1. Dealing with higher dimensions
What you've seen so far was the analysis of a single times series. But what if you have to deal with not only one but many time series? There are actually different situations depending on the number of time series to analyze. In the simplest case of 2 time series, visualization is not an issue, but as the number of time series grows, the tools required to visualize them become more and more sophisticated.
2. Multiple time series
In the situation where you have multiple time series, the goal is very often to identify how they interact with each other. For example you might want to evaluate how a stock price reacts to a change in interest rates. In this case, your first time series is the stock price and the second time series is the interest rates. We can extend this example and analyze the effect of a change in interest rates on a set of stocks. Here you will evaluate the impact of interest rates on each stocks individually. Broadly speaking the goal is to identify patterns in the distribution, central tendency and spread over pairs or groups of data. Let's look at an example.
3. 10 time series
In this chart with some effort you can distinguish 10 time series but it is already rather hard to identify patterns between pairs of time series.
4. 100 time series
Let's extend the example to a 100 time series chart. Can you see anything? I bet not. The bottom line is that the complexity of the analysis grows with the size of the dataset. Some of the tools we introduced before are well suited for low dimension problems (a few time series) but for proper multivariate analysis more sophisticated tools need to be introduced.
5. Let's practice!
In this chapter we will start by reviewing standard ways of visualizing relationships in low dimension datasets. Then we will move to higher dimension problems, extend standard concepts and introduce new visualisation tools. Let's do it!