This book provides a new contemporary time series approach for econometrics and finance. In a concrete manner a very general divergence between spectra is introduced, resulting in the development of a statistical inference that is efficient and robust, and leads to a new perspective. A measure of systemic risk is also developed in the energy market,which quantifies the cost of energy asset distress vis--vis the broader economy during crises, and examines the dynamic interaction between solvency and funding liquidity risk in banks using a panel vector autoregressive (VAR) model. This step shows that a forward-looking measure of capital shortfall under stress is both a predictor and an outcome of funding liquidity risk. Additionally, a new integrated likelihood-based approach for estimating nonlinear panel data models is described. Unlike existing integrated likelihoods, the new integrated likelihood is closer to a genuine likelihood. The book explains why this is due to first-order information unbiasedness, and why it seems to matter more for inference than for estimation. Results of studies in econometrics are provided for support.