In many studies, there are large data sets where the same set of variables are measured in different groups. The data is often high-dimensional in that the number of variables measured is larger than the number of observations. Consequently, even though the data sets are large, the sample size in the high-dimensional structure may be small. It is therefore beneficial to share information across the groups in order to draw inference or make predictions. This PhD project focuses on developing new methods for such information sharing. One way to borrow information across groups is by describing similarities in the covariance estimation of the high-dimensional structure. The different groups may share some common features, and one then wants to study how much information can be shared across the groups. In recent years, covariance estimation for multiple groups has been a key feature for drawing inference from heterogeneous populations. However, there has been less research on how we can use covariance estimation for multiple groups in a prediction setting. In this thesis, we will therefore develop a prediction framework applicable in high-dimensional settings, where information is shared across groups. We start by looking at an example from the short term rental market in the US to show how we can use information sharing methods in a prediction setting. Specifically, we hypothesize that the fraction of the market booked when there is a large event taking place in a given location, might share some common structure with similar events in other places. For example, San Francisco and New York are city-markets where larger events take place throughout the year, such as New York Fashion Week and Outside Lands in San Francisco. The type of question we want to answer is: can we use information from other large events (like Outside Lands in San Francisco) to predict how much of the New York market will be booked in 30 days during New York Fashion Week? Further, we also want to expand the framework to predict compound events/systemic risk, where the sum of several small events can lead to an extreme event. A recent example of an extreme event is the extreme weather Hans in Norway in August 2023. The weeks prior to the storm saw several smaller precipitation events and the soil was therefore saturated when the extreme weather happened. If this had not been the case, the floods would probably have been much smaller. By developing methods for sharing information in these situations, we can hopefully more precisely predict the timing and impact of an extreme event. In the first year of the project, we have curated the data set on the short term rental market and built the mathematical foundations of the modelling framework.