there I am trying to use autocorrelation and partial autocorrelation to get the p and q values of my first AR and MA model. I have followed the Box–Jenkins method up until now. Making my time series stationary and removing trend and seasonality. I am now trying to interpret my acf and pacf plots to get my parameter, but I am finding hard to understand some of my plots. While some of my time series plots are very obvious some are not. Take for instance a time series A when I plot the acf and pcf they both look the exact same to me and they seem as if they are both "cutting off"

ACF enter image description here


enter image description here

As you can see they both look equal both cutting off after the first significant lag. Excuse me if I am looking at this all wrong but I would appreciate any help here guiding me in the right direction. Thanks

Update Posting the data as requested. It is in regards to bitcoin closing price over the last few weeks. This data was then differentiated by one also tried standardizing the data using score (This was advised to me, will this have a negative impact?), The following is original data

2018-02-26    10366.70
2018-02-27    10725.60
2018-02-28    10397.90
2018-03-01    10951.00
2018-03-02    11086.40
2018-03-03    11489.70
2018-03-04    11512.60
2018-03-05    11573.30
2018-03-06    10779.90
2018-03-07     9965.57
2018-03-08     9395.01
2018-03-09     9337.55
2018-03-10     8866.00
2018-03-11     9578.63
2018-03-12     9205.12
2018-03-13     9194.85
2018-03-14     8269.81
2018-03-15     8300.86
2018-03-16     8338.35
2018-03-17     7916.88
2018-03-18     8223.68
2018-03-19     8630.65
2018-03-20     8913.47
2018-03-21     8929.28
2018-03-22     8728.47
2018-03-23     8879.62
2018-03-24     8668.12
2018-03-25     8495.78
2018-03-26     8209.40
2018-03-27     7833.04
2018-03-28     7954.48
2018-03-29     7165.70
2018-03-30     6890.52
2018-03-31     6973.53
2018-04-01     6844.23
2018-04-02     7083.80
2018-04-03     7456.11
2018-04-04     6853.84
2018-04-05     6811.47
2018-04-06     6636.32
2018-04-07     6911.09
2018-04-08     7023.52
2018-04-09     6770.73
2018-04-10     6834.76
2018-04-11     6968.32
2018-04-12     7889.25
2018-04-13     7895.96
2018-04-14     7986.24
2018-04-15     8329.11
  • $\begingroup$ Your software is plotting the zero order coefficients, which is both useless and confusing. You need to ignore those. Then you'll see that neither plot "cuts off", there are just no significant spikes, which is consistent with $p=q=0$ (white noise). $\endgroup$ – Chris Haug Apr 16 '18 at 14:09
  • $\begingroup$ @ChrisHaug Thanks for your reply. Makes sense what you are saying. Would "smoothing" of the data help in this case $\endgroup$ – Alexander Kirwan Apr 16 '18 at 15:26
  • $\begingroup$ What do you mean by "smoothing" and what are you trying to "help" by doing so? $\endgroup$ – Chris Haug Apr 16 '18 at 17:05

Only the data knows for sure what a useful model might be, The ACF and PACF can suggest non-stationarity but they do not disclose the latent cause of the non-stationarity as they are purely descriptive. This caveat is often overlooked in the first few courses in time series analysis. Often the presence of anomalies or level/step shifts or deterministic trends masks or confuses the identification of the underlying model. I suggest you post your actual data and I will use a "robot" to suggest an appropriate model.


The robot ( actually AUTOBOX in an automatic mode ) developed the following useful equation enter image description here . Essentially a difference operator (.906 is nearly 1.0) and two intercept changes . The residuals from the model are reasonably random enter image description here . The Actual vs Cleansed (adjusted) plot is here enter image description here . Actual,Fit and Forecast is here enter image description here .

In summary after adjusting for the two downwards level shifts ( intercept changes) the process is simply a random walk.

  • $\begingroup$ Hi thanks for your reply and the useful information I have updated the post with the data see above, thanks $\endgroup$ – Alexander Kirwan Apr 16 '18 at 15:37
  • $\begingroup$ so the data you posted was the result of differencing ? or is it the original observed data ? $\endgroup$ – IrishStat Apr 16 '18 at 16:17
  • $\begingroup$ Original, sorry I should have mentioned I will update $\endgroup$ – Alexander Kirwan Apr 16 '18 at 16:19

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