相关论文
2003
Regression Theory for Categorical Time Series

Categorical---or qualitative---time series data with random time-dependent covariates are frequently encountered in diverse applications as the list of examples shows. As with "ordinary'' time series, the data analyst is faced with the same problems of modeling, estimation, model checking, diagnostics and prediction. The present work shows that these questions can be attacked by means of regression theory for categorical time series whose foundation is based on generalized linear models and partial likelihood inference. A variety of models are provided to illustrate the selection of the link function and recent large sample results are reviewed. The theory is developed without resorting to the Markov assumption and to the notion of stationarity. Moreover, regression methods for categorical time series allow for parsimonious modeling and incorporation of random time-dependent covariates as opposed to other procedures. In particular, nominal and ordinal time series are analyzed and compared empirically to Markov chains and mixture transition distribution models.

2006 - Journal of Asian Economics
Maximum entropy ensembles for time series inference in economics

Abstract This paper uses three examples of potential interest to Asian economists to support a new tool for statistical inference with time series data. In traditional theory, an ensemble Ω represents the ‘population’ behind the observed time series. Vinod [Vinod, H. D., 2004. Ranking mutual funds using unconventional utility theory and stochastic dominance, Journal of Empirical Finance, 11(3) 2004, 353–377] proposed new maximum entropy (ME) bootstrap to construct J (=999, say) elements of Ω for inference using a seven-step algorithm designed to satisfy the ergodic theorem. The algorithm's practical appeal to applied econometricians is that it avoids all structural change and unit root type testing involving complicated asymptotics and all shape-destroying transformations like de-trending or differencing to achieve stationarity. This paper simplifies and speeds up the algorithm, extends it to panel data, discusses underlying assumptions and formal properties including proving that it satisfies Doob's theorem. We show that the constructed ensemble elements retain the basic shape and dependence structure of autocorrelation function (acf) and partial autocorrelation function (pacf) of the original time series.

2004 - Proceedings. 20th International Conference on Data Engineering
Online amnesic approximation of streaming time series

The past decade has seen a wealth of research on time series representations, because the manipulation, storage, and indexing of large volumes of raw time series data is impractical. The vast majority of research has concentrated on representations that are calculated in batch mode and represent each value with approximately equal fidelity. However, the increasing deployment of mobile devices and real time sensors has brought home the need for representations that can be incrementally updated, and can approximate the data with fidelity proportional to its age. The latter property allows us to answer queries about the recent past with greater precision, since in many domains recent information is more useful than older information. We call such representations amnesic. While there has been previous work on amnesic representations, the class of amnesic functions possible was dictated by the representation itself. We introduce a novel representation of time series that can represent arbitrary, user-specified amnesic functions. For example, a meteorologist may decide that data that is twice as old can tolerate twice as much error, and thus, specify a linear amnesic function. In contrast, an econometrist might opt for an exponential amnesic function. We propose online algorithms for our representation, and discuss their properties. Finally, we perform an extensive empirical evaluation on 40 datasets, and show that our approach can efficiently maintain a high quality amnesic approximation.

2014 - Proceedings of the 20th ACM SIGKDD international conference on Knowledge discovery and data mining
Correlating events with time series for incident diagnosis

As online services have more and more popular, incident diagnosis has emerged as a critical task in minimizing the service downtime and ensuring high quality of the services provided. For most online services, incident diagnosis is mainly conducted by analyzing a large amount of telemetry data collected from the services at runtime. Time series data and event sequence data are two major types of telemetry data. Techniques of correlation analysis are important tools that are widely used by engineers for data-driven incident diagnosis. Despite their importance, there has been little previous work addressing the correlation between two types of heterogeneous data for incident diagnosis: continuous time series data and temporal event data. In this paper, we propose an approach to evaluate the correlation between time series data and event data. Our approach is capable of discovering three important aspects of event-timeseries correlation in the context of incident diagnosis: existence of correlation, temporal order, and monotonic effect. Our experimental results on simulation data sets and two real data sets demonstrate the effectiveness of the algorithm.

