Forecasting daily time series using periodic unobserved components time series models

A periodic time series analysis is explored in the context of unobserved components time series models that include stochastic time functions for trend, seasonal and irregular effects. Periodic time series models allow dynamic characteristics (autocovariances) to depend on the period of the year, month, week or day. In the standard multivariate approach one can interpret a periodic time series analysis as a simultaneous treatment of typically yearly time series where each series is related to a particular season. Here, the periodic analysis applies to a vector of monthly time series related to each day of the month. Particular focus is on the forecasting performance and therefore on the underlying periodic forecast function, defined by the in-sample observation weights for producing (multi-step) forecasts. These weight patterns facilitate the interpretation of periodic model extensions. A statistical state space approach is used to estimate the model and allows for irregularly spaced observations in daily time series. Recent algorithms are adopted for the computation of observation weights for forecasting based on state space models with regressor variables. The methodology is illustrated for daily Dutch tax revenues that appear to have periodic dynamic properties. The dimension of our periodic unobserved components model is relatively large as we allow each element (day) of the vector of monthly time series to have a changing seasonal pattern. Nevertheless, even with only five years of data we find that the increased periodic flexibility can help in out-of-sample forecasting for two extra years of data.     

Detection of additive outliers in bilinear time series

Outliers are commonplace in applied time series analysis. Additive outliers could happen in linear time series as well as nonlinear time series. However, their existence is often ignored and their impact overlooked in nonlinear processes. The problem of detecting additive outliers in bilinear time series is considered in this work. We show how Gibbs sampler can be applied to detect aberrant observations in bilinear processes. We also discuss some major problems encountered in practice, such as how one can distinguish between ARMA model with outliers and a bilinear model without outliers. The methodology proposed is illustrated using some generated examples and the US monthly retail price of regular unleaded gasoline. The results obtained by the proposed procedure are informative. The major strength of this procedure is that it can identify those observations which would require more careful scrutinizing.     

Temperature prediction using fuzzy time series

A drawback of traditional forecasting methods is that they can not deal with forecasting problems in which the historical data are represented by linguistic values. Using fuzzy time series to deal with forecasting problems can overcome this drawback. In this paper, we propose a new fuzzy time series model called the two-factors time-variant fuzzy time series model to deal with forecasting problems. Based on the proposed model, we develop two algorithms for temperature prediction. Both algorithms have the advantage of obtaining good forecasting results.     

Parsimonious time series clustering using P-splines

We introduce a parsimonious model-based framework for clustering time course data. In these applications the computational burden becomes often an issue due to the large number of available observations. The measured time series can also be very noisy and sparse and an appropriate model describing them can be hard to define. We propose to model the observed measurements by using P-spline smoothers and then to cluster the functional objects as summarized by the optimal spline coefficients. According to the characteristics of the observed measurements, our proposal can be combined with any suitable clustering method. In this paper we provide applications based on non-hierarchical clustering algorithms. We evaluate the accuracy and the efficiency of our proposal by simulations and by analyzing two real data examples.     

Comparing time series using wavelet-based semblance analysis

Similarity measures are becoming increasingly commonly used in comparison of multiple datasets from various sources. Semblance filtering compares two datasets on the basis of their phase, as a function of frequency. Semblance analysis based on the Fourier transform suffers from problems associated with that transform, in particular its assumption that the frequency content of the data must not change with time (for time-series data) or location (for data measured as a function of position). To overcome these problems, semblance is calculated here using the continuous wavelet transform. When calculated in this way, semblance analysis allows the local phase relationships between the two datasets to be studied as a function of both scale (or wavelength) and time. Semblance analysis is demonstrated on synthetic datasets and on gravity and aeromagnetic data from the Vredefort Dome, South Africa. Matlab source code is available from the IAMG server at www.iamg.org.     

Multi-step time series prediction intervals using neuroevolution

Multi-step time series forecasting (TSF) is a crucial element to support tactical decisions (e.g., designing production or marketing plans several months in advance). While most TSF research addresses only single-point prediction, prediction intervals (PIs) are useful to reduce uncertainty related to important decision making variables. In this paper, we explore a large set of neural network methods for multi-step TSF and that directly optimize PIs. This includes multi-step adaptations of recently proposed PI methods, such as lower–upper bound estimation (LUBET), its ensemble extension (LUBEXT), a multi-objective evolutionary algorithm LUBE (MLUBET) and a two-phase learning multi-objective evolutionary algorithm (M2LUBET). We also explore two new ensemble variants for the evolutionary approaches based on two PI coverage–width split methods (radial slices and clustering), leading to the MLUBEXT, M2LUBEXT, MLUBEXT2 and M2LUBEXT2 methods. A robust comparison was held by considering the rolling window procedure, nine time series from several real-world domains and with different characteristics, two PI quality measures (coverage error and width) and the Wilcoxon statistic. Overall, the best results were achieved by the M2LUBET neuroevolution method, which requires a reasonable computational effort for time series with a few hundreds of observations.

