Math formulas inherit the font size of the surrounding text. If, say, a \small declaration is in effect at some point of the document, that will be the font size for a formula included there. So, in your case, I would write something like:
Code: Select all
\tiny
\[
\widehat{S}_{f}(s,t_{j-1})=\frac{S_f (s)}{P_f (s,t_{j-1})} %smaller font
\]
\normalsize
The \normalsize command just restores the "normal" size which was presumably in effect before the formula. You can try \small and \footnotesize instead of \tiny.
IMHO, \scriptstyle, as well as its companions \scriptscriptstyle and \textstyle, should not be used for globally change the font size in a formula. Spacing around the equal sign is not correct, the numerator and denominator are too cluttered.
gozzi84 wrote:How can I do then? .
That depends on the reasons which moved you to decrease the fontsize. For example, is there not enough room in the frame?