Approved for public release; distribution is unlimited / This thesis estimates the frequency response of a network where the only data is the output obtained from an Autoregressive-moving average (ARMA) model driven by a random input. Models of random processes and existing methods for solving ARMA models are examined. The estimation is performed iteratively by using the Yule-Walker Equations in three different methods for the AR part and the Cholesky factorization for the MA part. The AR parameters are estimated initially, then MA parameters are estimated assuming that the AR parameters have been compensated for. After the estimation of each parameter set, the original time series is filtered via the inverse of the last estimate of the transfer function of an AR model or MA model, allowing better and better estimation of each model's coefficients. The iteration refers to the procedure of removing the MA or AR part from the random process in an alternating fashion allowing the creation of an almost pure AR or MA process, respectively. As the iteration continues the estimates are improving. When the iteration reaches a point where the coefficients converse the last VIA and AR model coefficients are retained as final estimates. / http://archive.org/details/armamodeling00kaya / Lieutenant Junior Grade, Turkish Navy

No description available.

No description available.

Consider a Gaussian stationary stochastic vector process with the property that designated pairs of components are conditionally independent given the rest of the components. Such processes can be represented on a graph where the components are nodes and the lack of a connecting link between two nodes signifies conditional independence. This leads to a sparsity pattern in the inverse of the matrix-valued spectral density. Such graphical models find applications in speech, bioinformatics, image processing, econometrics and many other fields, where the problem to fit an autoregressive (AR) model to such a process has been considered. In this paper we take this problem one step further, namely to fit an autoregressive moving-average (ARMA) model to the same data. We develop a theoretical framework and an optimization procedure which also spreads further light on previous approaches and results. This procedure is then applied to the identification problem of estimating the ARMA parameters as well as the topology of the graph from statistical data. / <p>Updated from "Preprint" to "Article" QC 20130627</p>

Nesse trabalho, exploramos técnicas para análise de séries temporais para fins de previsão. Para tanto, foram considerados dados observados de três séries climáticas e de uma série econômica. Para análise das séries climáticas, foi considerada a modelagem multivariada em comparação com os subsequentes modelos univariados de cada série. Os modelos multivariados e univariados foram comparados com base em seus respectivos resultados preditivos. Para análise da série econômica, considerou-se a modelagem ARMA-GARCH, cuja média condicional e variância condicional são modeladas conjuntamente. Para essa mesma série foi realizada uma modelagem ARIMA em que considerou-se dois casos. No primeiro, a modelagem foi realizada na série original. No segundo, foi realizada na pré-modelagem uma filtragem na série, denominada de sistema de decomposição Wavelet- WavDS, com o objetivo de melhorar o poder preditivo. Na seleção dos modelos ARIMA, considerou-se a metodologia backtesting, em que as previsões são realizadas de forma sequencial, o modelo selecionado foi o que apresentou menor raiz quadrada do erro quadrático médio de previsão (REQM). Toda análise estatística realizada nesse trabalho foi com auxílio do software livre R. / In this study, we explored techniques of time-series analysis for prediction purposes. For that, we considered data observed from three climate series and one economic series. For the analysis of the climate series, we considered the multivariate modelling in comparison with the subsequent univariate models of each series. The multivariate and univariate models were compared based on their respective predictive results. For the analysis of the economic series, the ARMA-GARCH modeling was considered, whose conditional average and conditional variance are modeled together. For this same series, the ARIMA modeling was used, considering two cases. At first, the modeling was performed in the original series. In the second, we carried out a filtering in the series during pre-modeling, called Wavelet- WavDS decomposition system, in order to improve the predictive power. In the selection of ARIMA models, we considered the backtesting methodology in which forecasts are performed in sequence. The model selected showed the lowest square root mean of the prediction square error (REQM). All statistical analyses performed in this work were carried out using the free software R.