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filter

Kalman filter

CALLING SEQUENCE

[betat,betaf,sigmatt,sigmatf]=filter(param,func,y,x,F,z)

PARAMETERS

Input

* param = a vector of parameters (sqrt of variances)

* func = the function which transforms the parameters into the matrix of variances (Q and R) and, if necessary, into the matrices of prior values

* y = (nx1) data vector

* x = (nxk) data matrix

* F = transition matrix

* z = (nxl) data matrix

 

Output

* betat = vector of filtered beta at date t with the information available at date t (beta(t|t))

* betaf = vector of filtered beta at date t with the information available at date t-1 (beta(t|t-1)

* ferror = vector of errors at date t ( = y-x*beta(t|t))

* sigmatt = vector of filtered variances at date t with the information available at date t (sigma(t|t))

* sigmatf = vector of filtered variances at date t with the information available at date t-1 (sigma(t|t-1))

DESCRIPTION

Generates model filtered betas and variance, given values for Q and R in a Kalman model: y(t) = X(t)*B(t) + Z(t)*A + e(t), e(t) = N(0,R) B(t) = Z(t)*B(t-1) + v(t), v(t) = N(0,Q)

EXAMPLE

// Filter is used by the function kalman:
[betat,betaf,sigmatt,sigmatf]=filter(grocer_param,grocer_func,grocer_y,grocer_x,grocer_F)

AUTHOR

Eric Dubois 2002

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