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 = Pt1(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 Pt1:
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