Applied Time Series Modelling and Forecasting
provides a relatively non-technical introduction to applied time series econometrics and forecasting involving non-stationary data.  The emphasis is very much on the why and how and, as much as possible, the authors confine technical material to boxes or point to the relevant sources for more detailed information.
This book is based on an earlier title
Using Cointegration Analysis in Econometric Modelling
by Richard Harris.  As well as updating material covered in the earlier book, there are two major additions involving panel tests for unit roots and cointegration and forecasting of financial time series.  Harris and Sollis have also incorporated as many of the latest techniques in the area as possible including: testing for periodic integration and cointegration; GLS detrending when testing for unit roots; structural breaks and season unit root testing; testing for cointegration with a structural break; asymmetric tests for cointegration; testing for super-exogeniety; seasonal cointegration in multivariate models; and approaches to structural macroeconomic modelling.  In addition, the discussion of certain topics, such as testing for unique vectors, has been simplified.