我有一个每周的时代系列，我想为它找到最合适的模型。到目前为止，我已经尝试了 arima、带有 arima 误差的谐波回归、神经网络，最后我想决定哪一个更适合我的原始数据。时间序列看起来像这样，具有严重的季节性和循环模式： 我还将Ljung-Box测试和预测值的图放在这里：

# Arima 
fit <- training %>% auto.arima(lambda = 0)
fit %>% 
  checkresiduals()

    Ljung-Box test

data:  Residuals from ARIMA(3,1,0)
Q* = 23.619, df = 23, p-value = 0.4252

Model df: 3.   Total lags used: 26

#Harmonic regression with arima error
fit2 <- auto.arima(training, lambda = 0, seasonal = TRUE, xreg = fourier(training, K = 4))
fit2 %>%
  checkresiduals()

    Ljung-Box test

data:  Residuals from Regression with ARIMA(2,1,1) errors
Q* = 21.642, df = 15, p-value = 0.1175

Model df: 11.   Total lags used: 26

#Neural Network
fit3 <- nnetar(training, lambda = 0)
fit3

根据Ljung-Box测试，它们似乎都很好，但不知何故未能捕捉到这里时间序列的摆动形式，我不知道它有多重要。但我的主要问题是，当我检查准确性时，如果我选择 RMSE，我必须选择谐波回归，如果我选择 MAPE，我必须选择神经网络模型。而且我还想知道为什么 RMSE 和 MAPE 值在这里如此不同。

# Arima
accuracy(forecast(fit, h = 16), test)
                    ME     RMSE      MAE       MPE     MAPE      MASE       ACF1 Theil's U
Training set  1.948693 27.56683 19.09467 -4.402578 25.87164 0.5790763 0.21495069        NA
Test set     43.293579 61.02374 46.31065 32.745528 39.26652 1.4044442 0.09636865  1.158678

# Harmonic Regression
accuracy(forecast(h = 16, fit2, xreg = fourier(training, K = 4)), test)
                    ME    RMSE      MAE         MPE      MAPE      MASE      ACF1 Theil's U
Training set  4.323546 24.4800 16.05035   -1.464388  21.89874 0.4867525 0.1751586        NA
Test set     -2.495049 42.1323 33.03114 -171.095704 194.16485 1.0017220 0.2349017  4.288442

# Neural Network
accuracy(forecast(fit3, h = 16), test)

                    ME     RMSE      MAE       MPE     MAPE      MASE      ACF1 Theil's U
Training set  3.414448 22.63083 14.31504 -2.615375 16.93870 0.4341265 0.2253450        NA
Test set     40.095160 58.90628 44.16645 28.908539 37.72779 1.3394181 0.1107563  1.119875

非常感谢您的帮助，我非常感谢您提前。