Library: | kalman |
See also: | gkalfilter gkalsmoother gkalarray gkallag |
Quantlet: | gkalresiduals | |
Description: | Calculates the innovations v_t and the standardized v^s_t residuals for a state space form that is estimated with the Kalman filter. As input, the output from the Kalman filter is needed. See the help to gkalfilter or the tutorial for a thorough discussion of the model. |
Usage: | {V,Vs} = gkalresiduals(Y,ca,Ta,Ra,da,Za,Ha,gkalfilOut) | |
Input: | ||
Y | N_max x TIME matrix of observed time series, where N_max is the maximal number of variables observed at any instant t | |
ca | K x 1 x TIME array with observations c_t | |
Ta | K x K x TIME array with observations T_t | |
Ra | K x K x TIME array with covariance matrices R_t | |
da | N_max x 1 x TIME array with observations d_t | |
Za | N_max x K x TIME array with observations Z_t | |
Ha | N_max x N_max x TIME array with covariance matrices H_t | |
gkalfilOut | K x (K+1) x (TIME+1) array with the output of the Kalman filter | |
Output: | ||
V | N_max x TIME matrix with the innovations v_t | |
Vs | N_max x TIME matrix with the standardized residuals v^s_t |
library("kalman") library("plot") ; loads the quantlets from plot library Y = read("houseprice") mu = #(33,-13,1,1,1) Sig = 0.75*unit(5) ca = gkalarray(Y,#(0.1,0,0,0,0),0,0) T =(#(1.4,1)'|#(-0.4,0)')~0*matrix(2,3)|(0*matrix(3,2)~unit(3)) Ta = gkalarray(Y,T,0,0) Ra = gkalarray(Y,diag(#(0.4,0,0,0,0)),0,0) da = gkalarray(Y,#(0,0,0),0,0) Z = matrix(3)~0*matrix(3,4) IZ = 0*matrix(3,2)~(#(1:3)'|#(4:6)'|#(7:9)') XZ = read("housequality") Za = gkalarray(Y,Z,IZ,XZ) Ha = gkalarray(Y,2*unit(3),0,0) {gkalfilOut,loglike} = gkalfilter(Y,mu,Sig,ca,Ta,Ra,da,Za,Ha) {V,Vs} = gkalresiduals(Y,ca,Ta,Ra,da,Za,Ha,gkalfilOut) vs = reshape(Vs,rows(Vs)*cols(Vs)) ; generates a vector of standardized residuals vs = paf(vs,1-isNaN(vs)) ; deletes missing values QQ = grqqn(vs) ; generates a QQ plot disp = createdisplay(1,1) show(disp,1,1,QQ) setgopt(disp,1,1,"title","Q-Q Plot","border",0)
Continues the example of gkalfilter. The innovations and the residuals are calculated with the filter output. The resulting display shows the normal Q-Q plot for the standardized residuals.