[R] Forecasting and auto.arima issue - Time Series Analysis Assistance

[Abinash Adhikari]

Dear Sir,

This is Abinash, a Statistics and Data Science Explorer, based in India. To
inform you, I am currently working on an automated time series forecasting
rule engine where we will build time series models for daily/monthly
internet usage for different customers/segments etc. I was checking a test
case (a specific segment), where we have monthly internet usage values (in
MB) for 13 months starting from April 2014 and ending at April 2015. I
tried to find out a high precision model but ended with confusion about
selecting the best model. Below are the data and my findings. Please assist
me in selecting the right approach/model.

*The Time Series Data is as follows:*

                             TimeValueApr-14412May-14433.3Jun-14446.6Jul-14
468.9Aug-14441.2Sep-14467.2Oct-14480.4Nov-14519Dec-14510.6Jan-15523.7Feb-15
523Mar-15578.7Apr-15655.8

13 months’ internet usage values – the time series data

   1.

   This time series is non-seasonal (having only 13 values with frequency =
   12, monthly data)
   2.

   acf shows ma term as 1
   3.

   pacf shows ar term as 0
   4.

   kpss test shows difference should be of order 1 to make the data
   stationary
   5.

   adf test shows difference should be of order 3 to make the data
   stationary

Hence as per above acf, pacf, adf and kpss tests the final model should be
arima(0,3,1)

but I am getting aic = 106.1298 and mape = 5.900683 if I use the model
arima(0,3,1)

I am getting two better models with the below aic and MAPE

arima(1,3,0) aic = 102.7753, mape = 5.415326

arima(9,3,17) aic = 15.4278, mape = 0.0211097

Also, if I use *auto.arima* I am getting the arima model as *arima(0,1,0)
with drift* where aic = 107.5 and mape = 4.366589

I have finally chosen the model as arima(9,3,17), based on lowest aic
(15.43) and mape (0.0211). But I doubt how one can fit arima with *ar term
9 and ma term 17* when we have only *13 months'* values, and it is coming
as the best fitted model !!!

My questions are

   1.

   Have I fitted the models correctly?
   2.

   Can we fit the model arima(9,3,17) for a series which is having only 13
   month’s values ?
   3.

   Was the approach right?
   4.

   Is there any other better model that can be fitted to this data?
   5.

   Why auto.arima is not giving me the right model? Is there anything wrong
   in selecting model, defining parameters?

Please assist me in fitting a right model (arima or any other suitable
model) for this data which will have a high accuracy and a good logic
behind fitting the model, as the general approach (time series steps and
auto.arima) is failing here, it seems. Awaiting your positive response.
Glad to connect with you. Thanks in advance

Best Regards,
Abinash Adhikari,
Data Scientist (Statistician)
Contact Number: +91 9007654437

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