Singular spectrum analysis based on the perturbation theory

Singular Spectrum Analysis (SSA) has been exploited in different applications. It is well known that perturbations from various sources can seriously degrade the performance of the methods and techniques. In this paper, we consider the SSA technique based on the perturbation theory and examine its performance in both reconstructing and forecasting noisy series. We also consider the sensitivity of the technique to different window lengths, noise levels and series lengths. To cover a broad application range, various simulated series, from dynamic to chaotic, are used to verify the proposed algorithm. We then evaluate the performance of the technique using two real well-known series, namely, monthly accidental deaths in the USA, and the daily closing prices of several stock market indices. The results are compared with several classical methods namely, Box–Jenkins SARIMA models, the ARAR algorithm, GARCH model and the Holt–Winter algorithm.     

Forecasting mortality rate by multivariate singular spectrum analysis

In this paper, we investigate the possibility of using multivariate singular spectrum analysis (SSA), a nonparametric technique in the field of time series analysis, for mortality forecasting. We consider a real data application with 9 European countries: Belgium, Denmark, Finland, France, Italy, Netherlands, Norway, Sweden, and Switzerland, over a period 1900 to 2009, and a simulation study based on the data set. The results show the superiority of multivariate SSA in comparison with the univariate SSA, in terms of forecasting accuracy.     

Improving efficiency of data augmentation algorithms using Peskun’s theorem

Data augmentation (DA) algorithm is a widely used Markov chain Monte Carlo algorithm. In this paper, an alternative to DA algorithm is proposed. It is shown that the modified Markov chain is always more efficient than DA in the sense that the asymptotic variance in the central limit theorem under the alternative chain is no larger than that under DA. The modification is based on Peskun’s (Biometrika 60:607–612, 1973) result which shows that asymptotic variance of time average estimators based on a finite state space reversible Markov chain does not increase if the Markov chain is altered by increasing all off-diagonal probabilities. In the special case when the state space or the augmentation space of the DA chain is finite, it is shown that Liu’s (Biometrika 83:681–682, 1996) modified sampler can be used to improve upon the DA algorithm. Two illustrative examples, namely the beta-binomial distribution, and a model for analyzing rank data are used to show the gains in efficiency by the proposed algorithms.     

Bay of Bengal wave forecast based on genetic algorithm: A comparison of univariate and multivariate approaches

Prediction of significant wave height (SWH) field is carried out in the Bay of Bengal (BOB) using a combination of empirical orthogonal function (EOF) analysis and genetic algorithm (GA). EOF analysis is performed on 4 years (2005–2008) of numerical wave model generated SWH field, and analyzed fields of zonal (U) and meridional (V) winds. This is to decompose the space-time distributed data into spatial modes ranked by their temporal variances. Two different variants of GA are tested. In the first one, univariate GA is applied to the time series of the first principal component (PC) of SWH in the training dataset after a filtering with singular spectrum analysis (SSA) for effecting noise reduction. The generated equations are used to carry out forecast of SWH field with various lead times. In the second method, multivariate GA is applied to the SSA filtered time series of the first PC of SWH, and time- lagged first PCs of U and V and again forecast equations are generated. Once again the forecast of SWH is carried out with same lead times. The quality of forecast is evaluated in terms of root mean square error of forecast. The results are also compared with buoy data at a location. It is concluded that the method can serve as a cost-effective alternate prediction technique in the BOB.     

Solving stochastic chemical kinetics by Metropolis-Hastings sampling

This study considers using Metropolis-Hastings algorithm for stochastic simulation of chemical reactions. The proposed method uses SSA (Stochastic Simulation Algorithm) distribution which is a standard method for solving well-stirred chemically reacting systems as a desired distribution. A new numerical solvers based on exponential form of exact and approximate solutions of CME (Chemical Master Equation) is employed for obtaining target and proposal distributions in Metropolis-Hastings algorithm to accelerate the accuracy of the tau-leap method. Samples generated by this technique have the same distribution as SSA and the histogram of samples show it''s convergence to SSA     

Continuous functions minimization by dynamic random search technique

Random search technique is the simplest one of the heuristic algorithms. It is stated in the literature that the probability of finding global minimum is equal to 1 by using the basic random search technique, but it takes too much time to reach the global minimum. Improving the basic random search technique may decrease the solution time. In this study, in order to obtain the global minimum fastly, a new random search algorithm is suggested. This algorithm is called as the Dynamic Random Search Technique (DRASET). DRASET consists of two phases, which are general search and local search based on general solution. Knowledge related to the best solution found in the process of general search is kept and then that knowledge is used as initial value of local search. DRASET’s performance was experimented with 15 test problems and satisfactory results were obtained.     

