hp2 {hpfilter}

Two-Sided HP Filter

Description

hp2 applies a standard two-sided Hodrick-Prescott filter using sparse matrices to help reduce the compute time for large datasets. The smoothing parameter should reflect the cyclical duration or frequency of the data.

Usage

hp2(y, lambda = 1600)

Arguments

y

a dataframe of size Txn, where "T" is the number of observations for each variable (number of rows) and "n" - the number of variables in the dataframe (number of columns).

lambda

the smoothing parameter; a numeric scalar which takes the default value of 1600, if unspecified by the user.

Details

The length of the time series should be greater than four and the value of the smoothing parameter greater than zero for the code to function. Of course, having a sufficiently long time series is paramount to achieving meaningful results.

Value

a Txn dataframe, containing the trend data

Author(s)

Alexandru Monahov, <https://www.alexandrumonahov.eu.org/>

References

Balcilar, M. (2019). Miscellaneous Time Series Filters 'mFilter'. CRAN R Package Library.

Drehmann, M., and Yetman, J. (2018). Why You Should Use the Hodrick-Prescott Filter - at Least to Generate Credit Gaps. BIS Working Paper No. 744.

Eurostat (2023), Real Gross Domestic Product for European Union (28 countries) [CLVMNACSCAB1GQEU28], National Accounts - GDP.

Hamilton, J. D. (2017). Why You Should Never Use the Hodrick-Prescott Filter. Working Paper Series. National Bureau of Economic Research, May 2017.

Hodrick, R. J., and Prescott, E. C. (1997). Postwar U.S. Business Cycles: An Empirical Investigation. Journal of Money, Credit, and Banking 29: 1-16.

Hyeongwoo, K. (2004). "Hodrick-Prescott Filter". Notes, Auburn University.

Mcelroy, T. (2008). Exact formulas for the Hodrick-Prescott Filter. Econometrics Journal. 11. 209-217.

Meyer-Gohde, A. (2010). Matlab code for one-sided HP-filters. QM&RBC Codes 181, Quantitative Macroeconomics & Real Business Cycles.

Ravn, M., and Uhlig, H. (2002). On adjusting the Hodrick-Prescott filter for the frequency of observations, The Review of Economics and Statistics 2002; 84 (2): 371-376.

Shea, J. (2021). neverhpfilter: An Alternative to the Hodrick-Prescott Filter. CRAN R Package Library.

See Also

[hp1()]

Examples

# Generate the data and plot it
set.seed(10)
y <- as.data.frame(rev(diffinv(rnorm(100)))[1:100])+30
colnames(y) <- "gdp"
plot(y$gdp, type="l")

# Apply the HP filter to the data
ytrend = hp2(y)
ycycle = y - ytrend

# Plot the three resulting series
plot(y$gdp, type="l", col="black", lty=1, ylim=c(-10,30))
lines(ytrend$gdp, col="#066462")
polygon(c(1, seq(ycycle$gdp), length(ycycle$gdp)), c(0, ycycle$gdp, 0), col = "#E0F2F1")
legend("bottom", horiz=TRUE, cex=0.75, c("y", "ytrend", "ycycle"), lty = 1,
       col = c("black", "#066462", "#75bfbd"))