2013 - Bioinformatics
Efficient statistical significance approximation for local similarity analysis of high-throughput time series data

MOTIVATION Local similarity analysis of biological time series data helps elucidate the varying dynamics of biological systems. However, its applications to large scale high-throughput data are limited by slow permutation procedures for statistical significance evaluation. RESULTS We developed a theoretical approach to approximate the statistical significance of local similarity analysis based on the approximate tail distribution of the maximum partial sum of independent identically distributed (i.i.d.) random variables. Simulations show that the derived formula approximates the tail distribution reasonably well (starting at time points > 10 with no delay and > 20 with delay) and provides P-values comparable with those from permutations. The new approach enables efficient calculation of statistical significance for pairwise local similarity analysis, making possible all-to-all local association studies otherwise prohibitive. As a demonstration, local similarity analysis of human microbiome time series shows that core operational taxonomic units (OTUs) are highly synergetic and some of the associations are body-site specific across samples. AVAILABILITY The new approach is implemented in our eLSA package, which now provides pipelines for faster local similarity analysis of time series data. The tool is freely available from eLSA's website: http://meta.usc.edu/softs/lsa. SUPPLEMENTARY INFORMATION Supplementary data are available at Bioinformatics online. CONTACT fsun@usc.edu.

2015 - Biometrika
Information-theoretic optimality of observation-driven time series models for continuous responses

We investigate information-theoretic optimality properties of the score function of the predictive likelihood as a device for updating a real-valued time-varying parameter in a univariate observation-driven model with continuous responses. We restrict our attention to models with updates of one lag order. The results provide theoretical justification for a class of score-driven models which includes the generalized autoregressive conditional heteroskedasticity model as a special case. Our main contribution is to show that only parameter updates based on the score will always reduce the local Kullback–Leibler divergence between the true conditional density and the model-implied conditional density. This result holds irrespective of the severity of model misspecification. We also show that use of the score leads to a considerably smaller global Kullback–Leibler divergence in empirically relevant settings. We illustrate the theory with an application to time-varying volatility models. We show that the reduction in Kullback–Leibler divergence across a range of different settings can be substantial compared to updates based on, for example, squared lagged observations.

2015 - Atmospheric Environment
Imputation of missing data in time series for air pollutants

Abstract Missing data are major concerns in epidemiological studies of the health effects of environmental air pollutants. This article presents an imputation-based method that is suitable for multivariate time series data, which uses the EM algorithm under the assumption of normal distribution. Different approaches are considered for filtering the temporal component. A simulation study was performed to assess validity and performance of proposed method in comparison with some frequently used methods. Simulations showed that when the amount of missing data was as low as 5%, the complete data analysis yielded satisfactory results regardless of the generating mechanism of the missing data, whereas the validity began to degenerate when the proportion of missing values exceeded 10%. The proposed imputation method exhibited good accuracy and precision in different settings with respect to the patterns of missing observations. Most of the imputations obtained valid results, even under missing not at random. The methods proposed in this study are implemented as a package called mtsdi for the statistical software system R .

2016 - Agriculture
How Much Meteorological Information Is Necessary to Achieve Reliable Accuracy for Rainfall Estimations

This paper reports the study of the effect of the length of the recorded data used for monthly rainfall forecasting. Monthly rainfall data for three periods of 5, 10, and 49 years were collected from Kermanshah, Mashhad, Ahvaz, and Babolsar stations and used for calibration time series models. Then, the accuracy of the forecasting models was investigated by the following year’s data. The following was concluded: In temperate and semi-arid climates, 60 observation data is sufficient for the following year’s rainfall forecasting. The accuracy of the time series models increased with increasing amounts of observation data of arid and humid climates. Time series models are appropriate tools for forecasting monthly rainfall forecasting in semi-arid climates. Determining the most critical rainfall month in each climate condition for agriculture schedules is a recommended aim for future studies.