On the flow cost lowering problem

This paper presents the flow cost lowering problem (FCLP), which is an extension to the integral version of the well-known minimum cost flow problem (MCFP). While in the MCFP the flow costs are fixed, the FCLP admits lowering the flow cost on each arc by upgrading the arc. Given a flow value and a bound on the total budget which can be used for upgrading the arcs, the goal is to find an upgrade strategy and a flow of minimum cost. The FCLP is shown to be NP-hard even on series–parallel graphs. On the other hand the paper provides a polynomial time approximation algorithm on series–parallel graphs.     

Improvement of separability of time series in singular spectrum analysis using the method of independent component analysis

The separation of signal components is an important problem of time-series analysis. For example, the solution of this problem allows one to extract a trend and to separate harmonic signals with different frequencies. In the paper, the modification of the singular spectrum analysis (SSA) method is considered for improving the separability of time-series components. The new method is called SSA-AMUSE, since it is based on the AMUSE method, which is used to apply independent component analysis to signal separation. The suggested modification weakens the conditions of the so-called strong separability and, thus, improves the quality of the separation of time-series components by comparing similar methods. The paper contains proof of the algorithm, as well as the conditions of separability for the considered modification. Besides the exact separability, the asymptotic separability is also considered. The separability conditions are applied to the case of two harmonic time series. It appears that separability by SSA-AMUSE does not depend on the amplitudes of the separated harmonics, while the Basic SSA method requires different amplitudes. A numerical example demonstrates the advantage of the SSA-AMUSE method compared with a similar modification.     

A practicable branch-and-bound algorithm for globally solving linear multiplicative programming

To globally solve linear multiplicative programming problem (LMP), this paper presents a practicable branch-and-bound method based on the framework of branch-and-bound algorithm. In this method, a new linear relaxation technique is proposed firstly. Then, the branch-and-bound algorithm is developed for solving problem LMP. The proposed algorithm is proven that it is convergent to the global minimum by means of the subsequent solutions of a series of linear programming problems. Some experiments are reported to show the feasibility and efficiency of this algorithm.     

基于遗传算法和半参数回归的神经网络集成股市预测研究

股票时间序列预测在经济和管理领域具有重要的应用前景,也是很多商业和金融机构成功的基础.首先利用奇异谱分析对股市时间序列重构,降低噪声并提取趋势序列.再利用C-C算法确定股市时间序列的嵌入维数和延迟阶数,对股市时间序列进行相空间重构,生成神经网络的学习矩阵.进一步利用Boosting技术和不同的神经网络模型,生成神经网络集成个体.最后采用带有惩罚项的半参数回归模型进行集成,并利用遗传算法选择最优的光滑参数,以此建立遗传算法和半参数回归的神经网络集成股市预测模型.通过上证指数开盘价进行实例分析,与传统的时间序列分析和其他集成方法对比,发现该方法能获得更准确的预测结果.计算结果表明该方法能充分反映股票价格时间序列趋势,为金融时间序列预测提供一个有效方法.     

Predicting ambulance demand using singular spectrum analysis

This paper demonstrates techniques to generate accurate predictions of demand exerted upon the Emergency Medical Services (EMS) using data provided by the Welsh Ambulance Service Trust (WAST). The aim is to explore new methods to produce accurate forecasts that can be subsequently embedded into current OR methodologies to optimise resource allocation of vehicles and staff, and allow rapid response to potentially life-threatening emergencies. Our analysis explores a relatively new non-parametric technique for time series analysis known as Singular Spectrum Analysis (SSA). We explain the theory of SSA and evaluate the performance of this approach by comparing the results with those produced by conventional time series methods. We show that in addition to being more flexible in approach, SSA produces superior longer-term forecasts (which are especially helpful for EMS planning), and comparable shorter-term forecasts to well established methods.     

The influence of perceived stock value price histories in the mean–variance-instability model

The model introduced by H. Talpaz, A. Harpaz and J.B. Penson (1984. European Journal of Operational Research 14, 262–269) extends the mean–variance model introducing the concept of instability. In this way it is possible to see an investor's attitude towards predicted instability. In this paper we show how optimisation procedures based on penalty (or preferred) weighted instability matrices can be interpreted in terms of real time utility functions which depend on an `actual' and a `remembered' time series due to fading memory. This approach justifies some bounded normalised functions used to represent the investors preference between the irregular frequency fluctuations.     

Numerical Solution of the Two-Sided Space–Time Fractional Telegraph Equation Via Chebyshev Tau Approximation

The operational matrices of left Caputo fractional derivative, right Caputo fractional derivative, and Riemann–Liouville fractional integral, for shifted Chebyshev polynomials, are presented and derived. We propose an accurate and efficient spectral algorithm for the numerical solution of the two-sided space–time Caputo fractional-order telegraph equation with three types of non-homogeneous boundary conditions, namely, Dirichlet, Robin, and non-local conditions. The proposed algorithm is based on shifted Chebyshev tau technique combined with the derived shifted Chebyshev operational matrices. We focus primarily on implementing the novel algorithm both in temporal and spatial discretizations. This algorithm reduces the problem to a system of algebraic equations greatly simplifying the problem. This system can be solved by any standard iteration method. For confirming the efficiency and accuracy of the proposed scheme, we introduce some numerical examples with their approximate solutions and compare our results with those achieved using other methods.     

