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I am new to R. I am trying to apply forecasting model Time Series (TS) Model as follows:

  1. Plotting original data,
  2. Simple Moving Average,
  3. Auto correction(AC), Partial AC, Differencing of TS etc to get stationary time series,
  4. Fitting optimal model which gives minimum AIC, residuals from ARIMA/ARMA
  5. Normality test for residuals
  6. forecasting for future values

The forecast figures are not coming out with the accuracy that I expected. Please find following weekly incidents.

Can anyone please help me with the right approach and sample code?

There are some outliers in the data (# of incidents per week) due to new release of application, seasonality effect and holiday period. 

March 11, 2011/ March 25, 2011/ June 24, 2011/December 02, 2011/ December 30, 2011/ March 30, 2012/ April 20, 2012/ Time_Stamp Wkly_Cnt 1 November 19, 2010 9 2 November 26, 2010 22 3 December 03, 2010 11 4 December 10, 2010 12 5 December 17, 2010 18 6 December 31, 2010 17 7 January 07, 2011 14 8 January 14, 2011 21 9 January 21, 2011 16 10 January 28, 2011 22 11 February 04, 2011 20 12 February 11, 2011 31 13 February 18, 2011 38 14 February 25, 2011 37 15 March 04, 2011 32 16 March 18, 2011 34 17 April 01, 2011 28 18 April 08, 2011 32 19 April 15, 2011 30 20 April 29, 2011 30 21 May 06, 2011 25 22 May 13, 2011 19 23 May 20, 2011 17 24 May 27, 2011 28 25 June 03, 2011 13 26 June 10, 2011 17 27 June 17, 2011 17 28 July 01, 2011 14 29 July 08, 2011 22 30 July 15, 2011 19 31 July 22, 2011 11 32 July 29, 2011 14 33 August 05, 2011 14 34 August 12, 2011 21 35 August 19, 2011 20 36 August 26, 2011 16 37 September 02, 2011 16 38 September 09, 2011 10 39 September 16, 2011 24 40 September 23, 2011 12 41 September 30, 2011 17 42 October 07, 2011 32 43 October 14, 2011 29 44 October 21, 2011 19 45 October 28, 2011 13 46 November 04, 2011 12 47 November 11, 2011 18 48 November 18, 2011 14 49 November 25, 2011 17 50 December 09, 2011 36 51 December 16, 2011 20 52 December 23, 2011 22 53 January 06, 2012 31 54 January 13, 2012 29 55 January 20, 2012 20 56 January 27, 2012 27 57 February 03, 2012 14 58 February 10, 2012 23 59 February 17, 2012 20 60 February 24, 2012 15 61 March 02, 2012 26 62 March 09, 2012 19 63 March 16, 2012 25 64 March 23, 2012 26 65 April 06, 2012 12 66 April 13, 2012 20 67 April 27, 2012 20 68 May 04, 2012 16 69 May 11, 2012 17 70 May 18, 2012 17 71 May 25, 2012 20 72 June 01, 2012 14 73 June 08, 2012 23 74 June 15, 2012 21 75 June 22, 2012 22 76 June 29, 2012 19
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  • $\begingroup$ Someone (not me) voted to close your question. I think the reason is that it is not the policy of the site to take someones data and do an analysis for them. If you want help and would like to have it remain open you should change it substantially. Explain what procedures you used on the data. Tell us what final model you decided on. How did you deal with the outliers? Two members of CV are developers of automatic model selection in the ARIMA class of time series models. $\endgroup$ Commented Sep 24, 2012 at 17:02
  • $\begingroup$ In particular IrishStat has over the course of decades refined his autobox software to handle issues of outliers and interventions that can mess up conventional arima modeling. if he sees this post he may decide to apply his software to your data and give you an analysis as an answer. But you may want to know more than just that so that you can better understand how to do time series modeling for other problems. Others here may be able to help you with that if you modify your question so that we can give you advice and see where you might have gone wrong. $\endgroup$ Commented Sep 24, 2012 at 17:06
  • $\begingroup$ It is also possible that you did nothing wrong and your expectations about how accurately you can forecaast based on the given data set are too high. $\endgroup$ Commented Sep 24, 2012 at 17:07
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    $\begingroup$ See otexts.com/fpp for an introduction to time series forecasting in R. $\endgroup$ Commented Sep 25, 2012 at 3:07
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    $\begingroup$ Sudip, it is better to update your preceding question rather than posting a new one with same material. You may also want to register your account. $\endgroup$ Commented Sep 25, 2012 at 15:42

