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This data shows consumption pattern of a spare part in numbers for last three years. Now I need to forecast its consumption for next 6 months or 1 year. enter image description here

Below is the data for the same:

1. Feb-14   14
2. Mar-14   533
3. Apr-14   729
4. May-14   906
5. Jun-14   916
6. Jul-14   14
7. Aug-14   18
8. Sep-14   1512
9. Oct-14   858
10. Nov-14  373
11. Dec-14  723
12. Jan-15  287
13. Feb-15  1
14. Mar-15  51
15. Apr-15  771
16. May-15  844
17. Jun-15  663
18. Jul-15  351
19. Aug-15  152
20. Sep-15  716
21. Oct-15  0
22. Nov-15  1195
23. Dec-15  878
24. Jan-16  283
25. Feb-16  58
26. Mar-16  366
27. Apr-16  7
28. May-16  687
29. Jun-16  605
30. Jul-16  322
31. Aug-16  523
32. Sep-16  300
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    $\begingroup$ You have presented a problem but have not given a question. Edit the post to let us know what you want answered? $\endgroup$
    – Michael R. Chernick
    Jan 9, 2017 at 3:21

2 Answers 2

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Time series modelling is an iterative process much like peeling an onion. Often time monthly data exhibit quarterly effects and in this case a potential 6 month effect. I took your data into one of my favorite toys AUTOBOX ( which I helped to develop ) and specified a frequency of 12 since it was monthly data. The analysis suggested a very basic model with two anomalies enter image description here . The cleansed data is here enter image description here supporting the possible isolation/cleansing. The actual/fit/forecast plot is here enter image description here . Standard procedure is to examine the residual plot enter image description here and the ACF of the residuals enter image description here which suggests omitted structure as a 6 month pattern is present. This phenomena suggested a seasonality/cycle/repetitive pattern of 6 as being potentially more applicable. Re-identification led to this model enter image description here with two seasonal pulses and one anomaly. The Actual/Fit and Forecast graph is here enter image description here with a more acceptable ACF of residuals here enter image description here .

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You probably want to start with a ARMA model. In order to use an ARMA your data should be stationary, that is white noise with a constant variance. Arguably your data is not stationary as the variance decreases slightly as time progresses and there appears to be strong seasonality so you'll need to difference your data. Here is a good guide to ARIMA modelling which takes you through the steps at a gentle pace.

https://www.otexts.org/fpp/8

(It also includes a section on using auto.arima in R if you're an R user, be careful with this however as in my experience auto.arima doesn't always difference your data when it should be differenced)

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