Thesis (Ph. D.)--University of Wisconsin--Madison, 1969. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

The aim of this thesis is to investigate of bootstrap methods (Efron, 1979), in the the performance estimation of parameter estimates in non-linear time series models, in particular SETAR models (Tong, 1993). First and higher order SETAR models in known and unknown thresholds cases are considered. To assess the performance of bootstrap methods, we first give an extensive simulation study (by using simulated normal errors), in chapters 3 and 4, to investigate large and small sample behaviours of the true sampling distributions of parameter estimates of SETAR models and how they are affected by sample size. First and higher order SETAR models in the known and unknown threshold cases are considered. An introduction to the bootstrap methods (Efron, 1979 ) is given in chapter 5. The effect of sample size on the bootstrap distributions of parameter estimates of first and higher order SETAR models in the known and unknown threshold cases ( for given order, delay and number of thresholds ) are also investigated in this chapter, via simulation and by using the same models used in the simulated normal errors 'true distribution' case ( chapters 3 & 4). The results are compared with simulated normal case in order to assess the bootstrap results. Tong and Lim (1980) method is used for fitting SETAR models to bootstrap samples, which is also used in the initial fit. Moreover, applications of bootstrap to celebrated data sets, namely, the logarithmically transformed lynx data covering the period (182-1934); and the sunspot numbers covering the period (1700- 1920), are attempted. The cyclical behaviours of bootstrap models are also examined. Finally, in chapter 5, an attempt is also made to study the problem of non-linear properties of the skeleton of a non-linear autoregressive process (Jones, 1976) via simulation and we study in particular a limit cycle behaviour.

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Thesis (Ph. D.)--Ohio State University, 2007. / Title from first page of PDF file. Includes bibliographical references (p. 195-199).

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This article investigates the detection and identification problems for changing of regimes about non-linear time series process. We apply the concept of genetic algorithm and AIC criterion to test the changing of regimes. This way is different from traditional detection methods According to our statistical decision procedure, the mean of moving average and the genetic detection for the underlying time series will be considered to decide change points. Finally, an empirical application about the detection and identification of change points for the Taiwan Business Cycle is illustrated.

This article investigates the detection and identification problems for changing of regimes about non-linear time series process. We apply the concept of genetic algorithm and AIC criterion to test the changing of regimes. This way is different from traditional detection methods. According to our statistical decision procedure, the mean of moving average and the genetic detection for the underlying time series will be considered to decide change points. Finally, an empirical application about the detection and identification of change points for the Taiwan Business Cycle is illustrated.

<p> A unique approach for the modeling of phase noise is examined in this thesis. In previous work regarding phase noise theory, the memory property of phase is virtually ignored. The thesis introduces the Discrete Recursive Procedure (DRP): a systematic approach or methodology to predict phase noise using a discrete recursive algorithm taking into account the memory property of phase. This discrete recursive algorithm is a general extension of the Linear Time Varying (LTV) model and is referred to as the NonLinear Time Varying (NLTV) model. </p> <p> Simulations are performed using the DRP method. Phase fluctuation comparisons are made between the LTV and the NLTV models for an ideal oscillator. The simulation results show that the NLTV model taking into account the memory property of phase makes more realistic phase noise predictions than the LTV model for asymmetrical Impulse Sensitivity Function (ISF) cases. Phase noise simulation results using the NLTV model are given for a modified 810-MHz CMOS cross-coupled LC oscillator design. At 90kHz offset, the simulation prediction (-89 dBc/Hz) and the measurement readings (-93 dBc/Hz) are closely matched with a difference of approximately 4 dBc/Hz while the CAD simulation prediction ( -101. 8) has a difference of 9 dBc/Hz from the measurements. In the phase noise simulation for the 62-MHz BIT Colpitts oscillator design, the NLTV model predicts a -26 dBc/decade and -19.5 dBc/decade for the flicker noise and thermal noise regions in accordance with the theoretical -30 dBc/decade and -20 dBc/decade slopes. </p> / Thesis / Master of Applied Science (MASc)

Frequency domain models for power electronic circuits are either based on iterative techniques such as Newton's method or linearised around an operating point. Iterative frequency domain models provide great accuracy as they are capable of calculating the exact switching instants of the device. On the other hand, the accuracy of a linearised frequency domain model relies on the magnitude of input waveform to be small so that the circuit's operating point does not vary or varies very little. However, an important advantage of a linearised model is its ability to provide insight into waveform distortion interaction, more specifically, the frequency cross-coupling around a power electronic circuit. In general, a linearised model for harmonic analysis would not normally include the description of feedback control. Likewise a linearised model for control analysis would usually disregard frequency interactions above the fundamental (or the most significant component); that is assuming the cross-coupling between harmonic frequencies does not affect the dynamics of control. However, this thesis proposes that a linearised model for control analysis shall also include the complete description of frequency cross-coupling between harmonics to produce the correct dynamic response. This thesis presents a harmonic state-space (HSS) model of an HVdc converter that incorporates the full effect of varying switching instants, both through control and commutation period dynamics, while remaining within the constraints of a linear time-invariant (LTI) system. An example is given using the HSS model to explain how a close to fifth harmonic resonance contributes to the dominant system response through the frequency cross-coupling of the converter and the controller feedback loop. The response of the system is validated against a time domain model built in PSCAD/EMTDC, and more importantly, the correct response cannot be produced without including the harmonic interactions beyond the fundamental frequency component.

A systematic optimization of the Cohen class time-frequency transformation for detecting the parameters change is developed. The local moments approach to change detection is proposed and a general formula for the local moments is derived. The optimal kernel functions of the time-frequency transformation are determined based on the combined criteria of maximum sensitivity with respect to parameters change and minimum distortion of physical interpretation of the local moments. The sensitivity of the local moment with respect to a certain kind of inputs is analyzed and a most "convenient" and a "worst" input are identified. The results are presented in the form of the case studies for detecting parameters change in simple linear systems. / Graduation date: 1992