In this work we develop various frameworks for performing joint regularized estimation of multiple related high-dimensional time series. The general topic of estimating high-dimensional time series data has received a lot of attention over the years, with applications spanning from gene expression data to stock market returns, macro-econometric time series to brain fMRI measurements, to name a few. One of the most popular operational tools for such data are Vector Autoregressive models (VAR), the focal point of this work. This class of models allows to account for both the temporal dynamics of the variables under consideration and the contemporaneous dependence between them. The main characteristic of high dimensional problems is the excessive amount of unknown model parameters compared to the number of available observations, which renders most classical estimation methods infeasible. An example would be brain fMRI time series data collected over thousands of brain voxels (parameters) during a limited number of time points (observations). For that, we introduce regularized estimation via various Lasso procedures. In many cases one also encounters multiple related high-dimensional time series, e.g. brain fMRI measurements for patients with the same mental disease (ADHD, Autism, Alzheimer's etc). You expect to see certain features that are common for all subjects, and therefore would want to use the data from all the patients to improve the estimation procedure for each time series. We introduce multiple joint modeling frameworks that help to account for that assumed similarity between the related subjects. Those frameworks will leverage various penalties in order to enforce similarity of resulting estimates. In particular, Chapter 2 will implement fused Lasso penalty for econometric time series of multiple US states with similar economical infrastructure and industrial characteristics, while Chapter 3 will employ group Lasso penalty for the aforementioned application to brain fMRI time series data for groups of patients. While both Chapters 2 and 3 will provide simulation study results showing the superior performance of the joint method over classical estimation approaches, neither provides a well-defined inferential procedure to test for the temporal effect significance. Chapter 4 will contain a hypothesis testing procedure for group effects after performing regularized estimation for each member of the group. 10.