Forecasting Motor Vehicle Collision

Heston Model

Dr. Darren Shannon explores the innovative application of the Heston Stochastic Volatility model, traditionally used in finance, to forecast motor vehicle collision rates. He explains that the model's ability to estimate future asset values, such as stocks or commodities, can be adapted to predict collision rates due to observed similarities in data behavior 1. Darren's background in mathematics and quantitative finance, combined with his research on self-driving cars, led him to merge these fields to enhance transportation safety 2. The model's parameters, originally designed for financial markets, were reinterpreted to fit collision data, allowing for accurate predictions of crash rates 3.

Our approach was to see whether the Heston model could be applied well on crash rates, and thankfully the mathematics backed it up.

--- Darren Shannon

This innovative approach highlights the potential of financial models in addressing transportation challenges.

   

Model Comparison

The Heston model's performance was compared to traditional models like Arima and Vasicek, showing a notable improvement in forecasting accuracy. Darren Shannon reports that the Heston model achieved a mean average percentage error of around 5%, compared to 7% and 7.5% for the other models 4. This improvement is significant given the scale of collision rate data. Despite the mathematical similarities between stock market and traffic safety data, Darren notes key differences, such as the independence of crash rates from previous data, unlike stock prices which follow a Markovian property 5.

We found a pretty sizable improvement on the parameters or on the results that they produced.

--- Darren Shannon

These findings suggest that financial models can be effectively adapted for use in transportation safety.

   

Model Adaptation

Adapting the Heston model for collision forecasting involves accounting for unpredictable events and external influences like roadside safety initiatives. Darren Shannon discusses the model's flexibility in incorporating changes such as the introduction of autonomous vehicles, which could temporarily reduce crash rates 6. The model also considers the volatility of crash rates over time, using parameters that reflect current and long-term trends 7. Darren anticipates testing the model against new data, such as changes observed during the pandemic, to assess its robustness and adaptability 8.

We assumed that over the next 25 years, there will be a series of events that serve to reduce the crash rates at an accelerated pace.

--- Darren Shannon

This adaptability ensures the model remains relevant in dynamic environments.