Package {mhpfilter}

Type:	Package
Title:	Modified and Fully Modified Hodrick-Prescott Filters
Version:	1.0.0
Date:	2026-11-05
Description:	Decomposes macroeconomic time series into trend and cycle with the Hodrick-Prescott (HP) filter and two data-driven versions of it. The modified HP filter of McDermott (1997), assessed by Choudhary, Hanif and Iqbal (2014) <doi:10.1080/00036846.2014.894631>, chooses the smoothing parameter of every series by generalised cross-validation (as described in Coe and McDermott (1997) <doi:10.2307/3867497>). The fully modified HP filter of Hanif, Iqbal and Choudhary (2017, State Bank of Pakistan Working Paper 88) also reduces the end-point bias of the HP filter: it raises the smoothing parameter at the first and last observations, with linear or quadratic weights chosen to minimise the loss of Bloechl (2014, University of Munich Discussion Paper 2014-1). Every filter is a banded linear solve, so the searches are fast; batch processing of many series, comparisons of the filters, the filter weights, gain functions and end-point loss, simulation of trend-plus-cycle series and the power comparison of the paper, 'ggplot2' graphics, a plain-language interpretation of every result and a built-in 'shiny' application.
License:	MIT + file LICENSE
URL:	https://myaseen208.com/mhpfilter/, https://github.com/myaseen208/mhpfilter
BugReports:	https://github.com/myaseen208/mhpfilter/issues
Encoding:	UTF-8
Language:	en-US
LazyData:	true
Depends:	R (≥ 4.2)
Imports:	data.table, ggplot2, grDevices, Rcpp, scales, stats, utils
LinkingTo:	Rcpp, RcppArmadillo
Suggests:	bslib, DT, knitr, magick, pkgload, quarto, ragg, R.rsp, shiny, svglite, testthat (≥ 3.0.0), withr
VignetteBuilder:	quarto, R.rsp
Config/testthat/edition:	3
Config/skill/prefix:	mhp
RoxygenNote:	7.3.1
NeedsCompilation:	yes
Packaged:	2026-11-09 02:26:15 UTC; myaseen208
Author:	Muhammad Yaseen [aut, cre, cph], Javed Iqbal [ctb] (Original methodology author), M. Nadim Hanif [ctb, cph] (Original methodology author; author of the MATLAB code of the fully modified HP filter), M. Ali Choudhary [ctb] (Original methodology author)
Maintainer:	Muhammad Yaseen <myaseen208@gmail.com>
Repository:	CRAN
Date/Publication:	2026-11-09 08:50:09 UTC

mhpfilter: Modified and Fully Modified Hodrick-Prescott Filters

Description

mhpfilter splits a macroeconomic time series into a trend and a cycle with the filter of Hodrick and Prescott (1997) and with two versions whose settings come from the data: the modified HP filter of McDermott (1997), which chooses the smoothing parameter of each series by generalised cross-validation (Choudhary, Hanif and Iqbal 2014), and the fully modified HP filter of Hanif, Iqbal and Choudhary (2017), which also reduces the bias of the HP filter at the ends of the series by raising the smoothing parameter there, with weights that minimise the end-point loss of Bloechl (2014).

Details

Functions, in the order of an analysis:

• hp_filter, mhp_filter, fmhp_filter: the three filters.

• mhp_batch, fmhp_batch: many series at once.

• mhp_compare, batch_compare, fmhp_compare: the filters compared, by the moments of the cycles and the end-point loss.

• hp_weights, hp_gain, hp_loss, hp_schedule: the weights, gains and end-point loss of any HP-type filter.

• mhp_designs, mhp_simulate, fmhp_simulation: simulated series and the power comparison of the paper.

• autoplot.mhp, plot_comparison, plot_batch: graphics; get_lambda, get_gcv: accessors.

• mhp_interpret, mhp_cite: a plain-language interpretation and the references of a result; mhp_app: the built-in application.

Every filter is an S3 generic with a .default method. With as_dt = TRUE (the default) the filters return a data.table, as in version 0.1.0; with as_dt = FALSE a list with a class and the methods of mhp-methods. Utilities: mhp_theme, mhp_save, mhp_notation, mhp_reference.

Data. us_macro: quarterly real GDP, consumption and investment of the United States, 1959 to 2009.

Vignettes. Start with vignette("mhpfilter_01_getting_started", package = "mhpfilter"); browseVignettes("mhpfilter") lists all of them, in HTML and PDF.

Notation

Scalars are upper-case letters in normal face, indices lower-case italic, vectors lower-case bold and matrices upper-case bold; Greek letters follow the same rule. The full table is mhp_notation().

Author(s)

Muhammad Yaseen (myaseen208@gmail.com), ORCID 0000-0002-5923-1714.

References

Bloechl, A. (2014). Reducing the excess variability of the Hodrick-Prescott filter by flexible penalization. Discussion Paper 2014-1, University of Munich.

Choudhary, M. A., Hanif, M. N. and Iqbal, J. (2014). On smoothing macroeconomic time series using the modified HP filter. Applied Economics, 46(19), 2205–2214. doi:10.1080/00036846.2014.894631

Hanif, M. N., Iqbal, J. and Choudhary, M. A. (2017). Fully modified HP filter. SBP Working Paper Series, No. 88, State Bank of Pakistan.

Hodrick, R. J. and Prescott, E. C. (1997). Postwar U.S. business cycles: an empirical investigation. Journal of Money, Credit and Banking, 29(1), 1–16. doi:10.2307/2953682

McDermott, C. J. (1997). An automatic method for choosing the smoothing parameter in the HP filter. Unpublished, International Monetary Fund, Washington DC.

See Also

mhp-methods, mhp_notation

Plot the decomposition of a series

Description

autoplot() (and plot()) of a filter result draws the series with its trend and, below, the cycle, with the time of a ts on the horizontal axis. For the modified HP filter which = "gcv" draws the criterion against \lambda; for the fully modified HP filter which = "lambda" draws the smoothing parameters \lambda_t and which = "loss" the end-point loss.

Usage

autoplot.mhp(object, which = c("decomposition", "gcv", "lambda", "loss"), ...)

Arguments

Value

A ggplot object.

