Statgraphics for Windows
Model Comparison Report for Series #2
Only models A-C are shown
Data variable: Y
Number of observations = 101
Start index = 1.0
Sampling interval = 1.0
Number of periods withheld for validation: 20

Models
------
(A) Linear trend = 12.5432 + 0.185963 t 
(B) Random walk
(C) ARIMA(0,1,0) with constant  [random walk with drift]

Estimation Period
Model  MSE          MAE          MAPE         ME           MPE
------------------------------------------------------------------------
(A)    2.86312      1.38335      7.24474      2.6755E-15   -0.677354    
(B)    0.940123     0.790566     3.97834      0.254076     1.25625      
(C)    0.886679     0.762752     3.85985      -0.00515478  -0.0865215   

Model  RMSE         RUNS  RUNM  AUTO  MEAN  VAR
-----------------------------------------------
(A)    1.69208       **    ***   ***   OK   OK   
(B)    0.9696        OK    OK    OK    OK   OK   
(C)    0.941636      OK    OK    OK    OK   OK   

Validation Period
Model  MSE          MAE          MAPE         ME           MPE
------------------------------------------------------------------------
(A)    62.0503      7.36523      19.4095      7.36523      19.4095      
(B)    1.28683      0.972335     2.62909      0.640685     1.71384      
(C)    1.02186      0.835759     2.263        0.381454     1.00468      

Key:
RMSE = Root Mean Squared Error
RUNS = Test for excessive runs up and down
RUNM = Test for excessive runs above and below median
AUTO = Box-Pierce test for excessive autocorrelation
MEAN = Test for difference in mean 1st half to 2nd half
VAR = Test for difference in variance 1st half to 2nd half
OK = not significant (p >= 0.10)
* = marginally significant (0.05 < p <= 0.10)
** = significant (0.01 < p <= 0.05)
*** = highly significant (p <= 0.01)

Note that the random walk with drift model (C) is vastly better than the linear trend model (A)
in both the estimation and validation period. It is also slightly better than the random walk
model without drift (B) in the estimation period, and much better in the validation period,
since the series does have a significant trend.