Consider the return decomposition:
$r_t = \mu_{t-1} + \epsilon_t$
What does each component on the right hand side stand for and what does it capture from an investment point of view?
mu_t-1 is the best educated guess about r_t
ALT: mu_t-1 is the best educated guess about r_t at the time t-1
eps_t is the unpredictable component/'noise component'/innovation?
Explain the notation and meaning of the following equation:
$r_{t, t+j} = \mu_{t, t+j} + \epsilon_{t, t+j}$
The equation is the j-period ahead return decomposition as on time t.
ADD:
r_(t,t+j) is the realized return when buying an asset at timte t and selling at t+j
IDEA: r_(t,t+j) is the realized return when buying an asset at timte t+j-1 and selling at t+j
mu_(t,t+j) is the predicted value of r_(t,t+j) with the information of F_t: $\mu_{t, t+j} = E[r_{t, t+j}|F_t]$
eps_(t, t+j) is the realized random prediction error