Author(s)

Muhammad Yaseen (myaseen208@gmail.com)

Examples

data(us_macro)
f <-
  fmhp_filter(
      x               = us_macro$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
    )
ggplot2::autoplot(object = f)
plot(x = f, which = "lambda")

Fully modified HP filter of many series

Description

fmhp_batch() applies fmhp_filter() to every column of a matrix or data frame, as mhp_batch() does for the modified HP filter.

Usage

fmhp_batch(
  X,
  max_lambda = 3000L,
  k_linear = 15L,
  k_quadratic = NULL,
  alpha_linear = seq(0, 2000, 10),
  alpha_quadratic = seq(0, 2000, 5),
  schemes = c("linear", "quadratic"),
  form = c("rows", "differences"),
  lambda = NULL,
  log_scale = TRUE
)

## Default S3 method:
fmhp_batch(
  X,
  max_lambda = 3000L,
  k_linear = 15L,
  k_quadratic = NULL,
  alpha_linear = seq(0, 2000, 10),
  alpha_quadratic = seq(0, 2000, 5),
  schemes = c("linear", "quadratic"),
  form = c("rows", "differences"),
  lambda = NULL,
  log_scale = TRUE
)

Arguments

Value

A data.table with the columns series, t, original, trend, cycle and the attribute lambdas, a data.table with series, lambda, gcv, lambda_mhp, scheme, alpha, k and loss.

Author(s)

Muhammad Yaseen (myaseen208@gmail.com)

See Also

fmhp_filter, mhp_batch, plot_batch

Examples

data(us_macro)
X <- as.matrix(us_macro[, c("gdp", "consumption", "investment")])
fb <-
  fmhp_batch(
      X               = X
    , 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
    )
attr(x = fb, which = "lambdas")

Compare the HP, modified HP and fully modified HP filters

Description

fmhp_compare() filters one series with the three filters and compares their cycles and their end-point loss (Hanif et al. 2017, Tables 3a and 3b): the HP filter at the conventional \lambda of the frequency, the modified HP filter and the fully modified HP filter.

Usage

fmhp_compare(
  x,
  frequency = c("quarterly", "annual", "monthly"),
  max_lambda = 3000L,
  log_scale = TRUE,
  end_share = 0.1
)

## Default S3 method:
fmhp_compare(
  x,
  frequency = c("quarterly", "annual", "monthly"),
  max_lambda = 3000L,
  log_scale = TRUE,
  end_share = 0.1
)

Arguments

Details

Besides the moments of mhp_compare(), the table gives the total loss L of each filter (hp_loss()), its standard deviation of the cycle at the ends (the first and last end_share of the observations) and in the middle. A filter without end-point bias has a loss near zero and about the same cycle variability at the ends as in the middle.

Value

A data.table with one row per filter (HP, Modified HP, Fully modified HP) and the columns method, lambda, cycle_sd, cycle_mean, ar1, cycle_range, gcv, loss, sd_ends, sd_middle.

Author(s)

Muhammad Yaseen (myaseen208@gmail.com)

See Also

fmhp_filter, mhp_compare, hp_loss

Examples

data(us_macro)
fc <-
  fmhp_compare(
      x          = us_macro$gdp
    , frequency  = "quarterly"
    , max_lambda = 3000
    , log_scale  = TRUE
    , end_share  = 0.1
    )
fc

Fully modified Hodrick-Prescott filter

Description

fmhp_filter() applies the fully modified HP (FMHP) filter of Hanif, Iqbal and Choudhary (2017). It removes the two weaknesses of the HP filter at once: the smoothing parameter is chosen from the data (as in the modified HP filter of McDermott 1997), and the end-point bias is reduced by raising the smoothing parameter at the first and last k observations, with weights chosen to minimise the loss of Bloechl (2014), the distance of the gain of every estimate from the gain at the centre of the series.

Usage

fmhp_filter(
  x,
  max_lambda = 3000L,
  k_linear = 15L,
  k_quadratic = NULL,
  alpha_linear = seq(0, 2000, 10),
  alpha_quadratic = seq(0, 2000, 5),
  schemes = c("linear", "quadratic"),
  form = c("rows", "differences"),
  lambda = NULL,
  log_scale = TRUE,
  as_dt = TRUE
)

## Default S3 method:
fmhp_filter(
  x,
  max_lambda = 3000L,
  k_linear = 15L,
  k_quadratic = NULL,
  alpha_linear = seq(0, 2000, 10),
  alpha_quadratic = seq(0, 2000, 5),
  schemes = c("linear", "quadratic"),
  form = c("rows", "differences"),
  lambda = NULL,
  log_scale = TRUE,
  as_dt = TRUE
)

Arguments

Details

Gain and loss. Row t of the smoother \mathbf{B} holds the weights of \hat{g}_t; its gain at frequency \omega is

P_t(\omega) = \left|\sum_{j=1}^{T} b_{tj}\,e^{i\omega(j - t)}\right|

(Hanif et al. 2017, eq. 6), and the loss of the estimate is l(t) = \theta\sum_{\omega}[P_c(\omega) - P_t(\omega)]^2 over \omega = 0, 0.1, \dots, 3.1 with \theta = 0.1 and c the centre of the series (eq. 7); the total loss is L = \sum_t l(t) (eq. 8). See hp_loss().

End-point weights. The smoothing parameter of observation t is \lambda_t = \lambda in the middle and \lambda + \alpha j^{i} for the j-th observation from the middle among the last (and the first) k, j = 1, \dots, k, linear (i = 1) or quadratic (i = 2) (eqs. 9a and 9b). See hp_schedule().

The procedure (Section 5 of the paper):

1. \lambda^{\mathrm{MHP}} of the modified HP filter (mhp_filter()), searched over 1, \dots, max_lambda;

2. for each scheme (linear and quadratic), the weight \alpha of the grid that minimises the total loss L at \lambda^{\mathrm{MHP}};

3. with that weight, \lambda^{\mathrm{FMHP}} minimising McDermott's criterion again;

4. the scheme whose loss in step 2 is smaller gives the trend and the cycle.

The defaults are those of the published MATLAB code (Hanif 2017): max_lambda = 3000; linear weights on k = 15 end values with \alpha \in \{0, 10, \dots, 2000\}; quadratic weights on k = \mathrm{round}(\min(22, T/2 - 5)) end values with \alpha \in \{0, 5, \dots, 2000\}; logarithms of the series. The working paper states k = 20 in the text; set k_linear and k_quadratic to use it.

