I have a time series of x:libor and y:money rates. using the following polynomial y=b0+b1(x)+b2(x)^2, i get values of y that exceed (or are sometimes negative) the coveriance/variance for large multiples of vector x. (i) Is my problem one of an asymptote? and (ii) is a regime switch appropriate?
My guess (without seeing your data) is model specification bias (error) . Try building a Transfer Function ( a.k.a. dynamic regression) incorporating memory structure as needed and possibly (probably !) both ARIMA structure and identifiable deterministic structure such as pulses,step/level shifts/local time trends