1993 - Journal of Business & Economic Statistics
Unobserved-Component Time Series Models with Markov-Switching Heteroscedasticity: Changes in Regime and the Link between Inflation Rates and Inflation Uncertainty

In this article, I first extend the standard unobserved-component time series model to include Hamilton's Markov-switching heteroscedasticity. This will provide an alternative to the unobserved-component model with autoregressive conditional heteroscedasticity, as developed by Harvey, Ruiz, and Sentana and by Evans and Wachtel. I then apply a generalized version of the model to investigate the link between inflation and its uncertainty (U.S. data, gross national product deflator, 1958:1-1990:4). I assume that inflation consists of a stochastic trend (random-walk) component and a stationary autoregressive component, following Ball and Cecchetti, and a four-state model of U.S. inflation rate is specified. By incorporating regime shifts in both mean and variance structures, I analyze the interaction of mean and variance over long and short horizons. The empirical results show that inflation is costly because higher inflation is associated with higher long-run uncertainty.

1989 - Journal of Business & Economic Statistics
Time Series Models for Count or Qualitative Observations

Time series sometimes consist of count data in which the number of events occurring in a given time interval is recorded. Such data are necessarily nonnegative integers, and an assumption of a Poisson or negative binomial distribution is often appropriate. This article sets ups a model in which the level of the process generating the observations changes over time. A recursion analogous to the Kalman filter is used to construct the likelihood function and to make predictions of future observations. Qualitative variables, based on a binomial or multinomial distribution, may be handled in a similar way. The model for count data may be extended to include explanatory variables. This enables nonstochastic slope and seasonal components to be included in the model, as well as permitting intervention analysis. The techniques are illustrated with a number of applications, and an attempt is made to develop a model-selection strategy along the lines of that used for Gaussian structural time series models. The appli...

2017 - arXiv: Machine Learning
Conditional Time Series Forecasting with Convolutional Neural Networks

textabstractForecasting financial time series using past observations has been a significant topic of interest. While temporal relationships in the data exist, they are difficult to analyze and predict accurately due to the non-linear trends and noise present in the series. We propose to learn these dependencies by a convolutional neural network. In particular the focus is on multivariate time series forecasting. Effectively, we use multiple financial time series as input in the neural network, thus conditioning the forecast of a time series x(t) on both its own history as well as that of a second (or third) time series y(t). Training a model on multiple stock series allows the network to exploit the correlation structure between these series so that the network can learn the market dynamics in shorter sequences of data. We show that long-term temporal dependencies in and between financial time series can be learned by means of a deep convolutional neural network based on the WaveNet model [2]. The network makes use of dilated convolutions applied to multiple time series so that the receptive field of the network is wide enough to learn both short and long-term dependencies. The architecture includes batch normalization and uses a 1 × k convolution with parametrized skip connections from the input time series as well as the time series we condition on, in this way learning long-term interdependencies in an efficient manner [1]. This improves the forecast, while at the same time limiting the requirement for a long historical price series and reducing the noise. Knowing the strong performance of CNNs on classification problems we show that they can be applied successfully to forecasting financial time series, without the need of large samples of data. We compare the performance of the WaveNet model to a state-of-the-art fully convolutional network (FCN), and an autoregressive model popular in econometrics and show that our model is much better able to learn important dependencies in between financial time series resulting in a more robust and accurate forecast.

2010 - Math. Comput. Simul.
A high order fuzzy time series forecasting model based on adaptive expectation and artificial neural networks

Many fuzzy time series approaches have been proposed in recent years. These methods include three main phases such as fuzzification, defining fuzzy relationships and, defuzzification. Aladag et al. [2] improved the forecasting accuracy by utilizing feed forward neural networks to determine fuzzy relationships in high order fuzzy time series. Another study for increasing forecasting accuracy was made by Cheng et al. [6]. In their study, they employ adaptive expectation model to adopt forecasts obtained from first order fuzzy time series forecasting model. In this study, we propose a novel high order fuzzy time series method in order to obtain more accurate forecasts. In the proposed method, fuzzy relationships are defined by feed forward neural networks and adaptive expectation model is used for adjusting forecasted values. Unlike the papers of Cheng et al. [6] and Liu et al. [14], forecast adjusting is done by using constraint optimization for weighted parameter. The proposed method is applied to the enrollments of the University of Alabama and the obtained forecasting results compared to those obtained from other approaches are available in the literature. As a result of comparison, it is clearly seen that the proposed method significantly increases the forecasting accuracy.