Form of the weights. The published code multiplies row t of \mathbf{A} by \lambda_t, \hat{\mathbf{g}} = (\mathbf{I} + \mathrm{diag}(\lambda_t)\mathbf{A})^{-1} \mathbf{x} (form = "rows", the default). The penalised least-squares problem with a separate \lambda_r for each second difference gives instead \hat{\mathbf{g}} = (\mathbf{I} + \mathbf{K}^\top\mathrm{diag}(\lambda_r)\mathbf{K})^{-1}\mathbf{x}, a symmetric smoother (form = "differences", the scheme of eq. 9 written on the T - 2 differences). Both are solved in O(T) operations; the gains need two solves per frequency and the smoother itself is never formed.

With lambda given, the smoothing parameter is fixed (steps 1 and 3 are skipped): the HP filter with the endogenous weights of the paper (Table 3a, column "HP (our scheme)").

Value

With as_dt = TRUE, a data.table with the columns original, trend, cycle (and time for a ts) and the attributes lambda, gcv, lambda_mhp, scheme, alpha, k, loss and lambda_t. With as_dt = FALSE, a list of class c("mhp_fmhp", "mhp", "mhp_result", "list"):

original, trend, cycle

the series, its trend and its cycle (on the scale of the series).

lambda, gcv

\lambda^{\mathrm{FMHP}} and its criterion.

lambda_mhp

\lambda^{\mathrm{MHP}} of step 1.

scheme, alpha, k

the chosen scheme, its weight and its number of end values.

loss

the total loss L of the chosen scheme at \lambda^{\mathrm{MHP}} (the criterion of step 4).

lambda_t

the smoothing parameters of the trend.

schemes

data.table, one row per scheme: scheme, k, alpha, loss, lambda, gcv.

form, log_scale

the settings; then trend_log, cycle_log (with log_scale = TRUE), time and frequency (for a ts).

Methods: print(), plot(), ggplot2::autoplot(), hp_loss(), mhp_interpret().

Author(s)

Muhammad Yaseen (myaseen208@gmail.com), from the MATLAB code of Muhammad Nadim Hanif

References

Hanif, M. N., Iqbal, J. and Choudhary, M. A. (2017). Fully modified HP filter. SBP Working Paper Series, No. 88, State Bank of Pakistan.

Hanif, M. N. (2017). Fully modified HP filter function (MATLAB code). MATLAB Central File Exchange, 63198.

Bloechl, A. (2014). Reducing the excess variability of the Hodrick-Prescott filter by flexible penalization. Discussion Paper 2014-1, University of Munich.

McDermott, C. J. (1997). An automatic method for choosing the smoothing parameter in the HP filter. Unpublished, International Monetary Fund, Washington DC.

See Also

mhp_filter, fmhp_batch, fmhp_compare, hp_loss

Examples

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

Power comparison of the filters on simulated series

Description

fmhp_simulation() repeats the simulation study of Hanif, Iqbal and Choudhary (2017, Tables 1 and 2): for each design it simulates series with mhp_simulate(), filters them with the HP, modified HP and fully modified HP filters, and compares the root mean square error of the estimated cycles against the true one, over the whole series, its middle and its ends.

Usage

fmhp_simulation(
  designs = mhp_designs(),
  n_rep = 100L,
  T = 200L,
  trend = c("linear", "nonlinear"),
  aggregate = c("none", "systematic", "sum", "average"),
  lambda = NULL,
  max_lambda = 3000L,
  seed = NULL,
  form = c("rows", "differences")
)

Arguments

Details

The RMSE of a filter is \{T^{-1}\sum_t(\hat{c}_t - c_t)^2\}^{1/2}; the middle is the central 80% of the observations and the ends the first and last 10%. fmhp_better is the share of replicates in which the FMHP filter has a smaller RMSE than the HP filter (Table 1 of the paper reports it in percent). The series are filtered on their own scale (log_scale = FALSE).

Value

An object of class c("mhp_simulation", "mhp_result", "list"): rmse (a data.table with one row per design and filter: model, sd_ratio, ar1, ar2, method, rmse, rmse_middle, rmse_ends), power (one row per design: the share of replicates in which FMHP beats HP and MHP) and settings. plot() draws the RMSE by design.

Author(s)

Muhammad Yaseen (myaseen208@gmail.com)

References

Hanif, M. N., Iqbal, J. and Choudhary, M. A. (2017). Fully modified HP filter. SBP Working Paper Series, No. 88, State Bank of Pakistan.

See Also

mhp_simulate, fmhp_filter

Examples

sim <-
  fmhp_simulation(
      designs    = mhp_designs()[c(3, 13, 23)]
    , n_rep      = 2
    , T          = 120
    , trend      = "linear"
    , aggregate  = "none"
    , lambda     = NULL
    , max_lambda = 3000
    , seed       = 1
    , form       = "rows"
    )
sim$power

Extract the smoothing parameter or the criterion of a result

Description

get_lambda() returns the smoothing parameter and get_gcv() the value of McDermott's criterion of a result of hp_filter(), mhp_filter() or fmhp_filter(), whether it is a data.table (as_dt = TRUE) or a list (as_dt = FALSE).

Usage

get_lambda(x)

## Default S3 method:
get_lambda(x)

get_gcv(x)

## Default S3 method:
get_gcv(x)

Arguments

Value

get_lambda(): the smoothing parameter; get_gcv(): the criterion at that value.

Author(s)

Muhammad Yaseen (myaseen208@gmail.com)

Examples

data(us_macro)
m <-
  mhp_filter(
      x          = log(us_macro$gdp)
    , max_lambda = 100000
    , as_dt      = TRUE
    , log_scale  = FALSE
    , criterion  = c("approximate", "exact")
    )
get_lambda(x = m)
get_gcv(x = m)

Hodrick-Prescott filter with a fixed smoothing parameter

Description

hp_filter() splits a time series into a smooth trend and a cycle with the filter of Hodrick and Prescott (1997) and a smoothing parameter \lambda chosen by the user: 1600 for quarterly data, 100 for annual data and 129600 for monthly data are the conventional values (Ravn and Uhlig 2002).

