在R中选择ARIMA模型：3阶差分下双模型预测选型求助

Hey there! Let's work through picking the best ARIMA model for your 3rd-order differenced data (d.ratio). When deciding between two candidate models, here are the key, practical checks you should run:

• Prioritize Lower Information Criteria (AIC/BIC)
  Always start with comparing the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) values of the two models. These metrics balance how well the model fits your data against its complexity—lower values are better. If one model has a noticeably smaller AIC/BIC, that’s your top candidate. If the values are very close, move on to the next checks.

• Validate Residuals Are White Noise
  A good ARIMA model should leave no predictable pattern in its residuals. To confirm this:

  • Plot the ACF and PACF of the residuals. If all lagged values fall within the 95% confidence bands, there’s no remaining autocorrelation to exploit.
  • Run the Ljung-Box test. If the test’s p-value is greater than your chosen significance level (typically 0.05), you can’t reject the null hypothesis that the residuals are white noise—this is exactly what you want.
  • Check residual distribution with a histogram or Q-Q plot: approximate normality isn’t strictly required, but it makes your prediction intervals more reliable.

• Compare In-Sample Fit Metrics
  Look at error metrics like RMSE (Root Mean Squared Error) or MAE (Mean Absolute Error) for each model’s in-sample predictions. Lower values mean the model fits your existing d.ratio data more closely. You can also plot the model’s fitted values against the actual d.ratio series to visually assess which one tracks the data’s trends and fluctuations better.

• Opt for Parsimony When Performance Is Tied
  If two models perform similarly on the above metrics, go with the simpler one (the one with lower AR(p) or MA(q) order). Simpler models tend to generalize better to unseen data and are less likely to overfit your training set. For example, if you’re choosing between ARIMA(1,3,1) and ARIMA(2,3,2) with nearly identical AIC values, pick the first one.

• Test with Out-of-Sample Data
  The most reliable check is out-of-sample validation: hold back a portion of your data (e.g., the last 10-20% of d.ratio) as a test set. Train both models on the remaining data, predict the test set, and compare their prediction errors (RMSE, MAE, etc.). The model that performs better on the unseen test data is the one you should use for future forecasting.

If you can share the specific output of both models (like AIC/BIC values, residual test results, or order combinations), I can help you narrow it down even further!

内容的提问来源于stack exchange，提问作者KApril