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I have made non-stationary data stationary by differencing at lag 1 and then differencing the differences at lag 11. The data values for months 1/06 through 6/11 are in an Excel file at https://rapidshare.com/files/3190310580/data.xls, reproduced here:

5821    7652    8761    6578    4320    10982   4522    6573    16300   10982   4320    15100   9021    7821    16432   9649    7092    19821   3987    10753   25470   8721    15211   23112   8731    19532   27611   9843    17805   25761   14251   12769   30921   8911    16734   35421   20091   17234   32612   15432   19835   38631   16752   25433   33292   14526   11399   35467   8069    11985   18918   9316    10813   17854   3350    17436   19876   3276    9850    16771   4755    5358    18101   8659    11963   17466

I worked in Minitab with this data set and get the output for ARIMA(2,0,2) model.

Model 2 (AR2, MA2, DF=0)
Final Estimates of Parameters

Type       Coef  SE Coef       T      P
AR   1  -0.9821   0.0366  -26.80  0.000
AR   2  -0.9841   0.0357  -27.56  0.000
MA   1  -0.2964   0.1371   -2.16  0.036
MA   2  -0.3705   0.1412   -2.62  0.011


Number of observations:  54
Residuals:    SS =  2019255200 (backforecasts excluded)
              MS =  40385104  DF = 50


Modified Box-Pierce (Ljung-Box) Chi-Square statistic

Lag            12     24     36     48
Chi-Square   23.7   42.2   54.0   65.0
DF              8     20     32     44
P-Value     0.003  0.003  0.009  0.021

My problem is I don't know how to get the forecast value in Minitab with regard to the actual data set. How to get the graph? Is there any way to get the above result in one command in Minitab (making data stationary in Minitab)?

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If your data are not too big, you can insert them (or a subset) as plain text here; otherwise, please avoid providing link to XLS file (txt or csv is to be preferred). –  chl Sep 1 '11 at 6:53
    
Is this for some subject? –  Glen_b Nov 21 '13 at 21:57
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1 Answer

I was unable to download your data as it seemed to want passwords but I can only surmise that your are mis-identifying the ARMA structure. For example if you have a white noise series you can model [1-phiB][Y-u]=[1-thethaB] where phi=thetha. I have never seen ( or practically never ! ) an ar2 ; ma2 model. If you can post your data so we can get to it , I might be of more help. The coefficients of the AR structure seem to reflect non-stationarity thus you might really have a (0,2,2) model.

After receiving your data it is clear that you are totally mismodelling the series. The acf of the series is enter image description here which leads to a very simple model with frequency of 3 based upon the acf rather than 12 enter image description here which has a residual plot of enter image description here and an equation of enter image description here and a set of forecasts enter image description here

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my original data set was non-stationary. how to make it stationary.What are the values of (p,d,q) for ARIMA model? –  jerin Sep 1 '11 at 18:20
    
:jerin The data set needs to be differenced three periods. This will make it stationary. When you analyze the differenced data you can use an autoregressive model with 1 coefficient and backorder power of three. In summary it could be a (0,1,0)(1,0,0) with seasonality of order 3. –  IrishStat Sep 2 '11 at 20:51
    
Please make this data set Stationary..and post it....plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz help me –  jerin Sep 3 '11 at 21:14
    
jerrin: autobox.com/AUTOBOX-SE/stationary.csv contains the 63 values reflecting a seasonal differencing of order 3. By the way is this series a resultant of taking the ratio between two series like income per capita ? –  IrishStat Sep 4 '11 at 16:54
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@jerin "Please make this data set stationary" does not appear to be a legitimate question for CV; that's a request for someone to do your work for you. Please see the help which includes discussion of whats on topic. Further, use of extreme begging is both pointless (since everyone who asks a question can be presumed to want their questions answered), and carries the dubious implication that somehow you think people are withholding answers they would otherwise give, if only people with questions would plead more. –  Glen_b Nov 21 '13 at 22:03
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