R: The Hodrick-Prescott Filter or HP Filter

The article “R: The Hodrick-Prescott Filter or HP Filter” was originally posted on SHLee AI Financial Model blog

This post demonstrates how to apply the Hodrick-Prescott (HP) filter in R by using the hpfilter R library.

Previously, the HP filter was addressed using Python. This post presents an R version.

The Hodrick-Prescott filter models a time series (y_t) as

where τ_t and c_t are trend and cyclical components respectively.

To decompose in this way, we solve the following minimization problem.

λ is typically recommended as 100, 1600, and 14400 for annual, quarterly, and monthly frequency, respectively.

R code

The hpfilter R library provides two convenient functions for the HP filter: hp1() for the one-sided filter and hp2() for the two-sided filter. They are easy to use, as demonstrated in the code below.

It’s interesting that plotting results requires more lines of code compared to the HP filter code (just two lines), which is the main topic of this post.

#========================================================#
# Quantitative Financial Econometrics & Derivatives 
# ML/DL using R, Python, Tensorflow by Sang-Heon Lee 
#
# https://shleeai.blogspot.com
#---------------------------------------------------------
# Hodrick-Prescott (HP) filter - 1 sided & 2 sided
#========================================================#
 
graphics.off(); rm(list = ls())
 
library(quantmod)
library(hpfilter)
 
#------------------------------------------
# Download monthly AAPL stock data
#------------------------------------------
aapl <- getSymbols("AAPL", 
                   from = "2011-01-01", 
                   to = "2022-12-31", 
                   auto.assign = FALSE, 
                   periodicity = "monthly")
df <- as.data.frame(Ad(aapl))
date <- index(aapl) #as.data.frame(index(aapl))
 
y <- df; colnames(df) <- "AAPL"
 
#------------------------------------------
# Apply the HP filter (1-sided, 2-sided)
#------------------------------------------
yt1 = hp1(y, lambda = 14400); yc1 = y - yt1
yt2 = hp2(y, lambda = 14400); yc2 = y - yt2
 
#------------------------------------------
# Plot the three resulting series
#------------------------------------------
x11(width=7, height=6); 
plot(y$AAPL, type="l", col=1, lty=1, lwd=3, 
     ylab="", xlab="", xaxt = "n",
     ylim=c(min(yc1, yt1)*1.2,max(yc1, yt1)*1.1))
 
lines(yt1$AAPL, lwd=5, col=rgb(1,0,0, alpha=0.5))
lines(yt2$AAPL, lwd=5, col=rgb(0,0,1, alpha=0.5))
 
# Plotting polygons with 50% transparency
polygon(c(1, seq(yc1$AAPL), length(yc1$AAPL)), 
        c(0, yc1$AAPL, 0), 
        col = rgb(1, 0, 0, alpha = 0.3))
polygon(c(1, seq(yc2$AAPL), length(yc2$AAPL)), 
        c(0, yc2$AAPL, 0), 
        col = rgb(0, 0, 1, alpha = 0.3))
 
# Add x-axis with selected dates
sel_dates <- date[seq(18, length(date), by = 24)]
axis(1, at = which(date %in% sel_dates), 
     labels = substr(sel_dates,1,4))
 
# Legend
legend("topleft", cex=0.8, lty = 1,
       col = c(1,2,4,2,4), lwd=c(3,5,5,3,3), 
       c("Data", "Trend (1-sided)", "Trend (2-sided)", 
         "Cycle (1-sided)", "Cycle (2-sided)"))

Visit SHLee AI Financial Model blog for additional insights on this topic.