Example of Physics-Based Sentiment Forecasts

---

The figure below shows an example of our physics-based stock market sentiment forecasts. It shows the S&P 500 (brown line, log scale) from December 2000 through April 2024. It shows the actual 14-week Relative Strength Index, a widely used momentum measure, and our predicted 14-week RSI. 

The actual 14-week RSI is at the bottom of the figure (solid green, normalized). The predicted 14-week RSI is shown in the middle (dashed green, normalized).   

For this example, we selected six of our approximately two-dozen physics-based drivers that are individually statistically significant in explaining the variability of the actual 14-week RSI over the period from 1940 through late 2000. We then blended those drivers together to determine the single mix (weights of the drivers) that tracked most closely the actual 14-week RSI over the same period. The combination of drivers resulted in a statistically significant model with an F-statistic significant at below the 0.001 level.  

To be conservative, we held constant the drivers and weights determined at the end of 2000 for the following 20+ years (out-of-sample period). The strong relationship between the actual and predicted 14-week RSI during this out-of-sample period indicates the stability of the physical processes we exploit.  

In order to describe the explanatory power of the mix of physics-based variables in the out-of-sample period, we performed a simple regression analysis of the out-of-sample period. The regression analysis indicates that the explanatory power (r-squared) of the physics-based drivers is over 70%. This suggests that over 70% of the weekly variation in the actual 14-week RSI is explained by the physics-based drivers and less than 30% is explained by other influences. 

One can see in the figure above that the peaks and troughs of the actual 14-week RSI are reasonably highlighted by the predicted series, as are distinct multi-month patterns (e.g., 2016 and 2017). This example demonstrates the stability and regularity of the physical processes we exploit to create our sentiment forecasts. 

Regarding interpretation, one can infer that a deviation between the actual and predicted RSI indicates periods when economics, fundamentals, and current events had a large impact on the market. Those real-world effects during periods such as early in the Global Financial Crisis (2007 to 2009), are more apparent after adjusting for the naturally occurring shifts in sentiment as seen in the figure above. 

Stability of Factors

On an ongoing basis for forecasts, we update the models periodically.  That said, the main elements of the forecasts are unlikely to change meaningfully, given the stability demonstrated in this example. A majority of our two dozen drivers are unlikely to change because they are already consistent with established principles of math and physics.