Thesis (Ph.D.) - Cairo University - Institute of Statistical Studies and Research - Department of Statistics and Econometrics

The subject of this study is the direct identi{uFB01}cation and control of dynamic autoregressive moving average ARMA (n,n-1) models. First part, for univariate time series, the topic is viewed from the frequency domain perspective which turns to the reconstruction of the power spectral density (PSD) or autospectrum into a key issue. In the {uFB01}rst step of the study, concerns are with estimation of the continuous autoregressive moving average model (AM) described in the form of a differential equation with constant coef{uFB01}cients from uniformly sampled data using the dynamic data system (DDS) approach. The second step is to drive the impulse response function (IRF) represents the signal in time domain, and transform into the frequency domain by fourier transform (FT) for autocovariance function (ACF). The third step is analysis and representation of the autospectrum as system frequency response where its point of origin is in the frequency domain estimator. The fourth step is identi{uFB01}cation system stability by driving damping ratio (DR) and natural frequency (NF). Finally application in stock price system as economic time series. Second part, is for multivariate time series, {uFB01}rst step modeling nonstationary time series by decomposition it into the stochastic and sinusoidal model which represent the frequency component as the periodic of the sinusoidal model with speci{uFB01}c amplitude and phase for each periodic to remove the seasonality and deterministic trend. The second step is to convert nonstationary time series to stationary, the head step forecasting was obtained by conditional expectation

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