This book unlocks the door to many major questions regarding forecasting financial markets. We propose and analyze a distance measure using Kullback- Leibler Information Criterion (KLIC) as a unified statistical test of evaluating, comparing the predictive abilities of possibly misspecified density forecast models, and to assess which volatility and/or distribution are statistically more appropriate to mimic the time series behavior of a return series. The purpose is to determine which GARCH model (volatility) combined with conditional distribution, that allows for time varying variance in a process can adequately represent daily return volatility. The book will be a useful reference for researchers and practitioners in business, finance and insurance facing Value at Risk, volatility modeling, and analysis of serially correlated data. This book is also a useful text of financial time series for students with finance concentration in business, economics, mathematics and statistics who are interest in financial econometrics.