# Overlapping time series: is there any better way to visualize them?

I have this time series dataset:

The graph shows trend lines for 7 stock prices. They are very close and overlapping, but you will be able to get an idea that trend lines are layered (i.e. brown on the top and red/orange at the bottom, though far from conspicuous).

Is there any way to better visualize this data? like transforming $y$-axis to another scaling, mapping the whole thing onto cylinder/cone etc.? I tried with moving average, but the improvement is not so good.

NOTE: This is not an ML/DM problem. I am looking for a better/alternative/suitable visualization technique, that's all.

• One possibility is small multiples; you could plot each series in its own plot over a reference line which has the overall mean of all series (which line will be the same for every plot). Oct 26, 2013 at 8:53
• I edited out the word "jitters". In statistical graphics, jittering has a specific meaning of adding noise to points to shake them apart them visually. That doesn't seem intended here. Oct 26, 2013 at 9:44

Graphical comparison of time series is in principle straightforward: plot two or more series against time and look at the graph. Your example is one of many showing that it may not be so easy in practice.

This is pitched fairly generally. For stock prices, some of the strategies may not be especially relevant or successful, but they may have value for other kinds of series.

Some solutions, direct or indirect, include

• Graphical multiples, as already suggested by @Glen_b. Each series could be plotted separately. An extension to the idea of showing a reference series is this: For each series, plot the other series as backdrop in a subdued colour (e.g. a light gray) and then plot the series of interest on top in a more prominent colour.

• Smoothing the series first. Even if you are also interested in fine structure, smoothing can help establish general patterns of change and thus aid understanding.

• Looking at differences or ratios. One series of interest, or an average or other reference series, can be used to look at differences, or as appropriate ratios, of series rather than the series themselves. So, for example, plot (this series $-$ IBM) or (this series / IBM). If using ratios, then consider logarithmic scale too. (Ratios depend on all values being positive, or at least having the same sign, to work.)

• Changing the aspect ratio. Erratic series with numerous changes of direction are often best plotted with an aspect ratio yielding short, long graphs, which you may need to split into different sections. The ideal is that typical segments are at about $45^\circ$. (That is a counsel of perfection for very long series.)

• Sampling. Do you need every value? Would plotting every $k$th value be as informative visually? In some cases, sampling should include local maxima and minima to show important details. The principle here is that short-term changes are often noise and lacking in interest or intelligibility.

I am not certain, what exactly you are trying to capture, but as they are financial time series I've assembled some possible alternate methods to visualize the information.

• As they are stock time series, and I assume returns or price differences, I would recommend integrating (cumsum or cumprod) the series. The cumulative price series would be a better way to visually discern differences between the series.

• If you are trying to visually get a feel for difference of the series in the current form, I would consider breaking up the series into smaller time ranges (using something like panels or trellis plots), as the data looks too compressed to discern much. Here, one can see some correlation of daily series on monthly time intervals.

• You could also run overlapping density plots of each of the individual series to quickly ascertain differences in sample statistics (mean, variance, higher moments). In your case, I would expect to see some separation between the distributions, indicating differences in mean (drift), as well as differences in variance (volatility) between series.

The plots were generated via R.