DLMEXAM3.RPF

DLMEXAM3.RPF is an example of unconditional simulation of a state-space model. This uses the model for Nile river flow data common to the four simple DLM examples.

We first Kalman filter through the data period, which will give us the end-of-data mean and variance for the state.

dlm(a=1.0,c=1.0,sv=15099.0,sw=1469.1,presample=diffuse,y=nile,$

type=filter) / xstates vstates

We then simulate (10000 times) the model for 50 periods beyond the end of data observed data, keeping track of the maximum value achieved by the flow in each simulation. The DLM instruction that does the simulation uses the X0 and SX0 options for inputting the initial mean and variance as the final values from the Kalman filter. The output is through the YHAT option.

compute ndraws=10000

set maxflow 1 ndraws = 0.0

do draw=1,ndraws

dlm(a=1.0,c=1.0,sv=15099.0,sw=1469.1,$

x0=xstates(1970:1),sx0=vstates(1970:1),$

type=simulate,yhat=yhat) 1971:1 2020:1 xstates

set simflow 1971:1 2020:1 = %scalar(yhat)

ext(noprint) simflow

compute maxflow(draw)=%maximum

end do reps

Full Program

open data nile.dat
calendar 1871
data(format=free,org=columns,skips=1) 1871:1 1970:1 nile
*
* Kalman filter through the data period
*
dlm(a=1.0,c=1.0,sv=15099.0,sw=1469.1,presample=diffuse,y=nile,$
type=filter) / xstates vstates
*
* Simulate 10000 realizations of 50 data points from the end of the
* data, keeping track of the maximum flow for each.
*
compute ndraws=10000
set maxflow 1 ndraws = 0.0
do draw=1,ndraws
dlm(a=1.0,c=1.0,sv=15099.0,sw=1469.1,$
x0=xstates(1970:1),sx0=vstates(1970:1),$
type=simulate,yhat=yhat) 1971:1 2020:1 xstates
set simflow 1971:1 2020:1 = %scalar(yhat)
ext(noprint) simflow
compute maxflow(draw)=%maximum
end do reps
*
* Compute the percentiles of the simulated maximum flows.
*
stats(fractiles,nomoments) maxflow

Output

These use random numbers, so will not be directly reproducible.

Statistics on Series MAXFLOW

Annual Data From 1871:01 To 11870:01

Observations 10000

Minimum 582.448871 Maximum 2136.309977

01-%ile 789.668682 99-%ile 1668.108450

05-%ile 878.492495 95-%ile 1494.057919

10-%ile 932.974550 90-%ile 1407.535441

25-%ile 1022.242511 75-%ile 1272.742814

Median 1134.038069