There are broadly three aspects that one needs to spend time on,while learning about any statistical model. Intuition behind a model in describing a problem/phenomenon/scenario. Nitty gritty of the model : The assumptions of the model, its functional form, the math behind parameter estimation, the way to plot the data and perform diagnostics, do forecasting based on the model and do structural analysis with the model.

The book starts off by stating, Time series econometrics is concerned with the estimation of difference equations containing stochastic components. Hence the book naturally begins with a full-fledged chapter on difference equations. Difference Equations A few examples of difference equations are given such as Random walk model, Structural equation, Reduced form equation, Error correction model to show the reader that difference equations are everywhere in econometrics.Any time series model indeed is trying to explain a univariate variable or a multivariate vector in terms of lagged values, lagged differences, exogenous variables, seasonality variables etc.

Via Hyndsight :

Mathematics is not just solving for X. It’s also figuring out Y (Why). - Arthur Benjamin

Takeaway : The strength of this book is the focus on the simplest state space model and then showing all the aspects of Kalman Filter framework and related pseudo-codes for filtering, smoothing. The novelty of this book is the central focus on the idea of orthogonalization of observation data. This makes all the Kalman Filter related formulae take convenient forms that one can intuitively as well as rigorously understand. One thing missing from this book is the discussion of numerical stability of filtering and smoothing algorithms, considering that the purpose of the book is to enable the reader code up his/her own KF functions.