advice needed on what classes to take

I am an undergrad but plan to enter grad school to study statistics(PhD
programme in financial mathematics). Besides classes from statistics
department(probability theory, linear regression e.t.c.) ,i need advice,
what pure math classes i should take to prepare myself. I have taken
calculus(up to multivariable calculus and vector calculus), linear algebra
and discrete mathematics.

Should i also take classes like complex analysis, real analysis ?  Do these
classes have any(non vague) connection with statistics ? What about function
analysis , fourier analysis ?

Thanks in advance.