A Heuristic Search Procedure for Detecting Sudden Shifts in Stationary Time Series Data

A new heuristic search procedure is proposed for retrospectively detecting shifts (defined as sudden changes in the process mean) within a stationary time series subject to substantial white noise. After identifying the first, most significant shift, the search procedure is applied progressively to detect further shifts and also to define the timing, size and statistical significance of such shifts. Prior to the application of the procedure, the time series under review is evaluated to determine whether it is consistent with the shifting-mean model that underlies the heuristic. A feature of the search procedure is that it can be operated automatically, with searches terminated either when the segment of the data series within which the next identified shift occurs is shown not to be suitable for the application of the heuristic, or when the latest identified shift proves not to be statistically significant.     

The Effects of Combining Observation Periods in Time Series

This paper considers what happens when 'monthly' data, which can be modelled by a linear transform function together with a noise or error term, are aggregated to form 'annual' data. It is assumed that in the monthly model noise and input are independent, and it is shown that if the parameters of the annual model are so chosen that the input and noise are uncorrelated at all lags, then the parameters are functions of the structure generating the input series. However, if the annual noise and input are uncorrelated, the resulting model leads to the same estimate of gain and average lag as the monthly model. It is pointed out that this is at variance with reported empirical studies where annual models lead to much greater average lags. An example is given to show that the explanation may lie in the over-simplification of annual models. It is frequently assumed that a monthly Koyck model implies a similar annual model. This is not so, and the omission of a lagged term in the input series accounts for the bias in the average lag.     

On the generation of high-quality white noise series

A new approach to the simulation of white-noise time-series is presented. The approach is based on the frequency-domain property of white-noise as having a flat power spectrum density (PSD). From such a PSD, a linear complex spectrum of random-phase multisinusoidal series (MS) may be generated. Next, the fast Fourier transform is applied to this linear spectrum to generate a random-phase multisinusoidal N-sample series, simulating the white-noise series. The properties of some MS series are discussed including a gaussian white noise multisinusoidal series. The idea is illustrated by a number of examples. They demonstrate that the spectral and correlation properties of such series are enhanced in comparison to the properties of the random phases used to generate them. They also demonstrate that the spectral and correlation properties of such series are better, especially for short series, in comparison with standard white noise generators.     

A Case Study of the Residual-Based Cointegration Procedure

The study of long-run equilibrium processes is a significant component of economic and finance theory. The Johansen technique for identifying the existence of such long-run stationary equilibrium conditions among financial time series allows the identification of all potential linearly independent cointegrating vectors within a given system of eligible financial time series. The practical application of the technique may be restricted, however, by the pre-condition that the underlying data generating process fits a finite-order vector autoregression (VAR) model with white noise. This paper studies an alternative method for determining cointegrating relationships without such a precondition. The method is simple to implement through commonly available statistical packages. This 'residual-based cointegration' (RBC) technique uses the relationship between cointegration and univariate Box-Jenkins ARIMA models to identify cointegrating vectors through the rank of the covariance matrix of the residual processes which result from the fitting of univariate ARIMA models. The RBC approach for identifying multivariate cointegrating vectors is explained and then demonstrated through simulated examples. The RBC and Johansen techniques are then both implemented using several real-life financial time series.     

Explicit solutions of generalized Cauchy-Riemann systems using the transplant operator

In Kravchenko (2008) [8] it was shown that the tool introduced there and called the transplant operator transforms solutions of one Vekua equation into solutions of another Vekua equation, related to the first via a Schrödinger equation. In this paper we prove a fundamental property of this operator: it preserves the order of zeros and poles of generalized analytic functions and transforms formal powers of the first Vekua equation into formal powers of the same order for the second Vekua equation. This property allows us to obtain positive formal powers and a generating sequence of a “complicated” Vekua equation from positive formal powers and a generating sequence of a “simpler” Vekua equation. Similar results are obtained regarding the construction of Cauchy kernels. Elliptic and hyperbolic pseudoanalytic function theories are considered and examples are given to illustrate the procedure.     

Pointwise convergence of Fourier regularization for smoothing data

The classical smoothing data problem is analyzed in a Sobolev space under the assumption of white noise. A Fourier series method based on regularization endowed with generalized cross validation is considered to approximate the unknown function. This approximation is globally optimal, i.e., the mean integrated squared error reaches the optimal rate in the minimax sense. In this paper the pointwise convergence property is studied. Specifically, it is proved that the smoothed solution is locally convergent but not locally optimal. Examples of functions for which the approximation is subefficient are given. It is shown that optimality and superefficiency are possible when restricting to more regular subspaces of the Sobolev space.     

