I am trying to make a prediction on a time series that look like this (the trend, seasonality and residuals are extracted with a frequency of 12 months: data

It is a time series of approx 3500 values (10 years).

As you can see, there's high noise and high non stationarity, and we can observe seasonality. I want to fit both an ARIMA model and a recurrent neural network (RNN).

1) For the ARIMA model, should I differenciate to make the series stationary? If so, how do I get back to my original 'scale'? Or I should remove the trend and seasonality, work only with the residual part, and then add the original trend and seasonality at the end?

2) For the RNN model, would symbolic conversion reduce noise? Is there any other way to reduce the noise or some kind of data preprocessing that leads me into better results? Is there a way to smooth it for training and then 'de-smooth' it for prediction?

Any other ideas are more than welcome.

Thank you!

EDIT 1: You can find the dataset CSV file in the following link. In the image I only displayed one of the three columns (the values I deal with).


  • $\begingroup$ It is often unwise to use too much data as model structure may vary over time. Daily data for 4-5 years is normally sufficient to identify recurring patterns. My old eyes suggest some sort of error variance change perhaps starting at 2018 . Why don't you post a csv file of the original data indicating the start date and country of origin. $\endgroup$ – IrishStat Nov 6 '16 at 10:19
  • $\begingroup$ Thank you for your reply, IrishStat. I have edited my post and posted the CSV file. Please note that every column should be processed separately (non related to each other). $\endgroup$ – user3528810 Nov 6 '16 at 21:15

You posted three series each with 3831 daily values. To demonstrate an approach I took the most recent 1274 values (4 years) for series 1 and obtained enter image description here using AUTOBOX , a time series anlysis package that I helped develop.. A quick visual analysis suggest a possible level shift which was automatically detected using search heuristics. THe ACF OF the original series looked like this enter image description here . THe auromatic process detected the need for weekly determistic structure . two level shifts and an ARIMA model (1,0,0) ..enter image description here and enter image description here . The residials from this model are plotted here enter image description here with this ACF enter image description here . Note that the approximate (very) confidence limits are based upon 1/sqrt(1287) yielding unreasonably tight limits . Nothig to worry about ! THe Actual,Fit and Forecast graph is here enter image description here with the forecasts here enter image description here The residuenter image description hereal histogram is presented here and the Actual/Cleansed data plot here enter image description here. In this manner one can deal holistically with the data , yielding an equation that creats a random process leading to forecasts with reasonble limits. With the following residial acf table I wouldn't be concerned .enter image description here

hope this helps ...

  • $\begingroup$ Thank you for your extensive work, I have got new insight in these series. $\endgroup$ – user3528810 Nov 7 '16 at 15:38

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.