So I have the following time series plot and I am asked if the data is independent and identically distributed and I'm not quite sure how I would tell?

enter image description here

This represents the number of people going to a certain city over the months(x- axis) (10 year time period). Intuitively I don't think they are i.i.d, however, does the timeseries plot show otherwise? (This is my first time dealing with data visualization so I'm not well-versed with these things).

  • $\begingroup$ You might consider removing the followup question and posting it as a separate question, since it's not conceptually related and the policy here is to ask one question per post. This will hopefully help you get better answers. $\endgroup$ – user20160 Feb 11 at 1:47
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    $\begingroup$ I'm not sure of the best way to tell either but, if that is the case, then there's no reason to use a time series analysis because time series analysis is only useful when the observationsare autocorrelated in time. actually, one way would be to do an acf plot of the series. if any of the autocorrelations are non-zero ( you can use box-leung or portmanteau ) then the observations are not iid. there may be other ways but that's simple enough. note that no autocorrelation does not imply iid but, from a practical perspective, they're close. $\endgroup$ – mlofton Feb 11 at 4:30
  • $\begingroup$ Consider this Q&A, which gives examples of ACF plots for iid and Markovian sequences. $\endgroup$ – BruceET Feb 11 at 7:51

I agree with you that this example is probably not iid - a waveform can be seen by the naked eye. Spectral analysis could be used to investigate this. In a nutshell, the signal should be transformed from the time domain to the frequency domain and the power spectrum examined. If the result is an unsloped line (all power components are more or less equal) then the signal is white noise and hence, iid. In this case I'd expect to see a spike in the frequency domain.

Also for the record, if the signal is a random walk, then the power spectrum has a 1/f^2 form and pink noise is 1/f. Only white noise is 1/f^0 = 1 (constant power for all frequencies).


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