First Difference, Log Return

[keanpoh]

Hi,

I am doing my research regarding the relationship of Business cycle and Equity Risk Premium, using EGARCH-in-mean model. Data are all time series.

Business cycle variable is given by monthly Industrial Production (IP).
Equity Risk Premium = Market Return - Risk Free Rate
Market Return = Index monthly return
Risk-free-rate = 10 Year Government Bond converted to monthly return

Now, when I run my unit root test for IP, monthly index level (not converted to monthly return yet) and risk free rate, I found them all to be non-stationary. Thus, I converted IP, index level and risk free rate to stationary data series by taking their first difference. For example, entering d_ip = d(ip) command.

Now I have a new sets of stationary time series data, d_ip, d_index, d_rf, which are all first difference of their corresponding raw data.

Now, I need to get my market return, which is the (current index level - previous index level)/previous index level or I can use log normal to calculate the return.

My question is, do I use the first difference time series data for the calculation of log return? Or I can just use the raw time series for the calculation of log return?