May 1, 2025
This study defines the “empirical” Buffett indicator as \(lnBI^{[e]}_{t} \equiv lnS_{t} \; – \; \phi \cdot lnY_{t}\) with \(\widehat{\phi} \approx 1.037\) where \(S\) and \(Y\) are respectively the Wilshire 5000 index and GDP. The study estimated the coefficients of the error- correction model, and found that the empirical Buffett indicator is a mean-reverting Gaussian process with a Poisson jump process.
\[ \Delta lnBI^{[e]}_{t} = 0.04135 \cdot \{(-1.2227 + 0.5556 \cdot lnY_{t-1}) – lnBI^{[e]}_{t-1}\} \]
Its half-life is 16.762 quarters. The study also found four outliers in residuals that coincided with adverse economic events: the 1973 oil crisis, Black Monday, the dot-com crash, and the Lehman Shock. Furthermore, the study conducted simulations of the empirical Buffett indicator and the Wilshire 5000 index.
This study is still in progress and welcomes suggestions and comments. (asanohiro559@gmail.com)