The goal of this thesis work was to study the characteristics of the EEG signal and then, based on the insights gained from these studies, pursue an initial investigation into a processing method that would extract useful event related information from single trial EEG. The fundamental tool used to study the EEG signal characteristics was autoregressive modeling. Early investigations pointed to the need to employ robust techniques in both model parameter estimation and signal estimation applications. Pursuing robust techniques ultimately led to the development of a single trial processing method which was based on a simple neurological model that assumed an additive outlier nature of event related potentials to the ongoing EEG process. When event related potentials, such as motor related potentials, are generated by a unique additional process they are "added" into the ongoing process and hence, will appear as additive outlier content when considered from the point of view of the ongoing process. By modeling the EEG with AR models with robustly estimated (GM-estimates) parameters and by using those models in a robust signal estimator, a "cleaned" EEG signal is obtained. The outlier content, data that is extracted from the EEG during cleaning, is then processed to yield event related information. The EEG from four subjects formed the basis of the initial investigation into the viability of this single trial processing scheme. The EEG was collected under two conditions: an active task in which subjects performed a skilled thumb movement and an idle task in which subjects remained alert but did not carry out any motor activity. The outlier content was processed which provided single trial outlier waveforms. In the active case these waveforms possessed consistent features which were found to be related to events in the individual thumb movements. In the idle case the waveforms did not contain consistent features. Bayesian classification of active trials versus idle trials was carried out using a cost statistic resulting from the application of dynamic time warping to the outlier waveforms. Across the four subjects, when the decision boundary was set with the cost of misclassification equal, 93% of the active trials were classified correctly and 18% of the idle trials were incorrectly classified as active. When the cost of misclassifying an idle trial was set to be five times greater, 80% of the active trials were classified correctly and only 1.7% of the idle trials were incorrectly classified as active. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

Ip Ching-Tak. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 68-70). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- The Importance of Time Series Analysis with Outliers --- p.1 / Chapter 2 --- Outlier Analysis in Time Series --- p.4 / Chapter 2.1 --- Basic Idea --- p.4 / Chapter 2.2 --- Outliers in Time Series --- p.6 / Chapter 2.2.1 --- One Outlier Case --- p.6 / Chapter 2.2.2 --- Multiple Outliers Case --- p.8 / Chapter 2.3 --- Outlier Identification --- p.9 / Chapter 2.3.1 --- Outlier Detection of One Outlier Case --- p.9 / Chapter 2.3.2 --- Case of Unknown Model Parameters --- p.10 / Chapter 2.3.3 --- Iterative Identification Procedure --- p.10 / Chapter 3 --- ARMA Model Forecasting --- p.13 / Chapter 3.1 --- Unknown Model Problem --- p.13 / Chapter 3.1.1 --- AR Approximation --- p.14 / Chapter 3.1.2 --- ARMA Approximation --- p.15 / Chapter 3.1.3 --- "Comparison of AIC, AICC and BIC" --- p.16 / Chapter 3.2 --- A Simulation Study --- p.19 / Chapter 3.2.1 --- Results for One-Step-Ahead Forecast --- p.20 / Chapter 3.2.2 --- Results for the Mean of Multiple Forecasts --- p.22 / Chapter 4 --- ARIMA Model Forecasting --- p.24 / Chapter 4.1 --- Effect of Differencing on Time Series --- p.24 / Chapter 4.1.1 --- Outlier Free Model --- p.24 / Chapter 4.1.2 --- Outlier Model --- p.25 / Chapter 4.2 --- Unknown Model Problem --- p.28 / Chapter 4.2.1 --- AR Approximation --- p.28 / Chapter 4.2.2 --- ARMA Approximation --- p.28 / Chapter 4.3 --- Unknown Differencing Case --- p.29 / Chapter 4.4 --- A Simulation Study --- p.29 / Chapter 4.4.1 --- Results for One-Step-Ahead Forecast --- p.30 / Chapter 4.4.2 --- Results for the Mean of Multiple Forecasts --- p.32 / Chapter 5 --- Illustrative Examples --- p.34 / Chapter 5.1 --- Examples of Stationary Time Series --- p.34 / Chapter 5.1.1 --- Example 1 --- p.34 / Chapter 5.1.2 --- Example 2 --- p.36 / Chapter 5.2 --- Examples of Nonstationary Time Series --- p.37 / Chapter 5.2.1 --- Example 3 --- p.37 / Chapter 5.2.2 --- Example 4 --- p.38 / Chapter 6 --- Conclusion --- p.40 / Chapter A --- "Comparison of AIC, AICC and BIC" --- p.42 / Chapter A.1 --- AR Approximation Results --- p.42 / Chapter A.2 --- ARMA Approximation Results --- p.45 / Chapter B --- Simulation Results for ARMA Models --- p.47 / Chapter C --- Simulation Results for ARIMA Models --- p.56 / Chapter D --- SACF and SPACF of Examples --- p.65 / Bibliography --- p.68

