Best Time Series Model?



Hi All,

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:

Time Value
Apr-14 412
May-14 433.3
Jun-14 446.6
Jul-14 468.9
Aug-14 441.2
Sep-14 467.2
Oct-14 480.4
Nov-14 519
Dec-14 510.6
Jan-15 523.7
Feb-15 523
Mar-15 578.7
Apr-15 655.8

13 months’ internet usage values – the time series data

This time series is non-seasonal (having only 13 values with frequency = 12, monthly data)
acf shows ma term as 1
pacf shows ar term as 0
kpss test shows difference should be of order 1 to make the data stationary
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

Have I fitted the models correctly?
Can we fit the model arima(9,3,17) for a series which is having only 13 month’s values ?
Was the approach right?
Is there any other better model that can be fitted to this data?
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.