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I have the a time series data, the acf and pacf for which have been displayed below: enter image description here

enter image description here

I get that MA term is 1. But I'm confused about AR term since it is geometrically decaying from 7th lag. Do I need to transform the data again to eliminate this?

PS: This data has already been differenced once.

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  • $\begingroup$ Are these daily data? $\endgroup$ – Stephan Kolassa Sep 22 '18 at 11:33
  • $\begingroup$ @StephanKolassa Yes $\endgroup$ – Dom Jo Sep 22 '18 at 16:38
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Only your data knows for sure as there may be a weekly deterministic effect (seasonal pulses) and other "features" waiting to be discovered .... post your data and I will try and help further .. The acf and pacf are descriptive but only inferential iff ...no pulses , no level/step shifts , no seasonal pulses . no local time trends , constant error variance and parameters over time

after receipt of your data ( 366 days enter image description hereily values for 1 year ) . In summary ...when you have daily data there could be

  1. day-of-the-week effects not provable with your data
  2. week-of-the-year effects not provable with your data
  3. month-of-the-year effects provable
  4. day-of-the-month effects not provable with your data
  5. week-if-the-month effects not provable with your data
  6. holiday effects not provable with your data
  7. long weekend effects not provable with your data
  8. level shift effects not significant
  9. local time trends not significant
  10. arima effects not significant
  11. differencing effects not significant
  12. pulse effects significant
  13. paramater changes over time not provable with your data
  14. power transform effects significant

15 deterministic error var change not provable with your data

16 exogenous variables effect not provable with your data

The software I used identified a number of pulses ...1 period anomalies . See the Actual and Cleansed graph here enter image description here . The cleansed series led directly to a seasonal model with 10 predictors using a log transformation enter image description here.

The plot of the residuals is here enter image description here suggesting reduced variablity during the summer months. The residual acf is here enter image description here

Responding directly to your question the best arima model is (0,0,0)(0,0,0) with 10 Monthly Seasonal Indicators reflecting deterministic changes through the year.

The pulses that were identified are here : enter image description here and model summary here enter image description here

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  • $\begingroup$ How do I post a data here? $\endgroup$ – Dom Jo Sep 22 '18 at 16:39
  • $\begingroup$ If you can't post ...then email it to me and I will try to answer your question. $\endgroup$ – IrishStat Sep 22 '18 at 19:11
  • $\begingroup$ drive.google.com/open?id=1dhL0XvGFGWetbJqv-uLnSDZNpojHPh5X $\endgroup$ – Dom Jo Sep 23 '18 at 5:16
  • $\begingroup$ Here is the google drive link to my data. $\endgroup$ – Dom Jo Sep 23 '18 at 5:17
  • $\begingroup$ Thanks a lot. From where can I learn time series forecasting (theory and practicals in R/Python) given that I already know some basics.? $\endgroup$ – Dom Jo Sep 24 '18 at 12:46

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