Usage

hp_filter(x, lambda = 1600, as_dt = TRUE, log_scale = FALSE)

## Default S3 method:
hp_filter(x, lambda = 1600, as_dt = TRUE, log_scale = FALSE)

Arguments

Details

The trend \mathbf{g} = (g_1, \dots, g_T)^\top of the series \mathbf{x} minimises

\sum_{t=1}^{T}(x_t - g_t)^2 + \lambda\sum_{t=2}^{T-1}\left[(g_{t+1} - g_t) - (g_t - g_{t-1})\right]^2,

so that \hat{\mathbf{g}} = (\mathbf{I} + \lambda\mathbf{A})^{-1}\mathbf{x} = \mathbf{B}\mathbf{x} with \mathbf{A} = \mathbf{K}^\top\mathbf{K} and \mathbf{K} the (T - 2) \times T matrix of second differences (rows (1, -2, 1)). The cycle is \mathbf{c} = \mathbf{x} - \hat{\mathbf{g}}. The system is pentadiagonal, symmetric and positive definite and is solved in O(T) operations.

With log_scale = TRUE the filter is applied to \log x_t; the trend is returned as \exp(\hat{g}_t) and the cycle as x_t - \exp(\hat{g}_t), and the components on the log scale are added to the list result.

Value

With as_dt = TRUE, a data.table with the columns original, trend, cycle (and time for a ts) and the attribute lambda. With as_dt = FALSE, a list of class c("mhp_hp", "mhp", "mhp_result", "list") with original, trend, cycle, lambda, then log_scale, trend_log and cycle_log (with log_scale = TRUE) and time and frequency (for a ts). Methods: print(), plot(), ggplot2::autoplot(), mhp_interpret().

Author(s)

Muhammad Yaseen (myaseen208@gmail.com)

References

Hodrick, R. J. and Prescott, E. C. (1997). Postwar U.S. business cycles: an empirical investigation. Journal of Money, Credit and Banking, 29(1), 1–16. doi:10.2307/2953682

Ravn, M. O. and Uhlig, H. (2002). On adjusting the Hodrick-Prescott filter for the frequency of observations. The Review of Economics and Statistics, 84(2), 371–376. doi:10.1162/003465302317411604

See Also

mhp_filter, fmhp_filter, mhp_compare

Examples

data(us_macro)
gdp <- ts(data = us_macro$gdp, start = c(1959, 1), frequency = 4)
hp <-
  hp_filter(
      x         = log(gdp)
    , lambda    = 1600
    , as_dt     = TRUE
    , log_scale = FALSE
    )
hp
attr(x = hp, which = "lambda")

Gain functions of an HP-type filter

Description

hp_gain() gives the gain of the estimate at every time t as a function of the frequency (Hanif et al. 2017, eq. 6, Figures 2 and 2b): the factor by which the filter scales an oscillation of that frequency. In the middle of a series the gain of the trend falls to zero at high frequencies; at the ends it does not, so the trend there keeps part of the cycle.

Usage

hp_gain(
  x,
  lambda = 1600,
  form = c("rows", "differences"),
  theta = seq(0, pi, length.out = 101),
  rows = NULL
)

## Default S3 method:
hp_gain(
  x,
  lambda = 1600,
  form = c("rows", "differences"),
  theta = seq(0, pi, length.out = 101),
  rows = NULL
)

Arguments

Details

With b_{tj} the weights of hp_weights(), P_t(\omega) = |\sum_j b_{tj} e^{i\omega(j - t)}|. It is computed from two solves of the smoothing system per frequency.

Value

An object of class c("mhp_gain", "mhp_result", "list"): gain (a data.table with t, theta, gain for every time and frequency), lambda_t, form, rows. plot() draws the gains of the chosen rows.

Author(s)

Muhammad Yaseen (myaseen208@gmail.com)

See Also

hp_loss, hp_weights

Examples

g <-
  hp_gain(
      x      = 50
    , lambda = 100
    , form   = "rows"
    , theta  = seq(from = 0, to = pi, length.out = 101)
    , rows   = NULL
    )
plot(x = g)

End-point loss of an HP-type filter

Description

hp_loss() measures the end-point bias of a filter by the loss of Bloechl (2014) used by Hanif, Iqbal and Choudhary (2017): for every time t, the squared distance of the gain of its estimate from the gain at the centre of the series. The loss is zero in the middle and grows towards the ends; the fully modified HP filter chooses its end-point weights to make the total small.

Usage

hp_loss(
  x,
  lambda = 1600,
  form = c("rows", "differences"),
  theta = seq(0, 3.1, 0.1),
  weight = 0.1
)

## Default S3 method:
hp_loss(
  x,
  lambda = 1600,
  form = c("rows", "differences"),
  theta = seq(0, 3.1, 0.1),
  weight = 0.1
)

Arguments

Details

l(t) = \theta\sum_{\omega}\left[P_c(\omega) - P_t(\omega)\right]^2, \qquad L = \sum_{t=1}^{T} l(t),

with the gains P_t of hp_gain(), \omega = 0, 0.1, \dots, 3.1, \theta = 0.1 (their spacing) and c = \mathrm{round}(T/2) (Hanif et al. 2017, eqs. 7 and 8, and their MATLAB code). The loss depends on T and the smoothing parameters only, not on the data: for the HP filter with \lambda = 100 it is 1.731 to 1.735 for 41 to 55 observations, the values of Table 3a of the paper.

Value

An object of class c("mhp_loss", "mhp_result", "list"): loss (a data.table with t and loss), total (L), lambda_t, form. plot() draws l(t) against t (Figures 3 and 3b of the paper).

Author(s)

Muhammad Yaseen (myaseen208@gmail.com)

References

Bloechl, A. (2014). Reducing the excess variability of the Hodrick-Prescott filter by flexible penalization. Discussion Paper 2014-1, University of Munich.

Hanif, M. N., Iqbal, J. and Choudhary, M. A. (2017). Fully modified HP filter. SBP Working Paper Series, No. 88, State Bank of Pakistan.