     

Prediction of chaotic time series using computational intelligence

In this paper, two CI techniques, namely, single multiplicative neuron (SMN) model and adaptive neuro-fuzzy inference system (ANFIS), have been proposed for time series prediction. A variation of particle swarm optimization (PSO) with co-operative sub-swarms, called COPSO, has been used for estimation of SMN model parameters leading to COPSO-SMN. The prediction effectiveness of COPSO-SMN and ANFIS has been illustrated using commonly used nonlinear, non-stationary and chaotic benchmark datasets of Mackey–Glass, Box–Jenkins and biomedical signals of electroencephalogram (EEG). The training and test performances of both hybrid CI techniques have been compared for these datasets.     

Discrimination of locally stationary time series using wavelets

Time series are sometimes generated by processes that change suddenly from one stationary regime to another, with no intervening periods of transition of any significant duration. A good example of this is provided by seismic data, namely, waveforms of earthquakes and explosions. In order to classify an unknown event as either an earthquake or an explosion, statistical analysts might be helped by having at their disposal an automatic means of identifying, at any time, which pattern prevails. Several authors have proposed methods to tackle this problem by combining the techniques of spectral analysis with those of discriminant analysis. The goal is to develop a discriminant scheme for locally stationary time series such as earthquake and explosion waveforms, by combining the techniques of wavelet analysis with those of discriminant analysis.     

Generation of synthetic video traffic using time series

Generating traffic has always been an important part of network simulations but has turned to an even more challenging task with modern networks. The statistical properties of the input stochastic processes traced in the networks used all along Information Era turned out to be complicated and difficult to reproduce. Taking into account successful efforts in modeling Internet traffic with FARIMA time series models, this paper attempts to extend their applicability and employ them to generate synthetic video traffic. It is known that FARIMA can model both the Short Range (SRD) and Long Range Dependence (LRD) existing in video traffic; however the traces it produces fail to describe correctly the moments (mean, standard deviation, skewness, kurtosis) of the distribution behind the data. Since an efficient traffic generator should capture both the statistical properties and queuing behavior of video traffic we experiment with models such as FARIMA with Student's t errors and FARIMA-GARCH with Normal and Student's t errors, improving somewhat the accuracy of the generated traffic. Furthermore, the paper suggests the projection of the traces generated by a FARIMA model to values of a Lognormal distribution. It is shown that such a methodology produces synthetic traces that can emulate very closely the behavior of real traces. In order to quantify closeness the generated traces are fed into a simple FIFO queuing system with finite buffers, where loss probability is calculated and compared to that experienced by the corresponding real traces. Using five different real traces, MPEG-4 or H.263, it is shown that the proposed methodology produces traffic generators that can capture satisfactorily several statistical properties of the real traffic and also its queuing behavior for a wide range of buffer sizes and service rates.     

基于时间序列分析的应用层DDoS攻击检测

根据正常用户和攻击者在访问行为上的差异,提出一种基于IP请求熵(SRE)时间序列分析的应用层分布式拒绝服务(DDoS)攻击检测方法。该方法通过拟合SRE时间序列的自适应自回归(AAR)模型,获得描述当前用户访问行为特征的多维参数向量,并使用支持向量机(SVM)对参数向量进行分类来识别攻击。仿真实验表明,该方法能够准确区分正常流量和DDoS攻击流量,适用于大流量背景下攻击流量没有引起整个网络流量显著变化的DDoS攻击的检测。     

Detection of linear and nonlinear dependencies in time series using the method of surrogate data in S-PLUS

A general implementation of the method of surrogate data in the S programming language for use with the S-PLUS statistical package is presented. We illustrate the application of the S functions to testing hypotheses about a human heart rate time series and demonstrate that there is evidence for both linear and nonlinear dependencies. We expect these S functions will be useful for the application of the method of surrogate data to the analysis of biomedical time series using the S-PLUS statistical software package.     

Rotation-invariant similarity in time series using bag-of-patterns representation

For more than a decade, time series similarity search has been given a great deal of attention by data mining researchers. As a result, many time series representations and distance measures have been proposed. However, most existing work on time series similarity search relies on shape-based similarity matching. While some of the existing approaches work well for short time series data, they typically fail to produce satisfactory results when the sequence is long. For long sequences, it is more appropriate to consider the similarity based on the higher-level structures. In this work, we present a histogram-based representation for time series data, similar to the ??bag of words?? approach that is widely accepted by the text mining and information retrieval communities. We performed extensive experiments and show that our approach outperforms the leading existing methods in clustering, classification, and anomaly detection on dozens of real datasets. We further demonstrate that the representation allows rotation-invariant matching in shape datasets.     

