Sima Siami‐Namini
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A. Namin

Abstract:Forecasting time series data is an important subject in economics, business, and finance. Traditionally, there are several techniques to effectively forecast the next lag of time series data such as univariate Autoregressive (AR), univariate Moving Average (MA), Simple Exponential Smoothing (SES), and more notably Autoregressive Integrated Moving Average (ARIMA) with its many variations. In particular, ARIMA model has demonstrated its outperformance in precision and accuracy of predicting the next lags of time series. With the recent advancement in computational power of computers and more importantly developing more advanced machine learning algorithms and approaches such as deep learning, new algorithms are developed to forecast time series data. The research question investigated in this article is that whether and how the newly developed deep learning-based algorithms for forecasting time series data, such as "Long Short-Term Memory (LSTM)", are superior to the traditional algorithms. The empirical studies conducted and reported in this article show that deep learning-based algorithms such as LSTM outperform traditional-based algorithms such as ARIMA model. More specifically, the average reduction in error rates obtained by LSTM is between 84 - 87 percent when compared to ARIMA indicating the superiority of LSTM to ARIMA. Furthermore, it was noticed that the number of training times, known as "epoch" in deep learning, has no effect on the performance of the trained forecast model and it exhibits a truly random behavior.

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