State Space for Time-varying index alpha and beta
Posted: Sat May 17, 2014 5:14 am
Hey everyone,
I was wondering if someone could explain me a few things on creating a State Space model in Eviews with a Kalman Filter.
I am trying to replicate the research that has been done in "The Clean Techs equity indexes at stake: Risk and return dynamics
analysis" by Ortas and Moneva. They use a state space model of the following form to analyse the Risk/Return of several stock indexes:
R = a + B*Rm + e (signal equation)
B = B(-1) + v (state equation)
a = a(-1) + u (state equation)
Where R is the return of the index (- risk free rate), B is the index's Beta to the market return (- risk free rate), a is jensen's alpha and e,v and u are the residuals/disturbances.
Up until now I have managed to create the following:
@signal alt = sv1*world + [var = exp(c(1))]
@state sv1 = sv1(-1) + [var = exp(c(2))]
Where the state equation is the one for Beta
I also managed to utilise the Kalman Filter and get results for the time-varying beta. However, I am left with one big question:
- How do I add the state equation for the Alpha in the model? As I understand, it is the abnormal return of the index over that of the market, but how would I include that in the model? I am using the auto-specification method, with the return of the index as dependent variable and the market return as a Random walk regressor. How should I then include a? Can I calculate a as a variable before having calculated the time-varying Beta and then create the state space model? I thought that a period's a is just the difference between the return of the index and the expected return (which is beta*Rm)? This can then not be calculated before doing the whole state space right (because beta estimates would change when including a in the model)?
Thank you very much in advance for any answers, I would appreciate it a lot!
I was wondering if someone could explain me a few things on creating a State Space model in Eviews with a Kalman Filter.
I am trying to replicate the research that has been done in "The Clean Techs equity indexes at stake: Risk and return dynamics
analysis" by Ortas and Moneva. They use a state space model of the following form to analyse the Risk/Return of several stock indexes:
R = a + B*Rm + e (signal equation)
B = B(-1) + v (state equation)
a = a(-1) + u (state equation)
Where R is the return of the index (- risk free rate), B is the index's Beta to the market return (- risk free rate), a is jensen's alpha and e,v and u are the residuals/disturbances.
Up until now I have managed to create the following:
@signal alt = sv1*world + [var = exp(c(1))]
@state sv1 = sv1(-1) + [var = exp(c(2))]
Where the state equation is the one for Beta
I also managed to utilise the Kalman Filter and get results for the time-varying beta. However, I am left with one big question:
- How do I add the state equation for the Alpha in the model? As I understand, it is the abnormal return of the index over that of the market, but how would I include that in the model? I am using the auto-specification method, with the return of the index as dependent variable and the market return as a Random walk regressor. How should I then include a? Can I calculate a as a variable before having calculated the time-varying Beta and then create the state space model? I thought that a period's a is just the difference between the return of the index and the expected return (which is beta*Rm)? This can then not be calculated before doing the whole state space right (because beta estimates would change when including a in the model)?
Thank you very much in advance for any answers, I would appreciate it a lot!