time varying parameters estimation using ssm

Raamasrinivas Venkata

2020 5 12

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I am trying to estimate the parameters of the following state space model:

State equation:

x(t)= A*x(t-1) + B*v(t)

Observation equation:

y(t)= C(t)*x(t)+ G(t)*z(t) + D*e(t),

where the errors are independent Gaussian process and z(t) is a vector of exogenous predictors/control vector at time 't'; The elements of A, B and D are known to me. However, the matrices C and G contain the parameters I want to estimate and the parameters repeat in both the matrices. For example,

C= [0 theta(t);alpha(t) 1]

G=[gamma(t) 1 alpha(t) theta(t)]

How do i estimate the parameters using ssm? Kindly get back to me.

Thank you