Thesis (M. Phil.)--University of Hong Kong, 2005. / Title proper from title frame. Also available in printed format.

Electricity load forecasts now form an essential part of the routine operations of electricity companies. The complexity of the short-term load forecasting (STLF) problem arises from the multiple seasonal components, the change in consumer behaviour during holiday seasons and other social and religious events that affect electricity consumption. The aim of this research is to produce models for electricity demand that can be used to further the understanding of the dynamics of electricity consumption in South Wales. These models can also be used to produce weather corrected forecasts, and to provide short-term load forecasts. Two novel time series modelling approaches were introduced and developed. Profiles ARIMA (PARIMA) and the Variability Decomposition Method (VDM). PARIMA is a univariate modelling approach that is based on the hierarchical modelling of the different components of the electricity demand series as deterministic profiles, and modelling the remainder stochastic component as ARIMA, serving as a simple yet versatile signal extraction procedure and as a powerful prewhitening technique. The VDM is a robust transfer function modelling approach that is based on decomposing the variability in time series data to that of inherent and external. It focuses the transfer function model building on explaining the external variability of the data and produces models with parameters that are pertinent to the components of the series. Several candidate input variables for the VDM models for electricity demand were investigated, and a novel collective measure of temperature the Fair Temperature Value (FTV) was introduced. The FTV takes into account the changes in variance of the daily maximum and minimum temperatures with time, making it a more suitable explanatory variable for the VDM model. The novel PARIMA and VDM approaches were used to model the quarterly, monthly, weekly, and daily demand series. Both approaches succeeded where existing approaches were unsuccessful and, where comparisons are possible, produced models that were superior in performance. The VDM model with the FTV as its explanatory variable was the best performing model in the analysis and was used for weather correction. Here, weather corrected forecasts were produced using the weather sensitive components of the PARIMA models and the FTV transfer function component of the VDM model.

This thesis suggests a general approach for estimating the trend of a univariate time series. It begins by suggesting and defining a set of "desirable" trend properties, namely "Fidelity", "Smoothness", "Invariance" and "Additivity", which are then incorporated into the design of an appropriate non-stationary time series model. The unknown parameters of the model are then estimated using a wide selection of "optimal" procedures, each parameter having at least two such procedures applied to it. Attention is paid to the development of algorithms to implement the procedures in practice. The model is gradually extended from a basic, non-seasonal model consisting of a simple lagged trend to a general, seasonal model incorporating a variable parameter, general autoregressive trend.

The Ozark National Scenic Riverways (ONSR) has seen a wide range of recreationists since its establishment in 1964. To better understand these recreationists, Experience Use History (EUH) has been identified as a measure of exposure to ONSR. EUH is a construct used to identify how often a visitor frequents an area, as well as his or her history with that area. The purpose of this study is to identify the changes in river user demographics over the past 24 years and how these changes relate to EUH using time series analyses. Study field methods follow procedures of Rapid Assessment Visitor Inventory (RAVI), which has been periodically conducted at ONSR since 1972. This study utilizes questionnaires for which raw data were available, collected from 1986 through 2010 to conduct time series analyses of visitor demographics and EUH. EUH groupings were created using the methods of Smith et al. (2009), resulting in the identification of Casual Newcomers, Casual Veterans, Occasional, and Frequent visitors. While a wealth of information exists pertaining to EUH and general demographics, there is an absence of studies analyzing the dynamic relationship of these variables over time. This research examines for the first time if EUH classifications are also time-dependent or if they are functionally stable at a quarter-century time scale. EUH trends over time showed that Casual Newcomers have begun to transition into Casual Veterans throughout the riverways as their history and frequency of visits increased over the years. Changes in age, watercraft type, and gender were also detected resulting in an aging visitor group to ONSR, an increase in motorboat use, and a slow increase in the proportion of female visitors. Experiences, preferences, and attitudes were also analyzed in terms of both EUH and river district. Finally, average distance traveled by visitors was also analyzed showing ONSR to be a regional attraction attended by both urban and nonurban visitors. Overall this study suggests that visitor populations to ONSR are dynamic. Some of the most important findings of this study showed that EUH category for a given visitor can and does change over time. The Casual Newcomers and Casual Veterans had clear trends; all three river districts showed distinct trends of increasing Casual Veterans and decreasing Casual Newcomers over time but at varying rates of change in proportion. This finding coupled with the aging of visitors to ONSR, suggests that visitors are returning to the riverways and, over time, increasing in experience, thus transforming the Casual Newcomers into Casual Veterans.

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.

No abstract available. / Dissertation (MSc (Mathematical Statistics))--University of Pretoria, 2007. / Mathematics and Applied Mathematics / unrestricted

Causal analysis is a significant role-playing field in the applied sciences such as statistics, econometrics, and technometrics. Particularly, probability-raising models have warranted significant research interest. Most of the discussions in this area are philosophical in nature. Contemporarily, the econometric causality theory, developed by C.J.W. Granger, is popular in practical, time series causal applications. While this type of causality technique has many strong features, it has serious limitations. The processes studied, in particular, should be stationary and causal relationships are restricted to be linear. However, we cannot classify regime-switching processes as linear and stationary. I.J. Good proposed a probabilistic, event-type explication of causality that circumvents some of the limitations of Granger’s methodology. This work uses the probability raising causality ideology, as postulated by Good, to propose some causal analysis methodology applicable in a stochastic, non-stationary domain. There is a proposal made for a Good’s causality test, by transforming the originally specified probabilistic causality theory from random events to a stochastic, regime-switching framework. The researcher performed methodological validation via causality simulations for a Markov, regime-switching model. The proposed test can be used to detect whether none stochastic process is causal to the observed behaviour of another, probabilistically. In particular, the regime-switch causality explication proposed herein is pivotal to the results articulated. This research also examines the power of the proposed test by using simulations, and outlines some steps that one may take in using the test in a practical setting.

No description available.

Time series models have been widely used in simulating financial data sets. Finding a nice way to estimate the parameters is really important. One of the traditional ways is to use maximum likelihood estimation to make an approach. However, when the error terms don’t have normality, MLE would be less efficient. Quasi maximum likelihood estimation, also regarded as Gaussian MLE, would be more efficient. Considering the heavy-tailed financial data sets, we can use non-Gaussian quasi maximum likelihood, which needs less assumptions and conditions. We use real financial data sets to compare these estimators.

ARMA model selection with criterion such as AIC and BIC tends not to select a consistent ARMA model with high probability. Hence data splitting is not reliable. One technique was fairly reliable with large sample sizes, and a modification also worked.The DD plot for visualizing prediction regions can also be used to visualize three bootstrap confidence regions.