Block bootstrap for time series in R - r

Question

I'm using the function tsbootstrap() from the package tseries to generate block bootstrap samples, and to calculate the standard errors for the estimate of the parameters of a regime-switching autoregressive model (which I can obtain using the function msmFit() from the package MSwM).
Here is the code I'm using. Firstly I define a function for the statistic I want to use:
switching.par <- function(z) {
n<-length(z)
x<-z[1:(n-1)]
y<-z[2:n]
my.xy<- data.frame(x,y)
mod<-lm(y~x,data=my.xy)
mod.mswm=msmFit(mod,k=2,sw=c(T,T,T))
b1 <- mod.mswm#Coef[1,2]
b2 <- mod.mswm#Coef[2,2]
c1 <- mod.mswm#Coef[1,1]
c2 <- mod.mswm#Coef[2,1]
del1 <- mod.mswm#std[1]
del2 <- mod.mswm#std[2]
parameters<-c(b1, b2, c1, c2, del1, del2)
names(parameters)<-c("b1", "b2", "c1", "c2", "del1", "del2")
parameters
}
And then I use the tsbootstrap() function (where x is a monthly time series of 10-year US government bonds)
use.boot <- tsbootstrap(x, nb=1000, statistic=switching.par, type="block", b=9)
But I get the following error message:
Error in solve.default(res$Hessian) :
Lapack routine dgesv: system is exactly singular: U[4,4] = 0
Any insight on how to fix this problem? I think the error comes from the function msmFit() of the package.

Answer 1

The error as you correctly understood comes from the msmFit function that fails to converge.
I will give a bit of insight as to the error and then provide a solution that worked for me:
solve.default is a common error that you can see when an optimiser is being used. Usually the optimiser (such as optim) will try to calculate the hessian matrix in order to 'direct' itself to the optimal solution that minimises the underlying function. At some point the hessian matrix needs to be inverted and if it is singular the algorithm crashes. Practically this means that the optimiser failed to converge (i.e. couldn't find a solution).
This can be because of a number of reasons:
Too few observations
Bad starting values
Bad design of the function to be optimised (or used in the function)
Low number of maximum iterations
Literally no solution for the problem
Now let's go to your problem:
It seems that the default maximum iterations for msmFit is 100. Try increasing that to 500 as I do below. The design of the function seems ok to me. Now let's go to the low number of observations. The b argument of the tsbootstrap function as far as I understand from the documentation is a value that controls the observations that go to the switch function. Having it to 9 makes the msmFit function fail. I increased that to 50 (assuming that your df has 50 observations. Anything less than that will probably fail all the time). Also, having it produce 1000 bootstrap series will take a day to compute (at least on my machine).
With all the above in mind, the following seems to work on my machine (for just 10 bootstrap series) and it took ages.
switching.par <- function(z) {
n<-length(z)
x<-z[1:(n-1)]
y<-z[2:n]
my.xy<- data.frame(x,y)
mod<-lm(y~x,data=my.xy)
mod.mswm=msmFit(mod,k=2,sw=c(T,T,T), control=list(maxiter=500))
b1 <- mod.mswm#Coef[1,2]
b2 <- mod.mswm#Coef[2,2]
c1 <- mod.mswm#Coef[1,1]
c2 <- mod.mswm#Coef[2,1]
del1 <- mod.mswm#std[1]
del2 <- mod.mswm#std[2]
parameters<-c(b1, b2, c1, c2, del1, del2)
names(parameters)<-c("b1", "b2", "c1", "c2", "del1", "del2")
parameters
}
use.boot <- tsbootstrap(x, nb=10, statistic=switching.par, type="block", b=50)
Output:
> str(use.boot)
List of 5
$ statistic : num [1:10, 1:6] -0.0275 -0.1692 -0.0199 -0.0587 -0.0763 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : NULL
.. ..$ : chr [1:6] "t1" "t2" "t3" "t4" ...
$ orig.statistic: Named num [1:6] 0.0114 -0.1002 0.5155 0.5319 0.2868 ...
..- attr(*, "names")= chr [1:6] "t1" "t2" "t3" "t4" ...
$ bias : Named num [1:6] -0.2029 0.2041 0.0307 -0.0217 -0.036 ...
..- attr(*, "names")= chr [1:6] "t1" "t2" "t3" "t4" ...
$ se : Named num [1:6] 0.2076 0.1774 0.1686 0.1375 0.0533 ...
..- attr(*, "names")= chr [1:6] "t1" "t2" "t3" "t4" ...
$ call : language tsbootstrap(x = x, nb = 10, statistic = switching.par, b = 50, type = "block")
- attr(*, "class")= chr "resample.statistic"