1,833 research outputs found

    Recursive estimation of possibly misspecified MA(1) models: Convergence of a general algorithm

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    We introduce a recursive algorithm of conveniently general form for estimating the coefficient of a moving average model of order one and obtain convergence results for both correct and misspecified MA(1) models. The algorithm encompasses Pseudolinear Regression (PLR--also referred to as AML and RML1RML_1) and Recursive Maximum Likelihood (RML2RML_2) without monitoring. Stimulated by the approach of Hannan (1980), our convergence results are obtained indirectly by showing that the recursive sequence can be approximated by a sequence satisfying a recursion of simpler (Robbins-Monro) form for which convergence results applicable to our situation have recently been obtained.Comment: Published at http://dx.doi.org/10.1214/074921706000000932 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

    Forecasting trends with asset prices

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    In this paper, we consider a stochastic asset price model where the trend is an unobservable Ornstein Uhlenbeck process. We first review some classical results from Kalman filtering. Expectedly, the choice of the parameters is crucial to put it into practice. For this purpose, we obtain the likelihood in closed form, and provide two on-line computations of this function. Then, we investigate the asymptotic behaviour of statistical estimators. Finally, we quantify the effect of a bad calibration with the continuous time mis-specified Kalman filter. Numerical examples illustrate the difficulty of trend forecasting in financial time series.Comment: 26 pages, 11 figure

    Estimation of Autoregressive Parameters from Noisy Observations Using Iterated Covariance Updates

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    Estimating the parameters of the autoregressive (AR) random process is a problem that has been well-studied. In many applications, only noisy measurements of AR process are available. The effect of the additive noise is that the system can be modeled as an AR model with colored noise, even when the measurement noise is white, where the correlation matrix depends on the AR parameters. Because of the correlation, it is expedient to compute using multiple stacked observations. Performing a weighted least-squares estimation of the AR parameters using an inverse covariance weighting can provide significantly better parameter estimates, with improvement increasing with the stack depth. The estimation algorithm is essentially a vector RLS adaptive filter, with time-varying covariance matrix. Different ways of estimating the unknown covariance are presented, as well as a method to estimate the variances of the AR and observation noise. The notation is extended to vector autoregressive (VAR) processes. Simulation results demonstrate performance improvements in coefficient error and in spectrum estimation

    On the identification and parametric modelling of offshore dynamic systems

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    This thesis describes an investigation into the analysis methods arising from identification aspects of the theory of dynamic systems with application to full-scale offshore monitoring and marine environmental data including target spectra. Based on the input and output of the dynamic system, the System Identification (SI) techniques are used first to identify the model type and then to estimate the model parameters. This work also gives an understanding of how to obtain a meaningful matching between the target (power spectra or time series data sets) and SI models with minimal loss of information. The SI techniques, namely. Autoregressive (AR), Moving Average (MA) and Autoregressive Moving Average (ARMA) algorithms are formulated in the frequency domain and also in the time domain. The above models can only be economically applicable provided the model order is low in the sense that it is computationally efficient and the lower order model can most appropriately represent the offshore time series records or the target spectra. For this purpose, the orders of the above SI models are optimally selected by Least Squares Error, Akaike Information Criterion and Minimum Description Length methods. A novel model order reduction technique is established to obtain the reduced order ARMA model. At first estimations of higher order AR coefficients are determined using modified Yule-Walker equations and then the first and second order real modes and their energies are determined. Considering only the higher energy modes, the AR part of the reduced order ARMA model is obtained. The MA part of the reduced order ARMA model is determined based on partial fraction and recursive methods. This model order reduction technique can remove the spurious noise modes which are present in the time series data. Therefore, firstly using an initial optimal AR model and then a model order reduction technique, the time series data or target spectrum can be reduced to a few parameters which are the coefficients of the reduced order ARMA model. The above univariate SI models and model order reduction techniques are successfully applied for marine environmental and structural monitoring data, including ocean waves, semi-submersible heave motions, monohull crane vessel motions and theoretical (Pierson- Moskowitz and JONSWAP) spectra. Univariate SI models are developed based on the assumption that the offshore dynamic systems are stationary random processes. For nonstationary processes, such as, measurements of combined sea waves and swells, or coupled responses of offshore structures with short period and long period motions, the time series are modelled by the Autoregressive Integrated Moving Average algorithms. The multivariate autoregressive (MAR) algorithm is developed to reduce the time series wave data sets into MAR model parameters. The MAR algorithms are described by feedback weighting coefficients matrices and the driving noise vector. These are obtained based on the estimation of the partial correlation of the time series data sets. Here the appropriate model order is selected based on auto and cross correlations and multivariate Akaike information criterion methods. These algorithms are applied to estimate MAR power spectral density spectra and then phase and coherence spectra of two time series wave data sets collected at a North Sea location. The estimation of MAR power spectral densities are compared with spectral estimates computed from a two variable fast Fourier transform, which show good agreement

    Some Computational Aspects of Gaussian CARMA Modelling

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    Representation of continuous-time ARMA, CARMA, models is reviewed. Computational aspects of simulating and calculating the likelihood-function of CARMA are summarized. Some numerical properties are illustrated by simulations. Some real data applications are shown.CARMA, maximum-likelihood, spectrum, Kalman filter, computation

    Comparative review of methods for stability monitoring in electrical power systems and vibrating structures

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    This study provides a review of methods used for stability monitoring in two different fields, electrical power systems and vibration analysis, with the aim of increasing awareness of and highlighting opportunities for cross-fertilisation. The nature of the problems that require stability monitoring in both fields are discussed here as well as the approaches that have been taken. The review of power systems methods is presented in two parts: methods for ambient or normal operation and methods for transient or post-fault operation. Similarly, the review of methods for vibration analysis is presented in two parts: methods for stationary or linear time-invariant data and methods for non-stationary or non-linear time-variant data. Some observations and comments are made regarding methods that have already been applied in both fields including recommendations for the use of different sets of algorithms that have not been utilised to date. Additionally, methods that have been applied to vibration analysis and have potential for power systems stability monitoring are discussed and recommended. � 2010 The Institution of Engineering and Technology

    Real-time flutter analysis

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    The important algorithm issues necessary to achieve a real time flutter monitoring system; namely, the guidelines for choosing appropriate model forms, reduction of the parameter convergence transient, handling multiple modes, the effect of over parameterization, and estimate accuracy predictions, both online and for experiment design are addressed. An approach for efficiently computing continuous-time flutter parameter Cramer-Rao estimate error bounds were developed. This enables a convincing comparison of theoretical and simulation results, as well as offline studies in preparation for a flight test. Theoretical predictions, simulation and flight test results from the NASA Drones for Aerodynamic and Structural Test (DAST) Program are compared
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