You may as well analyse the skewness and kurtosis of the period of time PnL by taking 3rd and 4th times of $Y_t$ respectively. Presumably you are going to conclude that for two sequence with equivalent expectation and variance, you may favor the 1 with beneficial skew or decreased kurtosis, https://pnl65218.weblogco.com/34234281/getting-my-pnl-to-work