In this thesis, a Bayesian approach is adopted to handle parameter estimation and model uncertainty in autoregressive moving average (ARMA) time series models and dynamic linear models (DLM). Bayesian model uncertainty is handled in a parametric fashion through the use of posterior model probabilities computed via Markov chain Monte Carlo (MCMC) simulation techniques. Attention is focused on reversible jump Markov chain Monte Carlo (RJMCMC) samplers, which can move between models of different dimensions, to address the problem of model order uncertainty and strategies for proposing efficient sampling schemes in autoregressive moving average time series models and dynamic linear models are developed. The general problem of assessing convergence of the sampler in a dimension-changing context is addressed by computing estimates of the probabilities of moving to higher and lower dimensional spaces. Graphical and numerical techniques are used to compare different updating schemes. The methodology is illustrated by applying it to both simulated and real data sets and the results for the Bayesian model selection and parameter estimation procedures are compared with the classical model selection criteria and maximum likelihood estimation.

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This PhD thesis focuses on using time series models for counts in modelling and forecasting a special type of count series called intermittent series. An intermittent series is a series of non-negative integer values with some zero values. Such series occur in many areas including inventory control of spare parts. Various methods have been developed for intermittent demand forecasting with Croston’s method being the most widely used. Some studies focus on finding a model underlying Croston’s method. With none of these studies being successful in demonstrating an underlying model for which Croston’s method is optimal, the focus should now shift towards stationary models for intermittent demand forecasting. This thesis explores the application of a class of models for count data called the Integer Autoregressive Moving Average (INARMA) models. INARMA models have had applications in different areas such as medical science and economics, but this is the first attempt to use such a model-based method to forecast intermittent demand. In this PhD research, we first fill some gaps in the INARMA literature by finding the unconditional variance and the autocorrelation function of the general INARMA(p,q) model. The conditional expected value of the aggregated process over lead time is also obtained to be used as a lead time forecast. The accuracy of h-step-ahead and lead time INARMA forecasts are then compared to those obtained by benchmark methods of Croston, Syntetos-Boylan Approximation (SBA) and Shale-Boylan-Johnston (SBJ). The results of the simulation suggest that in the presence of a high autocorrelation in data, INARMA yields much more accurate one-step ahead forecasts than benchmark methods. The degree of improvement increases for longer data histories. It has been shown that instead of identification of the autoregressive and moving average order of the INARMA model, the most general model among the possible models can be used for forecasting. This is especially useful for short history and high autocorrelation in data. The findings of the thesis have been tested on two real data sets: (i) Royal Air Force (RAF) demand history of 16,000 SKUs and (ii) 3,000 series of intermittent demand from the automotive industry. The results show that for sparse data with long history, there is a substantial improvement in using INARMA over the benchmarks in terms of Mean Square Error (MSE) and Mean Absolute Scaled Error (MASE) for the one-step ahead forecasts. However, for series with short history the improvement is narrower. The improvement is greater for h-step ahead forecasts. The results also confirm the superiority of INARMA over the benchmark methods for lead time forecasts.

Since the introduction of CUSUM statistic by E.S. Page (1951), detection of change or a structural break in time series has gained significant interest as its applications span across various disciplines including economics, industrial applications, and environmental data sets. However, many of the early suggested statistics, such as CUSUM or MOSUM, lose their effectiveness when applied to time series data. Either the size or power of the test statistic gets distorted, especially for higher order autoregressive moving average processes. We use the test statistic from Gombay and Serban (2009) for detecting change in the mean of an autoregressive process and show how the application of sieve bootstrap to the time series data can improve the performance of our test to detect change. The effectiveness of the proposed method is illustrated by applying it to economic data sets.

Since the introduction of CUSUM statistic by E.S. Page (1951), detection of change or a structural break in time series has gained significant interest as its applications span across various disciplines including economics, industrial applications, and environmental data sets. However, many of the early suggested statistics, such as CUSUM or MOSUM, lose their effectiveness when applied to time series data. Either the size or power of the test statistic gets distorted, especially for higher order autoregressive moving average processes. We use the test statistic from Gombay and Serban (2009) for detecting change in the mean of an autoregressive process and show how the application of sieve bootstrap to the time series data can improve the performance of our test to detect change. The effectiveness of the proposed method is illustrated by applying it to economic data sets.

