How to visualize changes in time series variance

Question

I am exploring a time series with the aim of detecting obvious changes in variance over time (I have little experience in time series analysis). The hypothesis is that the series has become more stable over time (stable=decreased dispersion).

I am wondering whether there are any strategies to visually assess how a measure of dispersion (does not have to be variance) changes as the series progresses. I understand there are tests for the constant variance assumption. My outcome is a daily measure captured over 10 years, with changes between months being the relevant measure.

As a first step, I have plotted the monthly MAD (median absolute deviations) over time. However, I'm not sure that's a sensible approach.

Answer 1

I think this is an good question with a number of possible approaches. Sadly the change in variation over time has received far less study than the change in mean/median value in time series data.

I think there is a good R package for variance changes in time series called 'changepoint'

This has statistical tools for analysing if you have change-points where the variance alters during a series. Its visualisations are, however, much better for means than for variance. It also is dealing more with the times when the variance changes rather than trends over time.

You also seem interested in trends, I think your approach of plotting a variance measure (variance, deviation, MAD etc) is a good place to go. You then of course have another time series! you can analyse this with regression, ARIMA etc and generate trends and forecasts.

I hope this helps