With the tool of wavelets, we quantify investors' preferences over fluctuations in economy in the time-scale domain under leading utility models. We find that: (1) From the frequency aspect, the higher scale (which implies a longer cycle period) fluctuations in the consumption series/economy contribute more than the lower scales to the Habit formation life-time utility, while the result is reversed for the Epstein-Zin preference case. (2) From the time aspect, the investor's lifetime utility is dominated by his/her consumption at the current time and in the near future.

The second topic is on modeling the commonly seen financial time series with Fractional Brownian Motions. With the tool of multi-taper method, we design a method to determine whether a given time series may follow a Fractional Brownian Motion distribution. Then we will use this method to identify the ones that potentially follow a fractional Brownian motion distribution among several commonly seen financial time series, such as the US price to earning ratios and the three-month treasury bill rates. Finally, we will apply wavelet methods to estimate the value of the corresponding Hurst exponent in the FBM model.