This answer is built on the answer by jmbejara.
I really like the books he recommended in the last paragraph. They give you an general overview of the landscape on the mathematics involved in macroeconomics.
And immediately you get the following feeling. Economists do not have the background enough to really understand most of the methods they use. They take a more pragmatical, albeit superficial, view of mathematics. Just see the disparity of mathematical areas are crammed into any of those books. From measure theory, to PDE, ODE, Stochastic Calculus/Optimization - these for the solving of the models; Bayesian Statistics, Multivariate Time Series, etc. (for the more empirical part of the work, like model simulation, calibration, etc.). Intersect them all, and right there in the middle, you'll find the mathematics of macroeconomics.
It's almost impossible for economists to have a barely decent understanding of a so many diverse fiels, with their background which more than probably just consists of 2 calculus courses, 2 statistics courses and 2 to 3 econometric courses. Just watch any webcast from AEA with renown researchers, and you'll be amazed at the lack of precision, and exactly wonder how they are able to use some mathematical methods when they understanding of it is so superficial...
I know I'm venting a bit out my accumulated frustration, but since it seems that you're relatively inexperienced in the area, I thought my personal point of view might help you, even though I usually study by myself. Maybe with a formal education, things would be different, but I seriously doubt it.
I'll give two book recommendations for Time Series:
For univariate and small intro to multivariate, you have a great introductory book by Brockwell and Davis. For multivariate time series, choose Lütkepohl, it's the best of the whole group.