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I thought my network was experiencing outages. I collected bandwidth (Mbps) measurements every 30 min.

A cumulative probability distribution shows the probability that bandwidth will exceed any given value (e.g. P(x > X)). However, this was not very insightful.

A continuous wavelet transform using PyWavelets did not show any strong peaks (i.e. heat map of cwt in scale and time). That meant to me that there was not a consistent duration for the outages.

What would be some ways to analyze the signal to see the time scale of outages?

Sample Data

Measured Bandwidth over Time

Cumulative Probability enter image description here

CWT using PyWavelet enter image description here

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  • $\begingroup$ It is unlikely that the time series you have collected would reveal anything about your connectivity. If anything, it would reveal hourly events by which time an outage has already been "felt". You might need to increase the sampling frequency. Would it be possible to post a plot of the signal anyway? $\endgroup$ – A_A May 14 '20 at 11:00
  • $\begingroup$ What sampling would be appropriate? How can one know this without a priori knowledge of the network? Do DSL and Cable networks have outage patterns that are known? If so, what are they? Or what time scale are they? $\endgroup$ – user3533030 May 15 '20 at 16:03
  • $\begingroup$ Can I please ask if this was resolved? $\endgroup$ – A_A Jun 2 '20 at 8:44
  • $\begingroup$ No. It was not resolved. We can set aside that this data is network bandwidth. I am looking to understand if the signal presented has a characteristic length of time in which its value drops. If there the signal fades randomly in time for a consistent time of 90 min, this should be detectable by a wavelet whose extent is 90 min. Likewise, if the signal is "high" for 300 min before fading, this should be detectable by a wavelet whose extent is 300 min. I don't think anybody has addressed this concept. $\endgroup$ – user3533030 Jun 3 '20 at 1:01
  • $\begingroup$ I do not think that what is mentioned in this last comment is reflected in the question. And also, Wavelets are not necessarily the best tool to detect this. Would it be possible that you update the question so that it gets a chance to be answered? Otherwise it will keep circling the board as "unanswered". $\endgroup$ – A_A Jun 3 '20 at 9:30
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I thought my network was experiencing outages. I collected bandwidth (Mbps) measurements every 30 min.

. . .

What would be some ways to analyze the signal to see the time scale of outages?

An "outage" is a random event. Therefore, looking for regularity in outages might be hinting at something more widely already known.

The answers to the questions in the comments are very much dependent to the objectives. But I will try to make this a bit more constructive.

For example: The CDF presented is over 1400 instances at 30 minute intervals and it therefore gives you the probability of sustained download at a particular speed over 1400*30 minutes or about 30 days (If the horizontal axis depicts the index of the measurement). If you were asking if your line would sustain a download speed over the next 15 minutes, the answer would be "I don't know", because you have not measured anything more frequently than 15 minutes.

On their own, wavelets and discrete fourier analysis cannot tell you much. They can tell you that a particular segment of the signal suddenly requires many more components to describe it and this usually happens at discontinuities but this helps in recognising a "spike" which you can already do here by thresholding (for example).

Rather, if you suspect that there is some regularity in the outages and you want to estimate it, then what you can do is some form of time series decomposition.

You can run autocorrelation for example and this will already give you a handle on periodicity. Or a full blown discrete fourier transform (or even wavelet transform) to determine periodic components more accurately.

By determining the Trend and Seasonality components of your signal, you can then create "filters" to discover areas where it veers off its usual course. (And then of course, having discovered the timestamps of those events, you can analyse (or try to predict) the time that passess between them and see if there is anything useful in there).

But notice here, we always need a time reference. For example, when you assess Trend, a trend over what time scale? This will then determine how often you need to observe the signal.

Hope this helps.

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