See Also

fmhp_filter, hp_gain, fmhp_compare

Examples

hl <-
  hp_loss(
      x      = 55
    , lambda = 100
    , form   = "rows"
    , theta  = seq(from = 0, to = 3.1, by = 0.1)
    , weight = 0.1
    )
hl$total
plot(x = hl)

Smoothing parameters with raised end values

Description

hp_schedule() gives the smoothing parameter of every observation (or second difference) under the end-point schemes of Hanif, Iqbal and Choudhary (2017, eqs. 9a and 9b): \lambda in the middle and \lambda + \alpha j^{i} for the j-th of the k values at each end, counted from the middle (j = k at the first and last observation).

Usage

hp_schedule(T, lambda, alpha, k, power = 1, form = c("rows", "differences"))

Arguments

Value

A numeric vector of smoothing parameters.

Author(s)

Muhammad Yaseen (myaseen208@gmail.com)

See Also

fmhp_filter, hp_loss

Examples

hp_schedule(
    T      = 50
  , lambda = 100
  , alpha  = 10
  , k      = 20
  , power  = 1
  , form   = "rows"
  )

Weights of an HP-type filter

Description

hp_weights() gives the matrix \mathbf{B} of the trend \hat{\mathbf{g}} = \mathbf{B}\mathbf{x}: row t holds the weights of the estimate at time t. Symmetric in the middle of the series, the rows become asymmetric near the ends, the source of the end-point bias (Hanif et al. 2017, Figures 1 and 1a).

Usage

hp_weights(x, lambda = 1600, form = c("rows", "differences"), rows = NULL)

## Default S3 method:
hp_weights(x, lambda = 1600, form = c("rows", "differences"), rows = NULL)

Arguments

Value

An object of class c("mhp_weights", "mhp_result", "list"): weights (the T \times T matrix), lambda_t, form, rows. plot() draws the chosen rows.

Author(s)

Muhammad Yaseen (myaseen208@gmail.com)

See Also

hp_gain, hp_loss

Examples

w <-
  hp_weights(
      x      = 50
    , lambda = 100
    , form   = "rows"
    , rows   = NULL
    )
round(x = w$weights[1:3, 1:6], digits = 3)
plot(x = w)

Methods for mhpfilter results

Description

The analysis functions of mhpfilter return the named list they have always returned, now with the class c("mhp_<analysis>", "mhp_result", "list"). Components are read as before (x$ANOVA, x[["Means"]]); the methods below print, summarise and plot the result and turn any component into a data.table.

Usage

## S3 method for class 'mhp_result'
print(x, digits = 4L, ...)

## S3 method for class 'mhp_result'
summary(object, ...)

## S3 method for class 'summary.mhp_result'
print(x, ...)

## S3 method for class 'mhp_result'
format(x, ...)

## S3 method for class 'mhp_result'
as.data.table(x, keep.rownames = FALSE, ..., component = 1L)

## S3 method for class 'mhp_result'
as.data.frame(x, row.names = NULL, optional = FALSE, ..., component = 1L)

## S3 method for class 'mhp_result'
plot(x, ...)

Arguments

Value

print() returns x invisibly; summary() an object of class summary.mhp_result; format() a character string; as.data.table() and as.data.frame() the chosen component as a table; plot() a ggplot object.

Author(s)

Muhammad Yaseen (myaseen208@gmail.com)

Trend and cycle analysis in a web browser

Description

mhp_app() starts the application of mhpfilter: load a series (the example us_macro or a CSV file), filter it with the HP, modified HP or fully modified HP filter, compare the three filters, inspect their weights, gains and end-point loss, filter all the series of a file at once and run the power comparison of Hanif, Iqbal and Choudhary (2017). Every result page shows an interpretation computed from the results (mhp_interpret()), the output as R prints it, formatted tables, plots and the R code that repeats the analysis, each with a Copy button.

Usage

mhp_app(launch.browser = interactive(), ...)

mhp_app_object()

Arguments

Details

The application needs the suggested packages shiny, bslib and DT. Plots are sent to the browser as WebP images when magick is installed (smaller than PNG; PNG otherwise) and can be downloaded as PNG, PDF or WebP. Text is set in IBM Plex Sans and output in IBM Plex Mono when the browser can reach Google Fonts, in the system fonts otherwise.

Value

mhp_app() is called for its side effect and returns the value of shiny::runApp() when the application is closed; mhp_app_object() returns the application object (for shiny::runApp(), shiny::testServer() or deployment on a server).

Author(s)

Muhammad Yaseen (myaseen208@gmail.com)

See Also

mhp_filter, fmhp_filter, fmhp_compare, mhp_interpret

Examples

if (interactive()) {
  mhp_app(
      launch.browser = TRUE
    )
}

Modified HP filter of many series

Description

mhp_batch() applies mhp_filter() to every column of a matrix or data frame and returns one long table, with the smoothing parameter of each series in an attribute. Series of different lengths can share the matrix: leading and trailing missing values are dropped series by series.

Usage

mhp_batch(X, max_lambda = 100000L)

## Default S3 method:
mhp_batch(X, max_lambda = 100000L)

Arguments

Value

A data.table with the columns series, t, original, trend, cycle and the attribute lambdas, a data.table with series, lambda and gcv (as in version 0.1.0).

Author(s)

Muhammad Yaseen (myaseen208@gmail.com)

See Also

mhp_filter, fmhp_batch, batch_compare, plot_batch

Examples

data(us_macro)
X <- log(as.matrix(us_macro[, c("gdp", "consumption", "investment")]))
mb <-
  mhp_batch(
      X          = X
    , max_lambda = 100000
    )
attr(x = mb, which = "lambdas")

References of a result or of the package

Description

mhp_cite() gives the references of the methods behind a result of the package, or the references of every method in the package, as text or BibTeX. citation("mhpfilter") cites the package and its main methods.

Usage

mhp_cite(x = NULL, style = c("text", "bibtex"))

## Default S3 method:
mhp_cite(x = NULL, style = c("text", "bibtex"))

Arguments

Value

An object of class bibentry (printed in the chosen style).