2009 - IEEE Transactions on Energy Conversion
Wind Power Density Forecasting Using Ensemble Predictions and Time Series Models

Wind power is an increasingly used form of renewable energy. The uncertainty in wind generation is very large due to the inherent variability in wind speed, and this needs to be understood by operators of power systems and wind farms. To assist with the management of this risk, this paper investigates methods for predicting the probability density function of generated wind power from one to ten days ahead at five U.K. wind farm locations. These density forecasts provide a description of the expected future value and the associated uncertainty. We construct density forecasts from weather ensemble predictions, which are a relatively new type of weather forecast generated from atmospheric models. We also consider density forecasting from statistical time series models. The best results for wind power density prediction and point forecasting were produced by an approach that involves calibration and smoothing of the ensemble-based wind power density.

2005 - Eur. J. Oper. Res.
Neural network forecasting for seasonal and trend time series

Abstract Neural networks have been widely used as a promising method for time series forecasting. However, limited empirical studies on seasonal time series forecasting with neural networks yield mixed results. While some find that neural networks are able to model seasonality directly and prior deseasonalization is not necessary, others conclude just the opposite. In this paper, we investigate the issue of how to effectively model time series with both seasonal and trend patterns. In particular, we study the effectiveness of data preprocessing, including deseasonalization and detrending, on neural network modeling and forecasting performance. Both simulation and real data are examined and results are compared to those obtained from the Box–Jenkins seasonal autoregressive integrated moving average models. We find that neural networks are not able to capture seasonal or trend variations effectively with the unpreprocessed raw data and either detrending or deseasonalization can dramatically reduce forecasting errors. Moreover, a combined detrending and deseasonalization is found to be the most effective data preprocessing approach.

1996 - Fuzzy Sets Syst.
Forecasting enrollments based on fuzzy time series

Abstract This paper presents a new method to forecast university enrollments based on fuzzy time series. The data of historical enrollments of the University of Alabama shown in Song and Chissom (1993a, 1994) are adopted to illustrate the forecasting process of the proposed method. The robustness of the proposed method is also tested. The proposed method not only can make good forecasts of the university enrollments, but also can make robust forecasts when the historical data are not accurate. The proposed method is more efficient than the one presented in Song and Chissom (1993a) due to the fact that the proposed method uses simplified arithmetic operations rather than the complicated max-min composition operations presented in Song and Chissom (1993a).

2007 - World Academy of Science, Engineering and Technology, International Journal of Computer, Electrical, Automation, Control and Information Engineering
Fuzzy Metric Approach for Fuzzy Time Series Forecasting based on Frequency Density Based Partitioning

In the last 15 years, a number of methods have been proposed for forecasting based on fuzzy time series. Most of the fuzzy time series methods are presented for forecasting of enrollments at the University of Alabama. However, the forecasting accuracy rates of the existing methods are not good enough. In this paper, we compared our proposed new method of fuzzy time series forecasting with existing methods. Our method is based on frequency density based partitioning of the historical enrollment data. The proposed method belongs to the kth order and time-variant methods. The proposed method can get the best forecasting accuracy rate for forecasting enrollments than the existing methods. Keywords—Fuzzy logical groups, fuzzified enrollments, fuzzy sets, fuzzy time series.

2003 - IEEE transactions on neural networks
Support vector machine with adaptive parameters in financial time series forecasting

A novel type of learning machine called support vector machine (SVM) has been receiving increasing interest in areas ranging from its original application in pattern recognition to other applications such as regression estimation due to its remarkable generalization performance. This paper deals with the application of SVM in financial time series forecasting. The feasibility of applying SVM in financial forecasting is first examined by comparing it with the multilayer back-propagation (BP) neural network and the regularized radial basis function (RBF) neural network. The variability in performance of SVM with respect to the free parameters is investigated experimentally. Adaptive parameters are then proposed by incorporating the nonstationarity of financial time series into SVM. Five real futures contracts collated from the Chicago Mercantile Market are used as the data sets. The simulation shows that among the three methods, SVM outperforms the BP neural network in financial forecasting, and there are comparable generalization performance between SVM and the regularized RBF neural network. Furthermore, the free parameters of SVM have a great effect on the generalization performance. SVM with adaptive parameters can both achieve higher generalization performance and use fewer support vectors than the standard SVM in financial forecasting.

