Explain why it is sometimes necessary to apply a functional transformation of the data, such as a logarithmic or a Box-Cox transformation. Suppose that the price of a stock at time t is denoted as...

Explain why it is sometimes necessary to apply a functional transformation

of the data, such as a logarithmic or a Box-Cox transformation.

Suppose that the price of a stock at time t is denoted as Pt and that

the sequence of prices is described by the equation

Pt = Pt􀀀1(1 + rt);

where rt is the return at time t. By taking logarithms and using the approximation

log(1 + x) _ x for small values of x, show that

rt = _log Pt = log Pt 􀀀 log Pt􀀀1: