Testing for speculative bubbles using spot and forward prices

The probabilistic structure of periodically collapsing bubbles creates a gap between future spot and forward (or futures) asset prices in small samples. By exploiting this fact, we use two econometric methods, namely, the recursive unit root method of Phillips, Shi, and Yu (2015a,b) and the rolling regression method of Fama (1984), for detecting bubbles. Both methods do not rely on a particular model of asset price determination, they are robust to an explosive root in the process for market fundamentals, and are accompanied by a date-stamping strategy. By applying these methods to the German mark-US dollar and British pound-US dollar exchange rates, we provide evidence in favor of speculative bubbles in the foreign exchange market during the interwar German hyperinflation, but not during the recent floating-rate period. A further application to the S&P 500 index supports the existence of speculative bubbles in the US equity market