Analyzing very large time series using suffix arrays

Suffix arrays form a powerful data structure for pattern detection and matching. In a previous work, we presented a novel algorithm (COV) which is the only algorithm that allows the detection of all repeated patterns in a time series by using the actual suffix array. However, the requirements for storing the actual suffix strings even on external media makes the use of suffix arrays impossible for very large time series. We have already proved that using the concept of Longest Expected Repeated Pattern (LERP) allows the actual suffices to be stored in linear capacity O(n) on external media. The repeated pattern detection using LERP has analogous time complexity, and thus makes the analysis of large time series feasible and limited only to the size of the external media and not memory. Yet, there are cases when hardware limitations might be an obstacle for the analysis of very larger time series of size comparable to hard disk capacity. With the Moving LERP (MLERP) method introduced in this paper, it is possible to analyze very large time series (of size tens or hundreds thousands times larger than what the LERP can analyze) by maximal utilization of the available hardware. Further, when empirical knowledge related to the distribution of repeated pattern’s length is available, the proposed method (MLERP) can achieve better time performance compared to the standard LERP method and definitely much better than using any other pattern matching algorithm and applying brute force techniques which are unfeasible in logical (human) time frame. Thus, we may argue that MLERP is a very useful tool for detecting all repeated patterns in a time series regardless of its size and hardware limitations.     

Real-time network data analysis using time series models

With the expansion of computer networks, there is a strong need for monitoring their properties in order to diagnose any problems and manage them in the best possible way. This monitoring is particularly useful if performed in real-time, however, such an approach is rather difficult (if not impossible) to implement in networks with increased traffic, using a passive monitoring scheme. One way to overcome this problem is to selectively sample network data, which in turn opens new issues such as how frequently this sampling should be performed, so as to obtain useful and exploitable data. In this work it is shown that it is possible to accurately represent high-speed network traffic using suitable time series models and then determine the size of the sampling window, so as to detect packet loss. The resulting scheme is scalable, protocol-independent and able to raise alerts in real time.     

Discovering patterns in categorical time series using IFS

The detection of patterns in categorical time series data is an important task in many fields of science. Several efficient algorithms for finding frequent sequential patterns have been proposed. An online-approach for sequential pattern analysis based on transforming the categorical alphabet to real vectors and generating fractals by an iterated function systems (IFS) is suggested. Sequential patterns can be analyzed with standard methods of cluster analysis using this approach. A version of the procedure allows detecting patterns visually.     

Earthquake pattern analysis using subsequence time series clustering

Pattern Analysis and Applications - In this paper, a subsequence time-series clustering algorithm is proposed to identify the strongly coupled aftershocks sequences and Poissonian background...     

基于独立成分分析的含噪声时间序列预测

提出一种基于独立成分分析(ICA)的最小二乘支持向量机(LS-SVM),用于时间序列的多步超前独立预测.用ICA估计预测变量中的独立成分(IC),用不含噪声的IC重新构建时间序列.利用 -最近邻法( -NN)减小训练集的规模,提出一种新的距离函数以降低LS-SVM训练过程的计算复杂度,并用约束条件对预测值进行后处理.使用基于ICA的LS-SVM、普通LS-SVM与反向传播神经网络(BP-ANN),对多个时间序列进行对比预测实验.实验结果表明,基于ICA的LS-SVM的预测性能优于普通LS-SVM和BP-ANN.     

基于DCT的时序数据相似性搜索

数据的高维度是造成时序数据相似性搜索困难的主要原因。最有效的解决方法是对时序数据进行维归约，然后对压缩后的数据建立空间索引。目前维归约的方法主要是离散傅立叶变换(DFT)和离散小波变换(DWT)。提出了一种新的方法，利用离散余弦变换(DCT)进行维归约，并在此基础上给出了对时序数据进行范围查询和近邻查询的相似性搜索方法。与基于DFT、DWT的搜索方法相比，该方法在理论分析和实验结果上都显示出较高的效率。     

Image data compression using autoregressive time series models

A two-dimensional image model is formulated using a seasonal autoregressive time series. With appropriate use of initial conditions, the method of least squares is used to obtain estimates of the model parameters. The model is then used to regenerate the original image. Results obtained indicate this method could be used to code textures for low bit rates or be used in an application of generating compressed background scenes. A differential pulse code modulation (DPCM) scheme is also demonstrated as a means of archival storage of images along with a new quantization technique for DPCM. This quantization technique is compared with standard quantization methods.