I got 2 different forecasted results using different orders using SARIMA model. I am unable to choose the best model out of the two below. One have very low AIC but the SR1 co-efficient is close to 1 and standard error produces as NaN and 1.64 MAPE (Mean Absolure Percentage Error). Other model is with little bit higher AIC with 25% MAPE, for which the forecasted values look bit realistic. Please help me understand which is a better model and why?


structure(list(COUNT = c(17L, 1L, 5L, 8L, 45L, 21L, 18L, 43L, 
82L, 116L, 192L, 289L, 242L, 254L, 335L, 138L, 71L, 98L, 91L, 
138L, 175L, 232L, 155L, 376L, 197L, 271L, 421L, 112L, 140L), 
    Enrolment_date = structure(c(27L, 22L, 5L, 11L, 8L, 18L, 
    1L, 20L, 16L, 14L, 3L, 28L, 25L, 23L, 6L, 12L, 9L, 19L, 2L, 
    21L, 17L, 15L, 4L, 29L, 26L, 24L, 7L, 13L, 10L), .Label = c("Apr-18", 
    "Apr-19", "Aug-18", "Aug-19", "Dec-17", "Dec-18", "Dec-19", 
    "Feb-18", "Feb-19", "Feb-20", "Jan-18", "Jan-19", "Jan-20", 
    "Jul-18", "Jul-19", "Jun-18", "Jun-19", "Mar-18", "Mar-19", 
    "May-18", "May-19", "Nov-17", "Nov-18", "Nov-19", "Oct-18", 
    "Oct-19", "Sep-17", "Sep-18", "Sep-19"), class = "factor"), 
    t = structure(c(23L, 5L, 11L, 8L, 18L, 1L, 21L, 16L, 14L, 
    3L, 28L, 26L, 24L, 6L, 12L, 9L, 19L, 2L, 22L, 17L, 15L, 4L, 
    29L, 27L, 25L, 7L, 13L, 10L, 20L), .Label = c("Apr-18", "Apr-19", 
    "Aug-18", "Aug-19", "Dec-17", "Dec-18", "Dec-19", "Feb-18", 
    "Feb-19", "Feb-20", "Jan-18", "Jan-19", "Jan-20", "Jul-18", 
    "Jul-19", "Jun-18", "Jun-19", "Mar-18", "Mar-19", "Mar-20", 
    "May-18", "May-19", "Nov-17", "Nov-18", "Nov-19", "Oct-18", 
    "Oct-19", "Sep-18", "Sep-19"), class = "factor")), class = "data.frame", row.names = c(NA, 

ARIMA order(0,1,4) seasonal (1,2,0) code and results

arima.final <- arima(COUNT, order=c(0,1,4), seasonal= list(order = c(1,2,0), period=12), method="ML")

         ma1      ma2     ma3     ma4     sar1
      0.4754  -0.0199  0.3444  0.0176  -0.9757
s.e.  0.5120   0.7490  1.0154     NaN      NaN

sigma^2 estimated as 370.2:  log likelihood = -25.73,  aic = 63.45
Warning message:
In sqrt(diag(x$var.coef)) : NaNs produced

                   ME     RMSE      MAE      MPE     MAPE       MASE      ACF1
Training set 1.633801 7.148262 2.373956 1.280653 1.648743 0.03365608 0.3193717

ARIMA order (0,1,4) seasonal (1,1,0)

arima(x = COUNT, order = c(0, 1, 4), seasonal = list(order = c(1, 1, 0), period = 12), 
    method = "ML")

          ma1     ma2      ma3      ma4    sar1
      -0.3444  0.1261  -0.0079  -0.4118  0.2965
s.e.   0.2520  0.2881   0.3012   0.3577  0.3732

sigma^2 estimated as 6099:  log likelihood = -93.41,  aic = 198.82

                    ME    RMSE      MAE      MPE     MAPE      MASE      ACF1
Training set -11.81836 58.0095 34.38309 -12.3836 25.16372 0.4874564 -0.120772

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