Why is the Portmanteau test slower in Rcpp than in R? - r

Question

I need to do a power study of the main Portmanteau tests Article, for this I must evaluate them in different scenarios, sample sizes and different ARMA models (p, q) generating 180 scenarios which takes me close
  6 hours. Program my function in R and Rcpp, however I find the surprise that in C ++, it is slower, my question is why?
My R Code:
Portmanteau <- function(x,h=1,type = c("Box-Pierce","Ljun-Box","Monti"),fitdf = 0){
Ti <- length(x)
df <- h-fitdf
ri <- acf(x, lag.max = h, plot = FALSE, na.action = na.pass)
pi <- pacf(x, lag.max = h, plot = FALSE, na.action = na.pass)
if(type == "Monti"){d<-0} else{d<-1}
if(type == "Box-Pierce"){wi <- 1} else{wi <- (Ti+2)/seq(Ti-1,Ti-h)}
Q <- Ti*(d*sum(wi*identity(ri$acf[-1]^2))+(1-d)*sum(wi*identity(pi$acf^2)))
pv <- pchisq(Q,df,lower.tail = F)
result <- cbind(Statistic = Q, df,p.value = pv)
rownames(result) <- paste(type,"test")
return(result)
}
My Rcpp code
#include <Rcpp.h>
using namespace Rcpp;
// [[Rcpp::export]]
NumericVector PortmanteauC(NumericVector x, int h = 1,const char* type = "Box-Pierce" ,int fitdf = 0) {
Environment stats("package:stats");
Function acf = stats["acf"];
Function pacf = stats["pacf"];
Function na_pass = stats["na.pass"];
List ri = acf(x, h, "correlation", false, na_pass);
List pi = pacf(x, h, false, na_pass);
int Ti = x.size();
int df = h - fitdf;
double d;
NumericVector wi;
NumericVector rk = ri["acf"];
NumericVector pk = pi["acf"];
NumericVector S(h);
for(int i = 0; i < h; ++i){S[i] = Ti-i-1;}
rk.erase(0);
if(strcmp(type,"Monti") == 0){d=0;} else{d=1;}
if(strcmp(type,"Box-Pierce") == 0){wi = rep(1,h);} else{wi = (Ti+2)/S;}
double Q = Ti*(d*sum(wi*pow(rk,2)) + (1-d)*sum(wi*pow(pk,2)));
double pv = R::pchisq(Q,df,0,false);
NumericVector result(3);
result[0] = Q;
result[1] = df;
result[2] = pv;
return(result);
}
Example
set.seed(1)
y = arima.sim(model = list(ar = 0.5), n = 250)
mod = arima(y, order = c(1,0,0))
res = mod$residuals
Box-Pierce
library(rbenchmark)
benchmark(PortmanteauC(res, h=10, type = "Box-Pierce",fitdf = 1),replications = 500,Portmanteau(res,h = 10, type = "Box-Pierce", fitdf= 1),
Box.test(res, lag = 10, type = "Box-Pierce", fitdf= 1))[,1:4]
test replications elapsed relative
3 Box.test(res, lag = 10, type = "Box-Pierce", fitdf = 1) 500 0.17 1.000
2 Portmanteau(res, h = 10, type = "Box-Pierce", fitdf = 1) 500 0.44 2.588
1 PortmanteauC(res, h = 10, type = "Box-Pierce", fitdf = 1) 500 1.82 10.706
Ljun-Box
benchmark(Box.test(res, lag = 5, type = "Ljung-Box", fitdf= 1),replications = 500,
Portmanteau(res,h = 5, type = "Ljung-Box", fitdf= 1),
PortmanteauC(res,h = 5, type = "Ljung-Box", fitdf= 1))[,1:4]
test replications elapsed relative
1 Box.test(res, lag = 5, type = "Ljung-Box", fitdf = 1) 500 0.17 1.000
2 Portmanteau(res, h = 5, type = "Ljung-Box", fitdf = 1) 500 0.45 2.647
3 PortmanteauC(res, h = 5, type = "Ljung-Box", fitdf = 1) 500 1.84 10.824
I would have expected Rcpp to be much faster than the byte compiled R.

Answer 1

Let's analyze the performance properties of your R code. Since a individual call is so fast, that the sampling profiler provided by R cannot be used easily, I simply use repeat() to repeat the code until interrupted:
Portmanteau <- function(x,h=1,type = c("Box-Pierce","Ljun-Box","Monti"),fitdf = 0){
Ti <- length(x)
df <- h-fitdf
ri <- acf(x, lag.max = h, plot = FALSE, na.action = na.pass)
pi <- pacf(x, lag.max = h, plot = FALSE, na.action = na.pass)
if(type == "Monti"){d<-0} else{d<-1}
if(type == "Box-Pierce"){wi <- 1} else{wi <- (Ti+2)/seq(Ti-1,Ti-h)}
Q <- Ti*(d*sum(wi*identity(ri$acf[-1]^2))+(1-d)*sum(wi*identity(pi$acf^2)))
pv <- pchisq(Q,df,lower.tail = F)
result <- cbind(Statistic = Q, df,p.value = pv)
rownames(result) <- paste(type,"test")
return(result)
}
set.seed(1)
profvis::profvis({
repeat({
y = arima.sim(model = list(ar = 0.5), n = 250)
mod = arima(y, order = c(1,0,0))
res = mod$residuals
Portmanteau(res, h = 10, type = "Box-Pierce", fitdf = 1)
})
})
I let it run for about 49s. Part of the graphical output provided in RStudio can be seen here:
We learn from this:
arima() takes about seven times longer than Portmenteau(). Depending on the ratio of calls between these two functions, you might be optimizing the wrong function.
For the Portmenteau() call almost the complete time is spend in pacf() and acf(). These R functions are also used within your Rcpp code, but with the additional complexitiy of going back to R from C++. This explains why your C++ is slower than your R code.