The development of time series techniques associated with non stationary data, such as the testing for unit roots and cointegration has presented the applied worker with new challenges in the applied analysis of economic problems.This thesis uses some of these methods to consider a number of questions in the area of labour and financial markets.In particular the thesis considers the application of these methods to two general questions, the specification of the aggregate wage equation in Australia and the efficiency of the Australian stock market. More specifically the thesis focuses on the time series properties of variables commonly used in specifications of the wage equation and then tests them for cointegration. In the financial economics area the thesis tests for the gains to portfolio diversification from the perspective of an Australian investor and the applicability of the present value model of stock prices to the Australian stock market.

This study investigates unconditional convergence of Turkish regions and provinces. A recently introduced time series procedure developed by Nahar and Inder (2002) is used to test the convergence hypothesis for the period 1975-2001. Both the Ordinary Least Square and the Seemingly Unrelated Regression techniques are applied to analyze convergence of sixty five provinces, seven geographical regions as well as 12 NUTS - 1 regions of Turkey. The empirical findings indicate that most of the cases yield no evidence of convergence, which is a general result stated by the other studies in the literature regarding Turkey.

In today's industrial landscape, the pursuit of operational excellence has driven organizations to seek innovative approaches to ensure the uninterrupted functionality of machinery and equipment. Predictive maintenance (PM) provides a pivotal strategy to achieve this goal by detecting faults earlier and predicting maintenance before the system enters a critical state. This thesis proposed a fault detection and diagnosis (FDD) method for predictive maintenance using particle filter resampling and a particle tracking technique. To develop this FDD method, particle filter and hidden Markov model efficiency in the forecasting system state variables are studied on a hydraulic wind power transfer system with different noise levels and system faults. Furthermore, a particle tracker is developed to analyze the particle filter's resampling process and study the particle selection process. After that, the proposed FDD method was developed and validated through three simulation tests employing system degradation models. Furthermore, the system's remaining useful life (RUL) is estimated for those simulation tests.