One of the problems of navigating an autonomous car through a city is to extract robust signals in the face of all the noise that is present in the different sensors. Just taking something like an arithmetic mean of all the data points could possibly end in a catastrophe: if a part of a wall looks similar to the street and the algorithm calculates an average trajectory of the two this would end in leaving the road and possibly crashing into pedestrians. So we need some robust algorithm to get rid of the noise. The area of statistics that especially deals with such problems is called robust statistics and the methods used therein robust estimation.
Continue reading “Separating the Signal from the Noise: Robust Statistics for Pedestrians”
Asset returns have certain statistical properties, also called stylized facts. Important ones are:
- Absence of autocorrelation: basically the direction of the return of one day doesn’t tell you anything useful about the direction of the next day.
- Fat tails: returns are not normal, i.e. there are many more extreme events than there would be if returns were normal.
- Volatility clustering: basically financial markets exhibit high-volatility and low-volatility regimes.
- Leverage effect: high-volatility regimes tend to coincide with falling prices and vice versa.