Author(s)

Muhammad Yaseen (myaseen208@gmail.com)

Examples

mhp_cite(
    x     = NULL
  , style = "text"
  )
data(us_macro)
f <-
  mhp_filter(
      x          = log(us_macro$gdp)
    , max_lambda = 100000
    , as_dt      = FALSE
    , log_scale  = FALSE
    , criterion  = "approximate"
    )
mhp_cite(
    x     = f
  , style = "bibtex"
  )

Compare the HP and the modified HP filter

Description

mhp_compare() filters one series with the HP filter at the conventional \lambda of its frequency and with the modified HP filter, and compares the cycles; batch_compare() does the same for every column of a matrix.

Usage

mhp_compare(
  x,
  frequency = c("quarterly", "annual", "monthly"),
  max_lambda = 100000L
)

## Default S3 method:
mhp_compare(
  x,
  frequency = c("quarterly", "annual", "monthly"),
  max_lambda = 100000L
)

batch_compare(
  X,
  frequency = c("quarterly", "annual", "monthly"),
  max_lambda = 100000L
)

## Default S3 method:
batch_compare(
  X,
  frequency = c("quarterly", "annual", "monthly"),
  max_lambda = 100000L
)

Arguments

Details

The conventional values are \lambda = 1600 (quarterly), 100 (annual) and 129600 (monthly, Ravn and Uhlig 2002). ar1 is the first-order autocorrelation of the cycle, \sum_t c_t c_{t+1} / \sum_t c_t^2.

Value

mhp_compare(): a data.table with one row per method (HP, Modified HP) and the columns method, lambda, cycle_sd, cycle_mean, ar1, cycle_range, gcv. batch_compare(): a data.table with one row per series and the columns series, hp_lambda, mhp_lambda, hp_cycle_sd, mhp_cycle_sd, sd_diff, hp_ar1, mhp_ar1, ar1_diff, relative_sd.

Author(s)

Muhammad Yaseen (myaseen208@gmail.com)

See Also

fmhp_compare, plot_comparison

Examples

data(us_macro)
cmp <-
  mhp_compare(
      x          = log(us_macro$gdp)
    , frequency  = "quarterly"
    , max_lambda = 100000
    )
cmp
bc <-
  batch_compare(
      X          = log(as.matrix(us_macro[, c("gdp", "consumption", "investment")]))
    , frequency  = "quarterly"
    , max_lambda = 100000
    )
bc

The 30 simulation designs of Hanif, Iqbal and Choudhary (2017)

Description

mhp_designs() lists the 30 combinations of Table 1 of the paper: five ratios \sigma_\varepsilon / \sigma_\delta of the standard deviations of the trend and cycle shocks (10, 5, 2, 1, 0.5) crossed with six AR(2) cycles (\phi_1, \phi_2): (0.9, 0.01), (1.2, -0.25), (1.2, -0.4), (1.2, -0.55), (1.2, -0.75) and (0.8, 0). The designs of Choudhary, Hanif and Iqbal (2014, Table 1) have the same cycles and the ratios 10, 5, 1, 0.5 and 0.01.

Usage

mhp_designs(paper = c("2017", "2014"))

Arguments

Value

A data.table with the columns model (1 to 30, as in the paper), sd_ratio, ar1, ar2.

Author(s)

Muhammad Yaseen (myaseen208@gmail.com)

References

Choudhary, M. A., Hanif, M. N. and Iqbal, J. (2014). On smoothing macroeconomic time series using the modified HP filter. Applied Economics, 46(19), 2205–2214. doi:10.1080/00036846.2014.894631

Hanif, M. N., Iqbal, J. and Choudhary, M. A. (2017). Fully modified HP filter. SBP Working Paper Series, No. 88, State Bank of Pakistan.

See Also

mhp_simulate, fmhp_simulation

Examples

mhp_designs(
    paper = "2017"
  )

Modified Hodrick-Prescott filter: the smoothing parameter chosen from the data

Description

mhp_filter() applies the modified HP filter of McDermott (1997), studied by Choudhary, Hanif and Iqbal (2014): the smoothing parameter \lambda is the one of 1, 2, \dots, max_lambda that minimises a generalised cross-validation criterion, so that every series gets its own \lambda instead of the conventional 1600 or 100.

Usage

mhp_filter(
  x,
  max_lambda = 100000L,
  as_dt = TRUE,
  log_scale = FALSE,
  criterion = c("approximate", "exact")
)

## Default S3 method:
mhp_filter(
  x,
  max_lambda = 100000L,
  as_dt = TRUE,
  log_scale = FALSE,
  criterion = c("approximate", "exact")
)

Arguments

Details

For each candidate \lambda the trend \hat{\mathbf{g}}(\lambda) of hp_filter() is computed and

\mathrm{GCV}(\lambda) = \frac{1}{T}\left(1 + \frac{2T}{\lambda}\right)\sum_{t=1}^{T}\left(x_t - \hat{g}_t(\lambda)\right)^2

(Choudhary et al. 2014, eq. 6; Hanif et al. 2017, eq. 4); \hat\lambda minimises it. This is Silverman's (1984) approximation of generalised cross-validation (Craven and Wahba 1979),

\mathrm{GCV}(\lambda) = \frac{T^{-1}\sum_{t}(x_t - \hat{g}_t(\lambda))^2}{\left(1 - T^{-1}\mathrm{tr}\,\mathbf{B}(\lambda)\right)^2}

(Choudhary et al. 2014, eq. 5), which criterion = "exact" uses: the eigenvalues \mu_i of \mathbf{A}, computed once, give \mathrm{tr}\,\mathbf{B}(\lambda) = \sum_i (1 + \lambda\mu_i)^{-1} and the residual sum of squares for every \lambda in O(T) operations (the decomposition costs O(T^3), a fraction of a second for a few hundred observations). Each trend costs O(T) operations, so the search over 100000 values takes about a second for 200 quarterly observations.

The search is that of the authors' MATLAB code (modifiedhpfilternew.m, Choudhary et al. 2014), which omits the factor 1/T (it does not change the minimum) and works on the series as given; filter the logarithm of a series (as in the papers) with log_scale = TRUE or by passing log(x).

Changes from version 0.1.0. The criterion is unchanged (the help page of 0.1.0 printed the factor as 1 + 2/(T\lambda), but the code used 1 + 2T/\lambda); every trend is now a banded solve instead of a dense one, so results agree with 0.1.0 to rounding error at a fraction of the time.

