I have a daily time series that I am having issues forecasting accurately.The time series is stationary and it looks 
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 
and I can see in acf and pacf 
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/… $\endgroup$– IrishStatJun 13, 2018 at 21:22
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$\begingroup$ 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 . $\endgroup$– IrishStatJun 13, 2018 at 21:30
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$\begingroup$ 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.. $\endgroup$– IrishStatJun 13, 2018 at 22:28
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$\begingroup$ 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? $\endgroup$– user2823833Jun 14, 2018 at 1:02
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$\begingroup$ 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. $\endgroup$– IrishStatJun 14, 2018 at 1:19
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2 Answers
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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).
answered Jun 13, 2018 at 21:35
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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. $\endgroup$ Jun 14, 2018 at 1:10
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1$\begingroup$ 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. $\endgroup$ Jun 14, 2018 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. 
and predicted the next 31 days. . The Actual/Fit and Forecast is here ... 
with a less busy picture here
showing actual and forecasts without
limits . The residuals from the model suggest randomness ..
and here 
. The model is here in 3 parts 
and here 
some more pulses were identified leading to this 
with an ar(1) component
here are the stats for the model ..
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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. $\endgroup$ Jun 14, 2018 at 4:04
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