hp1 {hpfilter}

One-Sided HP Filter

Description

hp1 applies a one-sided Hodrick-Prescott filter derived using the Kalman filter to separate a time series into trend and cyclical components. The smoothing parameter should reflect the cyclical duration or frequency of the data.

Usage

hp1(y, lambda = 1600, x_user = NA, P_user = NA, discard = 0)

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.

x_user

user defined initial values of the state estimate for each variable in y. Takes the form of a 2xn matrix. Since the underlying state vector is 2x1, two values are needed for each variable in y. By default: if no values are provided, backwards extrapolations based on the first two observations are used.

P_user

a structural array with n elements, each of which being a 2x2 matrix of initial MSE estimates for each variable in y. By default: if no values are provided, a matrix with relatively large variances is used.

discard

the number of discard periods, expressed as a numeric scalar. The user specified amount of values will be discarded from the start of the sample, resulting in output matrices of size (T-discard)xn. By default: if no values are provided, is set to 0.

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 (T-discard)xn 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

[hp2()]

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 = hp1(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"))