使用auto.arima()结合xreg进行样本外预测的技术咨询

Hey there! Let's walk through how to approach building your monthly sales forecasting model with QUOTES as an exogenous predictor. Here's a practical, step-by-step guide tailored to your data:

• Fix date formatting: First, convert your Month column (like 201401) into a proper datetime type—this is non-negotiable for time series models to recognize temporal order.
  • In Python: pd.to_datetime(df['Month'], format='%Y%m')
  • In R: as.Date(paste0(df$Month, "01"), format="%Y%m%d")
• Spot relationships: Plot BILLINGS and QUOTES side-by-side over time. You might notice quotes lead to billings with a lag (e.g., quotes in January drive February sales)—if so, test shifting the QUOTES column (e.g., use QUOTES from the prior month as a predictor).
• Clean anomalies: Check for missing monthly data or extreme outliers. Fill gaps with interpolation if needed, and consider winsorizing outliers that are one-off errors (not true business trends).

Since you’re using QUOTES as a regressor, these are your top options:

• ARIMAX/SARIMAX: A classic time series choice that combines ARIMA with external predictors. Use auto-optimization tools to find the best AR/I/MA orders, or leverage ACF/PACF plots to tune manually.
  • Python (statsmodels) example:

    from statsmodels.tsa.statespace.sarimax import SARIMAX
    # Include seasonality with SARIMAX if your data has monthly cycles
    model = SARIMAX(df['BILLINGS'], order=(1,1,1), seasonal_order=(1,1,1,12), exog=df['QUOTES'])
    results = model.fit()
    

  • R (forecast package) example:

    library(forecast)
    model <- auto.arima(df$BILLINGS, xreg=df$QUOTES, seasonal=TRUE)
    

• Prophet with Regressors: Facebook Prophet is user-friendly for handling trends and seasonality, and it integrates external regressors seamlessly.
  • Python example:

    from prophet import Prophet
    # Rename columns to match Prophet's required format
    df_prophet = df.rename(columns={'Month': 'ds', 'BILLINGS': 'y', 'QUOTES': 'quotes'})
    model = Prophet(seasonality_mode='additive')
    model.add_regressor('quotes')  # Add your exogenous variable
    model.fit(df_prophet)
    

• Linear Regression with Time Features: If your data has clear linear trends, create time-based features (month dummies, a continuous trend index) alongside QUOTES for a simple interpretable model. Just check for autocorrelation in residuals—if present, add AR terms to fix it.

• Time-series cross-validation: Don’t use random train-test splits! Split your data sequentially (e.g., train on 2014-2017, test on 2018 Jan-Mar) to mimic real-world forecasting.
• Evaluate with relevant metrics: Use MAE (Mean Absolute Error), RMSE (Root Mean Squared Error), and MAPE (Mean Absolute Percentage Error) to compare model performance. MAPE is especially useful for understanding forecast error as a percentage of actual sales.
• Check residuals: Ensure your model’s residuals are white noise (no autocorrelation, mean zero). Use ACF plots or the Ljung-Box test—if residuals show patterns, your model is missing something (like an unaccounted lag in QUOTES or seasonal component).

• Get future QUOTES data: To forecast sales, you’ll need future values of QUOTES. If you don’t have actual future quotes, first build a separate time series model to forecast QUOTES, then feed those predictions into your sales forecast model.
• Produce and visualize forecasts: Most libraries (like statsmodels or Prophet) have built-in functions to generate forecasted values and confidence intervals. Plot these against your historical data to sanity-check the results.

• Test lagged QUOTES values: Don’t assume quotes impact sales immediately—test lags of 1, 2, or even 3 months to find which drives the best model performance.
• Account for seasonality: Monthly sales almost always have seasonal patterns (e.g., higher sales in holiday months). Make sure your model explicitly handles this (SARIMAX’s seasonal terms, Prophet’s built-in seasonality, or month dummies in linear regression).
• Don’t overfit: Resist the urge to add too many AR/MA terms or features. Use cross-validation to ensure your model generalizes to unseen data, not just your training set.

内容的提问来源于stack exchange，提问作者Dana Hagist