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I would recommend to read the free online textbook by Rob J Hyndman and George Athanasopoulos: http://otexts.com/fpp/. There you find R code and a package to do all those things.

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  • $\begingroup$ You might want to consider some questions he didn't ask and how to remedy them. Is there one or more level shifts in the series ? Are there local time trends in the series " Are there unspecified weekly effects that appear to be significant " Are there changes in the parameters over time ? Are there chnages in the variance of the errors over time ? Ignoring these questions/answers may have consequences. $\endgroup$ Commented Sep 25, 2012 at 12:49
  • $\begingroup$ @IrishStat You ask the right questions - maybe you want to post an answer containing questions and answers. My approach was: he/she wants to do a forecast. Instead of writing 100 lines here I give him/her a link to the best book (online, free) I know with all questions and answers and R code. I prefer this. $\endgroup$ Commented Sep 25, 2012 at 12:56
  • $\begingroup$ I completely understand that if upu simply wanted to answer his questions, your response is adequate. My point is that he is not asking enough questions , given his dataset. $\endgroup$ Commented Sep 25, 2012 at 13:07
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The weekly data can be modelled as enter image description here with ACTUAL-FIT-FORECAST asenter image description here . The residual ACF suggests an adequate model. enter image description here. The solution process is straigtforward in this case : Set uo a 51 weekly dummy model . AUTOBOX keeps two weeks as being significant. DEtect the need for a Level Shift at weeks 12 and 25 in the first year and incorporate two dummy level shift indicators into the regression then detect the 5 points in time where unusual values occurred and incorporate pulse indicators into the regression.

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  • $\begingroup$ The OPs problem may have been not handling the outliers and the level shifts. Even done right it looks to me like the residual variance and hence the prediction variance is still pretty high. Do you agree @IrishStat? $\endgroup$ Commented Sep 25, 2012 at 1:15
  • $\begingroup$ @Michael,Everything is relative,it all depends on how you look at things.I took the data and specified a few models & report the adjusted variance.Mean model=47.23;Trend model=48.25; simple ES= 39.66 ; Automatic ARIMA [without level shifts, pulses and seasonal pulse effects(2,0,0),(0,0,0) = 36.56];The model I reported =18.1.If you only have an automatic ARIMA program that ignores the need for unspecified deterinstic structure the reported model provides a reduction in variance of about 100% while if you only have a mean model the reduction is close to 160%.So it all depends on your base . $\endgroup$ Commented Sep 25, 2012 at 10:46
  • $\begingroup$ You make some very good points with your answer and comment. I agree that the added features in autobox produces better models than one that doesn't have those features and I think you have been able to demonstrate that with several examples on this site. My feeling was that the OP may have unrealistic expectations about how accurately he could forecast based on the original model and the available data. I wonder if he would still be unhappy with your improved model. There is only so much milk you can squeeze out of a cow! $\endgroup$ Commented Sep 25, 2012 at 11:35
  • $\begingroup$ @IrishStat What values did you use for the following dates: March 11, 2011/ March 25, 2011/ June 24, 2011/December 02, 2011/ December 30, 2011/ March 30, 2012/ April 20, 2012/? I ask because values for these dates are not given by the OP. The OP also refers to the data on these dates as outliers, but if I've understood the question correctly, they're actually missing values; not outliers. Has there been a misunderstanding regarding terminology here or am I in the wrong? $\endgroup$ Commented Jul 2, 2013 at 21:23

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