mhpfilter: Modified and Fully Modified Hodrick-Prescott Filters

Overview

mhpfilter splits macroeconomic time series into a trend and a cycle with the Hodrick-Prescott (HP) filter and two versions whose settings come from the data:

• hp_filter(): the HP filter with a fixed smoothing parameter (1600 quarterly, 100 annual);
• mhp_filter(): the modified HP filter of McDermott (1997), assessed by Choudhary, Hanif and Iqbal (2014): every series gets the smoothing parameter that minimises a generalised cross-validation criterion (the published approximation, or the exact criterion);
• fmhp_filter(): the fully modified HP filter of Hanif, Iqbal and Choudhary (2017), which also reduces the end-point bias of the HP filter by raising the smoothing parameter at the first and last observations, with linear or quadratic weights chosen to minimise the end-point loss of Bloechl (2014).

Around them:

• many series at once (mhp_batch(), fmhp_batch()), the filters compared (mhp_compare(), batch_compare(), fmhp_compare());
• the weights, gain functions and end-point loss of any HP-type filter (hp_weights(), hp_gain(), hp_loss(), hp_schedule());
• simulated trend-plus-cycle series and the power comparison of the papers (mhp_designs(), mhp_simulate(), fmhp_simulation());
• ggplot2 graphics, a plain-language interpretation of every result (mhp_interpret()), the references of every method (mhp_cite()) and an application that runs all of this without code (mhp_app()).

Version 1.0.0 keeps every function, argument and result of version 0.1.0 and adds the fully modified HP filter. Every filter is one banded linear solve, so the search over 100000 values of the smoothing parameter for 200 observations takes 1.3 s instead of 6.4 s, and longer series gain more; the fully modified HP filter reproduces the published MATLAB code, and the end-point losses of the HP filter in Tables 3a and 3b of Hanif et al. (2017) are reproduced.

Installation

install.packages("mhpfilter")
# development version
# install.packages("remotes")
remotes::install_github("myaseen208/mhpfilter")

Quick start

library(mhpfilter)
data(us_macro)
gdp <- ts(data = us_macro$gdp, start = c(1959, 1), frequency = 4)
fm <-
  fmhp_filter(
      x               = gdp
    , max_lambda      = 3000
    , k_linear        = 15
    , k_quadratic     = NULL
    , alpha_linear    = seq(from = 0, to = 2000, by = 10)
    , alpha_quadratic = seq(from = 0, to = 2000, by = 5)
    , schemes         = c("linear", "quadratic")
    , form            = "rows"
    , lambda          = NULL
    , log_scale       = TRUE
    , as_dt           = FALSE
    )
fm

Fully modified HP Filter Result
==============================
Observations: 203 
Fully modified lambda: 1448  (modified HP lambda: 683 )
End-point weights: quadratic, alpha = 15 on 22 end values; loss = 0.6163
GCV: 3.336e-04 
Filtered on the log scale; cycle = series - trend in levels

Cycle Statistics:
  Mean: -2.603 
  SD:   120.4 
  AR1:  0.9522 
  Range: 900 

Sources: Hanif et al. (2017); Hanif (2017); Bloechl (2014); McDermott (1997);
Hodrick and Prescott (1997). Full references: mhp_cite(x).

fmhp_compare(
    x          = gdp
  , frequency  = "quarterly"
  , max_lambda = 3000
  , log_scale  = TRUE
  , end_share  = 0.1
  )

              method lambda   cycle_sd    cycle_mean       ar1 cycle_range
1:                HP   1600 0.01543904  4.942713e-12 0.8668207  0.08590516
2:       Modified HP    683 0.01333176 -1.634336e-13 0.8280266  0.07801575
3: Fully modified HP   1448 0.01618038 -4.145448e-05 0.8815215  0.08713978
            gcv      loss    sd_ends  sd_middle
1:           NA 1.7617778 0.01458541 0.01568213
2: 0.0002819926 1.7652928 0.01202396 0.01366805
3: 0.0003335623 0.7898641 0.01930994 0.01538061

plot(x = fm)

Learn more

• Vignettes: browseVignettes("mhpfilter"), starting with mhpfilter_01_getting_started; PDF versions on the site.
• Site: https://myaseen208.com/mhpfilter/
• Notation: mhp_notation()
• References of the methods behind a result: mhp_cite()

Citation

Yaseen M (2026). _mhpfilter: Modified and Fully Modified
Hodrick-Prescott Filters_. R package version 1.0.0,
<https://CRAN.R-project.org/package=mhpfilter>.

BibTeX:

@Manual{mhpfilter,
  title = {{mhpfilter}: Modified and Fully Modified Hodrick-Prescott Filters},
  author = {Muhammad Yaseen},
  year = {2026},
  note = {R package version 1.0.0},
  url = {https://CRAN.R-project.org/package=mhpfilter},
}

Please also cite the methods you use: citation("mhpfilter") lists them with the package, and mhp_cite(x) gives the references of a single result.