Linear Regression with two variables

I am working with a data set of Volatility Swap prices, i.e. a matrix, where the rows represent dates, the columns maturities and the entries prices. My goal is now, to find coefficients and two functions, such that

a+b*v_t+c*v'_t = V_t(t+T)

where I know the right hand side from the data and try to find v_t and v'_t. I can fix the parameters a,b and c and minimize over the error at the end, but I do not know, how I can program Matlab to find the best data points v_t and v'_t for t running through time.

[Ingrid]

I do not know how to do this but I know the CAPTAIN toolbox provided functionalities for fitting when dealing with time series so you might want to google this to see if it suits your needs

Answer 1

[Torsten]

So a, b, c, V_t(t+T) are given und you search for (time-varying) v_t and v'_t to make

a+b*v_t+c*v'_t = V_t(t+T)

?

Choose v_t = 0 and v'_t = (V_t(t+T)-a)/c.

I guess this is not what you want, but you will have to explain more clearly what you are trying to do.

Best wishes

Torsten.

Answer 2

[Matthias Gattiker]

I know that V_t(t+T) follows approximately a certain formula, i.e. a+b*v_t+c*v'_t. I do know the V_t(t+T) exactly, as they are data points. So I would like to perform linear regression to get the best v_t and v'_t. The problem I am having, is that normally you have two sets of data on which you perform linear regression. If we fix t, I have 17 data points, one for each T, but still, I cannot figure out a matlab command which then performs a linear regression on these data points on which I can figure out v_t and v'_t.