# Visualizing multiple time series with a second time dimension

I have a number of time series, around 10~20. There is a primary time series and each of the other series represents an offset (lead or lag) from this series. Note that this lead or lag is not a lead/lag of the observed time series value but an offset of the underlying variable

$$y_{t}^{0} = f_{t}(x_{t})$$ $$y_{t}^{-1} = f_{t}(x_{t-1})$$ $$y_{t}^{-2} = f_{t}(x_{t-2})$$ $$y_{t}^{+1} = f_{t}(x_{t+1})$$

I am trying to think of a good way to visualize this. One attempt I had come up with was to use color as the lead/lag dimension, such as

I expect a roughly monotonic decrease in the series associated with increasing lags and a similarly roughly monotonic increases in the series associated with leads. A series which would be poorly behaved would look like the following picture.

As you can see the green and red lines are all intermixed, showing this monotonic property is not present. While this roughly accomplishes what I was setting out to do I don't find these graphs particularly easy to read / interpret.

Question

Are there new graphics that could represent this information or ideas on modifications (blending etc.) to the current charts to make them easier to interpret.