Comparison of seasonal random walk,
seasonal random trend, and other ARIMA
models on deflated auto sales data
Model Comparison
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Data variable: AUTOSALE/CPI
Number of observations = 263
Start index = 1/70
Sampling interval = 1.0 month(s)
Length of seasonality = 12
Number of periods withheld for validation: 24
Models
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(A) ARIMA(0,0,0)x(0,1,0)12 with constant <--Seasonal random walk
(B) ARIMA(1,0,0)x(0,1,0)12 with constant <-- ...with AR=1
(C) ARIMA(0,1,0)x(0,1,0)12 <--Seasonal random trend
(D) ARIMA(0,1,1)x(0,1,1)12 <-- ...with MA=1 and SMA=1
Estimation Period
Model MSE MAE MAPE ME MPE
------------------------------------------------------------------------
(A) 8.85824 2.28831 9.41851 0.0188148 -0.706667
(B) 4.20197 1.45045 5.70019 0.00586504 -0.265589
(C) 4.84114 1.5869 6.19928 -0.00721427 -0.1331
(D) 2.81782 1.25272 4.92789 0.0120522 -0.21509
Model RMSE RUNS RUNM AUTO MEAN VAR
-----------------------------------------------
(A) 2.97628 *** *** *** OK OK
(B) 2.04987 OK * *** OK ***
(C) 2.20026 OK * *** OK ***
(D) 1.67864 OK OK OK OK ***
Validation Period
Model MSE MAE MAPE ME MPE
------------------------------------------------------------------------
(A) 11.2222 3.01909 10.2064 -2.93276 -9.9272
(B) 4.09013 1.67456 5.70802 -0.800644 -2.77393
(C) 4.47723 1.60335 5.48813 -0.0117734 -0.127019
(D) 1.85595 1.01423 3.47177 -0.354179 -1.36136
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)