The first chapter proposes the range-based estimator M to avoid long run variance estimation in hypothesis testing about the population mean of a time series process. The denominator of M is the so-called adjusted range normalizer which makes use of the well-established properties for adjusted range (R/S) analysis in time series analysis. Compared to current hypothesis testing approach, M can get rid of choosing tuning parameter or kernel function. Moreover, M has salient property in the way that it takes into account of the extreme value property in time series data especially under heavy tail distributions. We perform asymptotic local power comparisons for M and related tests which show that M has remarkable asymptotic local power performance against a broad class of asymptotics local alternatives. Simulation studies reveal that (1) Size distortion for M is within acceptable level. (2) M has better size performance under IID stable distributions than related tests, especially under extremely heavy tail distribution. (3) Power performance is pronounced for M . We also reveal that incorporating MBB can improve the size performance of M in testing the process where the size performance is deviate much from the true significance level. Real data analysis indicates M has outstanding power performance especially when data depicts larger volatility and more observations are available. The second chapter adopts BML techniques and mutually analyzes commercial banks’ efficiency and profitability. The model used in our paper is the multi-task Gaussian process model in Bonilla (2008). By learning the tasks jointly, the multi-task Gaussian process model can improve the overall accuracy of predictions if task variables are highly correlated. We perform analysis separately using banks’ characteristics variables as input variables and also incorporating macroeconomics variables as input variables as well. Typical banks’ characteristics and macroeconomic variables are being considered. We also take account of the effect of bank size into our analysis. The model fits are all captured by negative marginal log-likelihood. The simulation results show that by decomposing banking sector data accordingto total asset values and including macroeconomic indicators as input variables, one can improve the model fit to certain degree.