Petrochemicals industry is one of the major industries in modern economy. Almost all synthetic chemicals or materials are related. Ethylene is the main product of this industry, which is produced from naphtha cracker. Butadiene is a by-product of naphtha cracking, but it is the most important raw material of synthetic rubbers. Most synthetic rubber plants do not have their own butadiene plant. All the materials were supplied from up-stream crackers. Due to the unstable supply and price surge recently, the cost of butadiene is higher than 70% of the total production cost in synthetic rubbers manufacturing. Huge price fluctuation in butadiene caused a big financial loss in 2008. These economic situations have made the price prediction an important issue for synthetic rubber manufacturers. In this research, we reviewed the historical price data of crude oil, naphtha, ethylene, propylene, butadiene and MTBE from the upper stream of petrochemicals in supply and the price of nature rubber, synthetic rubbers in demand. This study intends to find the petrochemicals price variation factors and uses butadiene as example. ¡§Time series¡¨ and OLS methods are used to build price prediction models to explain the price fluctuation in the past. Our research has found that the monthly price of butadiene is highly related to last month¡¦s price of butadiene, crude oil price and even related to last 9 month butadiene price. This may be because of the regular economical circulation and naphtha crackers annual turn around. The price of spot trading is related to the last week¡¦s price of butadiene and its co-product propylene. Those findings are valuable for synthetic rubber manufacturer in raw material procurement.

Includes bibliographical references (p. 29-30).

Thesis (M. Phil.)--Hong Kong University of Science and Technology, 2003. / Includes bibliographical references (leaves 63-64). Also available in electronic version. Access restricted to campus users.

Thesis (M. Phil.)--Hong Kong University of Science and Technology, 2003. / Includes bibliographical references (leaves 37-39). Also available in electronic version. Access restricted to campus users.

Thesis (M. Phil.)--University of Hong Kong, 2002. / Includes bibliographical references (leaves 76-80).

In financial markets, transaction durations refer to the duration time between two consecutive trades. It is common that more frequent trades are expected to be followed by shorter durations between consecutive transactions, while less frequent trades are expected to be followed by longer durations. Autoregressive conditional duration (ACD) model was developed to model transaction durations, based on the assumption that the expected average duration is dependent on the past durations. Empirically, transaction durations possess much longer memory than expected. The autocorrelation functions of durations decay slowly and are still significant after a large number of lags. Therefore, the fractionally integrated autoregressive conditional duration (FIACD) model was proposed to model this kind of long memory behavior. The ACD model possesses short memory as the dependence of the past durations will die out exponentially. The FIACD model possesses much longer memory as the dependence of the past durations will decay hyperbolically. However, the modeling result would be misleading if the actual dependence of the past durations decays between exponential rate and hyperbolic rate. Neither of these models can truly reveal the memory properties in this case. This thesis proposes a new duration model, named as the hyperbolic autoregressive conditional duration (HYACD) model, which combines the ACD model and the FIACD model into one. It possesses both short memory and long memory properties and allows the dependence of the past durations to decay between the exponential rate and the hyperbolic rate. It also indicates whether the dependence is close to short memory or long memory. The model is applied to the transaction data of AT&T and McDonald stocks traded on NYSE and statistically positive results are obtained when it is compared to the ACD model and the FIACD model. / published_or_final_version / Statistics and Actuarial Science / Master / Master of Philosophy

published_or_final_version / Statistics / Master / Master of Philosophy

Thesis (M. Phil.)--University of Hong Kong, 1994. / Includes bibliographical references (108-113).