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I have a daily time series that I am having issues forecasting accurately.The time series is stationary and it looks enter image description here I have tried ARIMA(3,1,1),(0,1,1)- 7 Period, auto.arima(D=1), Holt-Winters, nnetar, tbats, hybridModel and accuracy(RMSE) of test dataset is about 4 which is not good at all. Seasonality in time series looks like enter image description here and I can see in acf and pacf enter image description here plots that there is weekly seasonality. Is there any other method/technique I could use to forecast this daily time series more accurately? I can send the data if needed.

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  • $\begingroup$ send the data .... in a csv file ... show first date and country also take a look at stats.stackexchange.com/questions/313810/… $\endgroup$ – IrishStat Jun 13 '18 at 21:22
  • $\begingroup$ Information such as national holidays should be treated as exogenous not endogenous and should therefore be included in the model as external regressors. . This is also true of day-of-the-week ... day-of-the-month ... week-of-the-month ... month-of-the-year ....AND of course any level shifts or seasonal pulses or time trends or pulses ... In addition there may be the need to include arima structure. ARIMA modelling by itself is useless for data that is driven by HABITS . $\endgroup$ – IrishStat Jun 13 '18 at 21:30
  • $\begingroup$ simple solutions that ignore detecting anomalies and level shifts and time trends while assuming that day-of-the-week factors are constant over time and also require the user to input the window of response around each holiday should be studiously avoided.as it is important to fully extract/detect latent structure.. $\endgroup$ – IrishStat Jun 13 '18 at 22:28
  • $\begingroup$ Thanks for the reply IrisgStat. Would you happen to have an example of timeseries prediction with external regressors?. Also, how/where do i attach my dataset? $\endgroup$ – user2823833 Jun 14 '18 at 1:02
  • $\begingroup$ I sure do .. a couple of hem . I just don't know how to upload a csv file to a SE post.. Please either tell me how to do that or contact me offline and I will email it you. $\endgroup$ – IrishStat Jun 14 '18 at 1:19
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Your series is not stationary - by definition a seasonal series is not stationary. If it were stationary then the d order in your ARIMA model would be 0.

For complex seasonalities, your best option is TBATs. You can also try Facebook Prophet if your time series is daily or above (based on your plot I assume that it is).

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  • $\begingroup$ Hi Alex, thanks for they reply. I guess I was misinformed about a seasonal series properties but it does make sense what you say. I already used TBAT and it it did not do so great. I will check out Facebook Prophet and come back to you about outcome. $\endgroup$ – user2823833 Jun 14 '18 at 1:10
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    $\begingroup$ Alex - Facebook Prophet turned out to be very helpful. Did not increase accuracy as much but I will take advantage of the capability it has to add holidays and see if that helps. I appreciate your help. $\endgroup$ – user2823833 Jun 14 '18 at 20:32
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I took your 1461 daily values http://www.autobox.com/dave/moroni.csv representing visits to a particular lab/clinic for the 4 year period 2014-2017. enter image description here

and predicted the next 31 days. . The Actual/Fit and Forecast is here ... enter image description here with a less busy picture here showing actual and forecasts withoutenter image description here limits . The residuals from the model suggest randomness ..

enter image description here and here enter image description here

. The model is here in 3 parts enter image description here and here enter image description here some more pulses were identified leading to this enter image description here with an ar(1) component

here are the stats for the model ..

enter image description here

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  • $\begingroup$ Thank you for the insights IrishStat. Your quick reply took me for surprise(less than 10 minutes). I will try a machine learning technique to be able to incorporate variables that could impact prediction. $\endgroup$ – user2823833 Jun 14 '18 at 4:04
  • $\begingroup$ ............................................................................................................. $\endgroup$ – IrishStat Jan 4 at 13:12

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