Value

With as_dt = TRUE, a data.table with the columns original, trend, cycle (and time for a ts) and the attributes lambda and gcv. With as_dt = FALSE, a list of class c("mhp_mhp", "mhp", "mhp_result", "list") with original, trend, cycle, lambda, gcv as in version 0.1.0, then gcv_path (the criterion for every \lambda of the search), log_scale, criterion, trend_log and cycle_log (with log_scale = TRUE), time and frequency (for a ts). Methods: print(), plot(), ggplot2::autoplot(), mhp_interpret().

Author(s)

Muhammad Yaseen (myaseen208@gmail.com)

References

Choudhary, M. A., Hanif, M. N. and Iqbal, J. (2014). On smoothing macroeconomic time series using the modified HP filter. Applied Economics, 46(19), 2205–2214. doi:10.1080/00036846.2014.894631

Craven, P. and Wahba, G. (1979). Smoothing noisy data with spline functions. Numerische Mathematik, 31, 377–403. doi:10.1007/BF01404567

Silverman, B. W. (1984). A fast and efficient cross-validation method for smoothing parameter choice in spline regression. Journal of the American Statistical Association, 79(387), 584–589. doi:10.1080/01621459.1984.10478084

McDermott, C. J. (1997). An automatic method for choosing the smoothing parameter in the HP filter. Unpublished, International Monetary Fund, Washington DC; described in Coe, D. T. and McDermott, C. J. (1997). Does the gap model work in Asia? IMF Staff Papers, 44(1), 59–80. doi:10.2307/3867497

See Also

hp_filter, fmhp_filter, mhp_batch, get_lambda

Examples

data(us_macro)
gdp <- ts(data = us_macro$gdp, start = c(1959, 1), frequency = 4)
mhp <-
  mhp_filter(
      x          = log(gdp)
    , max_lambda = 100000
    , as_dt      = FALSE
    , log_scale  = FALSE
    , criterion  = "approximate"
    )
mhp
plot(x = mhp)

Plain-language interpretation of a result

Description

mhp_interpret() turns a result of the package into a short report: a headline, findings, recommendations and cautions, computed from its numbers, with the sources of the method. It covers the filters (hp_filter(), mhp_filter(), fmhp_filter(), as lists or as data.tables), the end-point loss (hp_loss()) and the power comparison (fmhp_simulation()).

Usage

mhp_interpret(x, top = 3L, ...)

## Default S3 method:
mhp_interpret(x, top = 3L, ...)

## S3 method for class 'mhp_interpretation'
print(x, ...)

## S3 method for class 'mhp_interpretation'
format(x, style = c("text", "markdown"), width = getOption("width", 80L), ...)

Arguments

Details

For a filter the report compares the chosen smoothing parameter with the conventional one of the frequency (1600 quarterly, 100 annual, 129600 monthly; known when the series is a ts), names the largest booms and recessions of the cycle, and warns when a search ended at its limit or the series is short. For the fully modified HP filter it also gives the reduction of the end-point loss against the HP filter with the same \lambda.

Value

An object of class "mhp_interpretation": a list with analysis, title, headline, findings, recommendations, cautions, facts (the numbers behind the sentences), guide (how to read the method) and sources. format() gives it as text or Markdown.

Author(s)

Muhammad Yaseen (myaseen208@gmail.com)

See Also

mhp_cite, mhp_app

Examples

data(us_macro)
gdp <- ts(data = us_macro$gdp, start = c(1959, 1), frequency = 4)
f <-
  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
    )
mhp_interpret(
    x   = f
  , top = 3
  )

Notation of mhpfilter

Description

The symbols used in the help pages and vignettes of mhpfilter, with their meaning and the argument or result component that holds them. The notation follows one rule throughout: scalars are upper-case letters in normal face (P, R), indices lower-case italic (i, j), vectors lower-case bold (\mathbf{y}, \boldsymbol{\beta}) and matrices upper-case bold (\mathbf{X}, \boldsymbol{\Sigma}).

Usage

mhp_notation(format = c("table", "path", "tex"))

Arguments

Value

See format.

Author(s)

Muhammad Yaseen (myaseen208@gmail.com)

See Also

Other mhpfilter utilities: mhp_reference(), mhp_save(), mhp_theme()

Examples

mhp_notation(
    format = c("table", "path", "tex")[1]
  )

Published values used by the tests and vignettes

Description

Reads inst/extdata/reference.csv: one row per published number, with its source, the R call that recomputes it with this package (call), the expression that extracts the number from the result (extract, in terms of x), the printed value and the digits to compare. The same file drives the test of published values and the vignette that reproduces the published examples. Each distinct call is evaluated once.

Usage

mhp_reference(source = NULL, evaluate = FALSE, level = 1)

Arguments

Value

A data.table with columns id, source, quantity, call, extract, value, digits, level, note (and computed, agrees).

Author(s)

Muhammad Yaseen (myaseen208@gmail.com)

See Also

Other mhpfilter utilities: mhp_notation(), mhp_save(), mhp_theme()

Examples

ref <-
  mhp_reference(
      source   = NULL
    , evaluate = FALSE
    , level    = 1
    )
ref

mhp_reference(
    source   = "."
  , evaluate = TRUE
  , level    = 1
  )

Save a figure (vector PDF by default)

Description

A wrapper of ggsave with the defaults of the package: a vector PDF through cairo_pdf (embedded fonts, correct glyphs), A4 landscape (11.69 x 8.27 inches) and 600 dpi for raster formats. The device follows the file extension for other formats (.png, .svg, .tiff, ...).

Usage

mhp_save(
  plot = ggplot2::last_plot(),
  filename,
  path = NULL,
  width = 11.69,
  height = 8.27,
  units = c("in", "cm", "mm"),
  dpi = 600,
  scale = 1,
  device = NULL,
  limitsize = TRUE,
  ...
)

## Default S3 method:
mhp_save(
  plot = ggplot2::last_plot(),
  filename,
  path = NULL,
  width = 11.69,
  height = 8.27,
  units = c("in", "cm", "mm"),
  dpi = 600,
  scale = 1,
  device = NULL,
  limitsize = TRUE,
  ...
)

Arguments

Value

The file name, invisibly.

