Main results
Estimated parameters
#> Airline:
#> Innovation variance: 0.005302598
#> theta: -0.4695642
#> btheta: -0.4222849Original series (solid) and signal extraction estimates (dashed)
This document reproduces with rjd3sts the example N°6 of the paper:
Bell W.R. (2011). REGCMPNT - A Fortran Program for Regression Models with ARIMA Component Errors. Journal of Statistical Software. Volume 41, Issue 7.
Details on the considered model can be retrieved from the original paper (pages 17-20).
Remark: the code presented below will be further simplified (the definition of the equation will be suppressed, as it is already the case for non-weighted state components).
y<-log(nr055)
# create the model
model<-rjd3sts::model()
# create the components and add them to the model
# airline block
airline<-rjd3sts::sarima("airline", 12, c(0,1,1), c(0,1,1))
# fixed AR model for the sampling error
ar<-rjd3sts::ar("ar", ar=c(0.6, 0.246), fixedar=TRUE, variance=0.34488, fixedvariance=TRUE)
rjd3sts::add(model, airline)
rjd3sts::add(model, ar)
# creation of the unique equation
eq<-rjd3sts::equation("eq")
rjd3sts::add_equation(eq, "airline")
rjd3sts::add_equation(eq, "ar", loading = rjd3sts::var_loading(pos=0, weights = h))
rjd3sts::add(model, eq)
# estimate the model
# it is important to note that we don't use the concentrated likelihood (which is the default option,
# faster and more stable)
# In this case the optimization procedure is BFGS instead of Levenberg-Marquardt.
rslt<-rjd3sts::estimate(model, y, concentrated=FALSE)#> Airline:
#> Innovation variance: 0.005302598
#> theta: -0.4695642
#> btheta: -0.4222849