混料试验的D—最优对称设计,算法及应用

本文着重研究了混料试验的D—最优对称设计.基于Fedorov及Atwood的迭代方法,作者给出一个构造D—最优对称设计的改进算法.这个新算法由双循环迭代构成:从初始设计中减去最小方差对称点的设计测度;增加设计测度于最大方差的对称设计点,同时,本算法还只在对称子区域中寻找最大方差设计点,这样就使得Fedorov算法的收敛速度有了显著地提高,并能构造出更高效的D—最优对称设计.另外还给出一些构造实例.     

Portfolio performance evaluation in a mean–variance–skewness framework

Astronomical amounts of money are being invested in financial markets. Consequently the evaluation of portfolio performance has created a great deal of interest among practitioners as well as academic researchers. The literature suggests that portfolio efficiency based on mean–variance–skewness is more desirable than the one based on mean–variance. However, there are no well-established procedures to measure efficiency in this framework, mainly due to the computational difficulties. The aim of this paper is to develop a portfolio performance measure based on mean–variance–skewness framework by utilizing a non-parametric efficiency analysis tool, namely ‘Data Envelopment Analysis’.     

On Data-Driven Computation of Information Transfer for Causal Inference in Discrete-Time Dynamical Systems

In this paper, we provide a novel approach to capture causal interaction in a dynamical system from time series data. In Sinha and Vaidya (in: IEEE conference on decision and control, pp 7329–7334, 2016), we have shown that the existing measures of information transfer, namely directed information, Granger causality and transfer entropy, fail to capture the causal interaction in a dynamical system and proposed a new definition of information transfer that captures direct causal interactions. The novelty of the information transfer definition used in this paper is the fact that it can differentiate between direct and indirect influences Sinha and Vaidya (2016). The main contribution of this paper is to show that the proposed definition of information transfers in Sinha and Vaidya (2016) and Sinha and Vaidya (in: Indian control conference, pp 303–308, 2017) can be computed from time series data, and thus, the direct influences in a dynamical system can be identified from time series data. We use transfer operator theoretic framework, involving Perron–Frobenius and Koopman operators for the data-driven approximation of the system dynamics and computation of information transfer. Several examples, involving linear and nonlinear system dynamics, are presented to verify the efficiency of the developed algorithm.

     

Improving an interior-point approach for large block-angular problems by hybrid preconditioners

The computational time required by interior-point methods is often dominated by the solution of linear systems of equations. An efficient specialized interior-point algorithm for primal block-angular problems has been used to solve these systems by combining Cholesky factorizations for the block constraints and a conjugate gradient based on a power series preconditioner for the linking constraints. In some problems this power series preconditioner resulted to be inefficient on the last interior-point iterations, when the systems became ill-conditioned. In this work this approach is combined with a splitting preconditioner based on LU factorization, which works well for the last interior-point iterations. Computational results are provided for three classes of problems: multicommodity flows (oriented and nonoriented), minimum-distance controlled tabular adjustment for statistical data protection, and the minimum congestion problem. The results show that, in most cases, the hybrid preconditioner improves the performance and robustness of the interior-point solver. In particular, for some block-angular problems the solution time is reduced by a factor of 10.     

A probe into the chaotic nature of daily streamflow time series by correlation dimension and largest Lyapunov methods

Two chaotic indicators namely the correlation dimension and the Lyapunov exponent methods are investigated for the daily river flow of Kizilirmak River. A delay time of 60 days used for the reconstruction is chosen after examining the first minimum of the average mutual information of the data. The sufficient embedding dimension is estimated using the false nearest neighbor algorithm, which has a value of 11. Based on these embedding parameters the correlation dimension of the resulting attractor is calculated, as well as the average divergence rate of nearby orbits given by the largest Lyapunov exponent. The presence of chaos in the examined river flow time series is evident with the low correlation dimension (2.4) and the positive value of the largest Lyapunov exponent (0.0061).     

The New k-Windows Algorithm for Improving thek -Means Clustering Algorithm

The process of partitioning a large set of patterns into disjoint and homogeneous clusters is fundamental in knowledge acquisition. It is called Clustering in the literature and it is applied in various fields including data mining, statistical data analysis, compression and vector quantization. The k-means is a very popular algorithm and one of the best for implementing the clustering process. The k-means has a time complexity that is dominated by the product of the number of patterns, the number of clusters, and the number of iterations. Also, it often converges to a local minimum. In this paper, we present an improvement of the k-means clustering algorithm, aiming at a better time complexity and partitioning accuracy. Our approach reduces the number of patterns that need to be examined for similarity, in each iteration, using a windowing technique. The latter is based on well known spatial data structures, namely the range tree, that allows fast range searches.