2010 - Expert Syst. Appl.
A neural network-based fuzzy time series model to improve forecasting

Neural networks have been popular due to their capabilities in handling nonlinear relationships. Hence, this study intends to apply neural networks to implement a new fuzzy time series model to improve forecasting. Differing from previous studies, this study includes the various degrees of membership in establishing fuzzy relationships, which assist in capturing the relationships more properly. These fuzzy relationships are then used to forecast the stock index in Taiwan. With more information, the forecasting is expected to improve, too. In addition, due to the greater amount of information covered, the proposed model can be used to forecast directly regardless of whether out-of-sample observations appear in the in-sample observations. This study performs out-of-sample forecasting and the results are compared with those of previous studies to demonstrate the performance of the proposed model.

2006 - Physica A-statistical Mechanics and Its Applications
The application of neural networks to forecast fuzzy time series

Fuzzy time series models have been applied to handle nonlinear problems. To forecast fuzzy time series, this study applies a backpropagation neural network because of its nonlinear structures. We propose two models: a basic model using a neural network approach to forecast all of the observations, and a hybrid model consisting of a neural network approach to forecast the known patterns as well as a simple method to forecast the unknown patterns. The stock index in Taiwan for the years 1991–2003 is chosen as the forecasting target. The empirical results show that the hybrid model outperforms both the basic and a conventional fuzzy time series models.

2008 - Proc. VLDB Endow.
Querying and mining of time series data: experimental comparison of representations and distance measures

The last decade has witnessed a tremendous growths of interests in applications that deal with querying and mining of time series data. Numerous representation methods for dimensionality reduction and similarity measures geared towards time series have been introduced. Each individual work introducing a particular method has made specific claims and, aside from the occasional theoretical justifications, provided quantitative experimental observations. However, for the most part, the comparative aspects of these experiments were too narrowly focused on demonstrating the benefits of the proposed methods over some of the previously introduced ones. In order to provide a comprehensive validation, we conducted an extensive set of time series experiments re-implementing 8 different representation methods and 9 similarity measures and their variants, and testing their effectiveness on 38 time series data sets from a wide variety of application domains. In this paper, we give an overview of these different techniques and present our comparative experimental findings regarding their effectiveness. Our experiments have provided both a unified validation of some of the existing achievements, and in some cases, suggested that certain claims in the literature may be unduly optimistic.

An efficient time series forecasting model based on fuzzy time series

Pritpal Singh
|
Bhogeswar Borah
|
Pritpal Singh
|
B. Borah

Abstract:In this paper, we present a new model to handle four major issues of fuzzy time series forecasting, viz., determination of effective length of intervals, handling of fuzzy logical relationships (FLRs), determination of weight for each FLR, and defuzzification of fuzzified time series values. To resolve the problem associated with the determination of length of intervals, this study suggests a new time series data discretization technique. After generating the intervals, the historical time series data set is fuzzified based on fuzzy time series theory. Each fuzzified time series values are then used to create the FLRs. Most of the existing fuzzy time series models simply ignore the repeated FLRs without any proper justification. Since FLRs represent the patterns of historical events as well as reflect the possibility of appearances of these types of patterns in the future. If we simply discard the repeated FLRs, then there may be a chance of information lost. Therefore, in this model, it is recommended to consider the repeated FLRs during forecasting. It is also suggested to assign weights on the FLRs based on their severity rather than their patterns of occurrences. For this purpose, a new technique is incorporated in the model. This technique determines the weight for each FLR based on the index of the fuzzy set associated with the current state of the FLR. To handle these weighted FLRs and to obtain the forecasted results, this study proposes a new defuzzification technique. The proposed model is verified and validated with three different time series data sets. Empirical analyses signify that the proposed model have the robustness to handle one-factor time series data set very efficiently than the conventional fuzzy time series models. Experimental results show that the proposed model also outperforms over the conventional statistical models.

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