| 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.