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>

Detecting abnormal operating conditions, which will lead to faults developing later, has important economic implications for industries trying to meet their performance and production goals. It is unacceptable to wait for failures that have potential safety, environmental and financial consequences. Moving from a “reactive” strategy to a “proactive” strategy can improve critical equipment reliability and availability while constraining maintenance costs, reducing production deferrals, decreasing the need for spare parts. Once the fault initiates, predicting its progression and deterioration can enable timely interventions without risk to personnel safety or to equipment integrity. This work presents an online-integrated condition monitoring and prognostics framework that addresses the above issues holistically. The proposed framework aligns fully with ISO 17359:2011 and derives from the I-P and P-F curve. Depending upon the running state of machine with respect to its I-P and P-F curve an algorithm will do one of the following: (1) Predict the ideal behaviour and any departure from the normal operating envelope using a combination of Evolving Clustering Method (ECM), a normalised fuzzy weighted distance and tracking signal method. (2) Identify the cause of the departure through an automated diagnostics system using a modified version of ECM for classification. (3) Predict the short-term progression of fault using a modified version of the Dynamic Evolving Neuro-Fuzzy Inference System (DENFIS), called here MDENFIS and a tracking signal method. (4) Predict the long term progression of fault (Prognostics) using a combination of Autoregressive Integrated Moving Average (ARIMA)- Empirical Mode Decomposition (EMD) for predicting the future input values and MDENFIS for predicting the long term progression of fault (output). The proposed model was tested and compared against other models in the literature using benchmarks and field data. This work demonstrates four noticeable improvements over previous methods: (1) Enhanced testing prediction accuracy, (2) comparable processing time if not better, (3) the ability to detect sudden changes in the process and finally (4) the ability to identify and isolate the problem source with high accuracy.

Radar signal processing techniques aim to suppress clutter to enable target detection. Many clutter suppression techniques have been developed to improve the detection performance in literature. Among these methods, the most widely known is MTI plus coherent integrator, which gives sufficient radar performance in various scenarios. However, when the correlation coefficient of clutter is small or the spectral separation between the target and clutter is small, classical approaches to clutter suppression fall short. In this study, we consider the ARMA spectral estimation performance in sea clutter modelled by compound K-distribution through Monte Carlo simulations. The method is applied for varying conditions of clutter spikiness and auto correlation sequences (ACS) depending on the radar operation. The performance of clutter suppression using ARMA spectral estimator, which will be called ARMA-CS in this work, is analyzed under varying ARMA model orders. To compare the clutter suppression of ARMA-CS with that of conventional methods, we use improvement factor (IF) which is the ratio between the output Signal to Interference Ratio (SIR) and input SIR as performance measure. In all cases, the performance of ARMA-CS method is better than conventional clutter suppression methods when the correlation among clutter samples is small or the spectral separation between target and clutter is small.

Detecting abnormal operating conditions, which will lead to faults developing later, has important economic implications for industries trying to meet their performance and production goals. It is unacceptable to wait for failures that have potential safety, environmental and financial consequences. Moving from a “reactive” strategy to a “proactive” strategy can improve critical equipment reliability and availability while constraining maintenance costs, reducing production deferrals, decreasing the need for spare parts. Once the fault initiates, predicting its progression and deterioration can enable timely interventions without risk to personnel safety or to equipment integrity. This work presents an online-integrated condition monitoring and prognostics framework that addresses the above issues holistically. The proposed framework aligns fully with ISO 17359:2011 and derives from the I-P and P-F curve. Depending upon the running state of machine with respect to its I-P and P-F curve an algorithm will do one of the following: (1) Predict the ideal behaviour and any departure from the normal operating envelope using a combination of Evolving Clustering Method (ECM), a normalised fuzzy weighted distance and tracking signal method. (2) Identify the cause of the departure through an automated diagnostics system using a modified version of ECM for classification. (3) Predict the short-term progression of fault using a modified version of the Dynamic Evolving Neuro-Fuzzy Inference System (DENFIS), called here MDENFIS and a tracking signal method. (4) Predict the long term progression of fault (Prognostics) using a combination of Autoregressive Integrated Moving Average (ARIMA)- Empirical Mode Decomposition (EMD) for predicting the future input values and MDENFIS for predicting the long term progression of fault (output). The proposed model was tested and compared against other models in the literature using benchmarks and field data. This work demonstrates four noticeable improvements over previous methods: (1) Enhanced testing prediction accuracy, (2) comparable processing time if not better, (3) the ability to detect sudden changes in the process and finally (4) the ability to identify and isolate the problem source with high accuracy.