Maximum likelihood estimation for all-pass time series models

An autoregressive-moving average model in which all roots of the autoregressive polynomial are reciprocals of roots of the moving average polynomial and vice versa is called an all-pass time series model. All-pass models generate uncorrelated (white noise) time series, but these series are not independent in the non-Gaussian case. An approximate likelihood for a causal all-pass model is given and used to establish asymptotic normality for maximum likelihood estimators under general conditions. Behavior of the estimators for finite samples is studied via simulation. A two-step procedure using all-pass models to identify and estimate noninvertible autoregressive-moving average models is developed and used in the deconvolution of a simulated water gun seismogram.     

General model selection estimation of a periodic regression with a Gaussian noise

This paper considers the problem of estimating a periodic function in a continuous time regression model with an additive stationary Gaussian noise having unknown correlation function. A general model selection procedure on the basis of arbitrary projective estimates, which does not need the knowledge of the noise correlation function, is proposed. A non-asymptotic upper bound for L₂{\mathcal{L}_2} -risk (oracle inequality) has been derived under mild conditions on the noise. For the Ornstein–Uhlenbeck noise the risk upper bound is shown to be uniform in the nuisance parameter. In the case of Gaussian white noise the constructed procedure has some advantages as compared with the procedure based on the least squares estimates (LSE). The asymptotic minimaxity of the estimates has been proved. The proposed model selection scheme is extended also to the estimation problem based on the discrete data applicably to the situation when high frequency sampling can not be provided.     

基于ARMA模型和自由振动提取技术的海洋平台结构参数识别

用随机减量方法提取海洋平台结构在随机环境荷载非白噪声输入下的自由振动信号和用ARMA(Auto Regressive Moving Average)模型对自由振动数据建模。为了消除平台输出信号中有色噪声的影响,在随机减量系统中加人了一个虚拟系统,并采用导通条件和前导点技术使自由振动提取过程仍在有色输人的状态下进行。同时为了消除参数识别的多值性,提出了采用MA系数修正技术识别海洋平台结构的频率和阻尼动力参数的方法,最后用该套技术对海洋平台结构试验模型进行了参数识别,结果表明该方法具有较好的效果和在线识别使用价值。     

An exact minimum variance filter for a class of discrete time systems with random parameter perturbations

An exact, closed-form minimum variance filter is designed for a class of discrete time uncertain systems which allows for both multiplicative and additive noise sources. The multiplicative noise model includes a popular class of models (Cox-Ingersoll-Ross type models) in econometrics. The parameters of the system under consideration which describe the state transition are assumed to be subject to stochastic uncertainties. The problem addressed is the design of a filter that minimizes the trace of the estimation error variance. Sensitivity of the new filter to the size of parameter uncertainty, in terms of the variance of parameter perturbations, is also considered. We refer to the new filter as the ‘perturbed Kalman filter’ (PKF) since it reduces to the traditional (or unperturbed) Kalman filter as the size of stochastic perturbation approaches zero. We also consider a related approximate filtering heuristic for univariate time series and we refer to filter based on this heuristic as approximate perturbed Kalman filter (APKF). We test the performance of our new filters on three simulated numerical examples and compare the results with unperturbed Kalman filter that ignores the uncertainty in the transition equation. Through numerical examples, PKF and APKF are shown to outperform the traditional (or unperturbed) Kalman filter in terms of the size of the estimation error when stochastic uncertainties are present, even when the size of stochastic uncertainty is inaccurately identified.     

A homogenous random fractal model for time series produced by constant energy molecular dynamics simulations

In the present work we present an analysis of time series of instantaneous temperature and pressure produced during microcanonical (constant energy) molecular dynamics (MD). Simulations were applied to a nickel oxide grain boundary for a temperature range from about 0.15T_m up to about 0.80T_m, T_m being the melting point of the system. We performed a series of analysis for these time series including test for randomness, power spectrum, Hurst exponent, structure function test and test for multifractality. The obtained results show evidence of an homogenous random fractal model. Pressure time series presents 1/f^α noise over the whole range of frequencies of the system while temperature time series presents a white noise behavior. The origins of this observed behavior are discussed. A comparison also is made with results already obtained from constant temperature MD where the temperature time series present a two-regime behavior: white noise at low frequencies and 1/f^α at high frequencies with α increasing as a function of temperature. The origins of this difference in the behavior are discussed.     

