Introduction

The Baregg Tunnel dataset contains daily traffic count (number of vehicles) passing through the tunnel from November 2003 through November 2005. The data is recorded on a day-to-day frequency.

Forecast daily traffic volume and determine which modeling approach provides the most accurate predictions for future periods.

Naïve Model v/s Linear Regression

Validation period: Jul 2005 – Nov 2005.

Data Exploration

Observations

  • Clear weekly seasonality

  • Mild upward trend

  • No extreme outliers

Data Partitioning

Training: Nov 1, 2003 – Jun 30, 2005 Validation: Jul 1, 2005 – Nov 30, 2005

Model Fitting

## # A tibble: 1 × 10
##   .model .type      ME   RMSE    MAE   MPE  MAPE  MASE RMSSE  ACF1
##   <chr>  <chr>   <dbl>  <dbl>  <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 Naive  Test  -12734. 16821. 13606. -12.5  13.1  2.78  1.97 0.376

## # A tibble: 1 × 10
##   .model .type     ME  RMSE   MAE   MPE  MAPE  MASE RMSSE  ACF1
##   <chr>  <chr>  <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 LinReg Test  -1603. 5869. 3900. -1.82  3.70 0.798 0.686 0.622

Forecast with Both Models

Interpretation

  • Naïve forecast is flat

  • Linear Regression captures weekly ups and downs

  • Regression tracks actual traffic more closely

Accuracy Metrics

## # A tibble: 2 × 5
##   .model      ME   RMSE    MAE  MAPE
##   <chr>    <dbl>  <dbl>  <dbl> <dbl>
## 1 LinReg  -1603.  5869.  3900.  3.70
## 2 Naive  -12734. 16821. 13606. 13.1
## MASE Naïve: 1.444
## MASE Linear Regression: 0.414

Interpretation

MASE < 1 → model beats Naïve benchmark

Linear Regression MASE < Naïve → better performance

ME, RMSE, MAE also lower for regression

Observations

  • Residuals fluctuate randomly - Mostly white noise

  • Histogram centered at 0 - No bias

  • ACF shows minimal spikes - Most autocorrelation captured

Conclusion

Recommendation: Use Linear Regression (TSLM) for daily traffic forecasts at Baregg Tunnel.

Daily traffic exhibits strong weekly patterns. Linear Regression with trend + weekly seasonality provides accurate forecasts and should be used over the Naïve benchmark.