Stochastic virus dynamics with Beddington-DeAngelis functional response

Stochastic virus dynamics modeled by a system of stochastic differential equations with Beddington-DeAngelis functional response and driven by white noise is investigated. The global existence of positive solutions and the existence of stationary distribution are proved. Upper and lower bounds of the pathwise and asymptotic moments for the positive solutions are sharply estimated. The absorbing property in time average is shown and the moment Lyapunov exponents are proved to be nonpositive.     

Generating functionals ofS-matrix and schwinger functions in WN-analysis. I

It is shown that the generating functionals of S-matrix and Schwinger functions are U-functionals of white noise analysis. This result is applied to the regularization of the generating functionals. Translated from Teoreticheskaya i Matematicheskaya Fizika. Vol. 111. No. 1, pp. 3–14. April, 1997.     

VALUE-AT-RISK的核估计理论

如何根据历史数据估计Value-at-Risk（VaR）;是风险分析与管理中一个重要的基本问题.木文基于非参数核估计方法,通过拟合实际数据过程的分布,构造了VaR的估计.在合适的相依数据条件下,证明了该估计量的渐近正态性,并给出了渐近方差的估计.由此表明:本文所构造的估计量不仅比参数模型具有更广泛的适应性,而且如同参数模型具有n~（-1/2）的收敛速度.本文假设的数据过程避免使用混合性,可很好地适用于金融管理中广泛应用的ARMA与GARCH模型族及非线性模型.     

Autoregression Model of Time Series with Matrix Cross-Section Data北大核心CSCD

矩阵型截面数据时间序列的优点在于可以同时刻画多个对象的多个属性.本文重点研究了矩阵型截面数据时间序列的自回归模型,给出了该模型的参数估计、模型识别、白噪声检验三个方面的理论结果.最后再利用矩阵型截面数据时间序列自回归模型,对两支银行股的日收益率序列和日成交量变化率序列进行建模分析.     

M-estimation of wavelet variance

The wavelet variance provides a scale-based decomposition of the process variance for a time series or a random field and has been used to analyze various multiscale processes. Examples of such processes include atmospheric pressure, deviations in time as kept by atomic clocks, soil properties in agricultural plots, snow fields in the polar regions and brightness temperature maps of South Pacific clouds. In practice, data collected in the form of a time series or a random field often suffer from contamination that is unrelated to the process of interest. This paper introduces a scale-based contamination model and describes robust estimation of the wavelet variance that can guard against such contamination. A new M-estimation procedure that works for both time series and random fields is proposed, and its large sample theory is deduced. As an example, the robust procedure is applied to cloud data obtained from a satellite.     

On the invertibility of seasonally adjusted series

This paper examines the implications of the seasonal adjustment by an ARIMA model based (AMB) approach in the context of seasonal fractional integration. According to the AMB approach, if the model identified from the data contains seasonal unit roots, the adjusted series will not be invertible that has serious implications for the posterior analysis. We show that even if the ARIMA model identified from the data contains seasonal unit roots, if the true data generating process is stationary seasonally fractionally integrated (as it is often found in economic data), the AMB seasonal adjustment produces dips in the periodogram at seasonal frequencies, but the adjusted series still can be approximated by an invertible process. We also perform a small Monte Carlo study of the log-periodogram regression with tapered data for negative seasonal fractional integration. An empirical application for the Spanish economy that illustrates our results is also carried out at the end of the article.     

Comparison of Efficient Seasonal Indexes

Estimates of a seasonal index in the standard manner (from a moving average) introduce systematic error into the seasonal estimates if a trend is present. This paper shows that a logarithmic modification of the standard moving average procedure will cause it to be consistent with a trend and is an efficient alternative. This paper also compares several other efficient seasonal indexing procedures appropriate for routine business applications and shows some numerical results. The results indicate that it is possible to achieve an improvement in the precision of the seasonal index, in the seasonally adjusted data and in forecasts based upon this data, by considering logarithmic alternatives to standard seasonal indexing procedures. This improvement may be accomplished without a substantial increase in complexity or in the associated computational burden. The opportunities for improvement are shown to be greatest when the data contain substantial trend and seasonal aspects and when the trend has a percentage form. Some suggestions for forecasters are offered.     

Implementing Symmetries of a Free Bose Field via White Noise Operators

Linear symmetries of a free Bose field are exploited in the framework of Hida's white noise functionals triple. General symplectic automorphisms on the single particle space are implemented by generalized operators. The intertwining operators are constructed in a physically intuitive way, characterized analytically in terms of symbols, and factorized into three fundamental parts according to Wick ordering procedure. In particular, the classical Shale's theorem is rederived.