Author(s)

Muhammad Yaseen (myaseen208@gmail.com)

See Also

Other mhpfilter utilities: mhp_notation(), mhp_reference(), mhp_theme()

Examples

library(ggplot2)
p <-
  ggplot(data = data.frame(x = 1:10, y = (1:10)^2), mapping = aes(x = x, y = y)) +
  geom_line() +
  mhp_theme(
      base_size       = 11
    , base_family     = "serif"
    , ticks_inward    = TRUE
    , legend_position = "bottom"
    )
f <- tempfile(fileext = ".pdf")
mhp_save(
    plot      = p
  , filename  = f
  , path      = NULL
  , width     = 11.69
  , height    = 8.27
  , units     = c("in", "cm", "mm")[1]
  , dpi       = 600
  , scale     = 1
  , device    = NULL
  , limitsize = TRUE
  )
mhp_save(
    plot      = p
  , filename  = basename(f)
  , path      = tempdir()
  , width     = 11.69
  , height    = 8.27
  , units     = c("in", "cm", "mm")[1]
  , dpi       = 600
  , scale     = 1
  , device    = grDevices::cairo_pdf
  , limitsize = TRUE
  )
mhp_save(
    plot      = p
  , filename  = tempfile(fileext = ".png")
  , path      = NULL
  , width     = 6
  , height    = 4
  , units     = c("in", "cm", "mm")[1]
  , dpi       = 300
  , scale     = 1
  , device    = NULL
  , limitsize = TRUE
  )

Simulate a series with a known trend and cycle

Description

mhp_simulate() generates a series x_t = g_t + c_t from the data generating process of Hanif, Iqbal and Choudhary (2017, eqs. 10a and 10b), after Harvey and Jaeger (1993) and Guay and St-Amant (2005): a random walk trend with drift and an AR(2) cycle,

g_t = \mu + \tau_t + g_{t-1} + \varepsilon_t, \qquad c_t = \phi_1 c_{t-1} + \phi_2 c_{t-2} + \delta_t,

with \varepsilon_t \sim N(0, \sigma_\varepsilon^2) and \delta_t \sim N(0, \sigma_\delta^2). Quarterly series can be aggregated to annual ones as in the paper.

Usage

mhp_simulate(
  T = 200L,
  sd_ratio = 1,
  ar = c(1.2, -0.4),
  sd_cycle = 1,
  drift = 0.5,
  trend = c("linear", "nonlinear"),
  aggregate = c("none", "systematic", "sum", "average"),
  seed = NULL
)

Arguments

Details

The paper does not give the drift \mu or the form of the nonlinear trend term \tau_t. Here \tau_t = 0 for trend = "linear", and \tau_t = \mu\sin(2\pi t/T) for trend = "nonlinear", a drift that rises and falls once over the sample. The cycle starts from a burn-in of 100 values. Aggregation to annual data takes every fourth value ("systematic"), the sum of four consecutive values ("sum") or their average ("average"), for the series and both components.

Value

A data.table with the columns t, x, trend, cycle.

Author(s)

Muhammad Yaseen (myaseen208@gmail.com)

References

Guay, A. and St-Amant, P. (2005). Do the Hodrick-Prescott and Baxter-King filters provide a good approximation of business cycles? Annales d'Economie et de Statistique, 77, 133–155. doi:10.2307/20079119

Harvey, A. C. and Jaeger, A. (1993). Detrending, stylized facts and the business cycle. Journal of Applied Econometrics, 8(3), 231–247. doi:10.1002/jae.3950080302

See Also

mhp_designs, fmhp_simulation

Examples

s <-
  mhp_simulate(
      T         = 200
    , sd_ratio  = 1
    , ar        = c(1.2, -0.4)
    , sd_cycle  = 1
    , drift     = 0.5
    , trend     = "linear"
    , aggregate = "none"
    , seed      = 1
    )
s

ggplot2 theme of mhpfilter

Description

The theme used by every plot() method of mhpfilter (identical in all packages of the author): theme_classic with a serif font, black axis lines, ticks pointing inwards and no grid, close to the look of TikZ/pgfplots figures in LaTeX documents. The plot() methods also use scales::pretty_breaks(n = 10) on every continuous axis. Save figures with mhp_save.

Usage

mhp_theme(
  base_size = 11,
  base_family = "serif",
  ticks_inward = TRUE,
  legend_position = "bottom"
)

Arguments

Value

A ggplot2 theme.

Author(s)

Muhammad Yaseen (myaseen208@gmail.com)

See Also

Other mhpfilter utilities: mhp_notation(), mhp_reference(), mhp_save()

Examples

library(ggplot2)
p <-
  ggplot(data = data.frame(x = 1:20, y = cumsum(sin(1:20))), mapping = aes(x = x, y = y)) +
  geom_line()
p +
  mhp_theme(
      base_size       = 11
    , base_family     = "serif"
    , ticks_inward    = TRUE
    , legend_position = "bottom"
    )
p +
  mhp_theme(
      base_size       = 12
    , base_family     = "serif"
    , ticks_inward    = FALSE
    , legend_position = "right"
    ) +
  scale_x_continuous(breaks = scales::pretty_breaks(n = 10))

Plot the results of many series

Description

plot_batch() draws the cycles (or trends) of a result of mhp_batch() or fmhp_batch(), one panel per series or all in one panel, with the smoothing parameter of each series in its label.

Usage

plot_batch(x, show = c("cycle", "trend"), facet = TRUE, highlight = NULL)

Arguments

Details

Change from version 0.1.0. The faceted plot passed linewidth twice (a warning) and ignored highlight; both are corrected.

Value

A ggplot object.

Author(s)

Muhammad Yaseen (myaseen208@gmail.com)

Examples

data(us_macro)
mb <-
  mhp_batch(
      X          = log(as.matrix(us_macro[, c("gdp", "consumption", "investment")]))
    , max_lambda = 100000
    )
plot_batch(
    x         = mb
  , show      = "cycle"
  , facet     = TRUE
  , highlight = NULL
  )

Plot the HP and modified HP filters of one series

Description

plot_comparison() draws the series with the trends of the HP filter (at the conventional \lambda of its frequency) and of the modified HP filter, and optionally the cycles; with fmhp = TRUE the fully modified HP filter is added.

Usage

plot_comparison(
  x,
  frequency = c("quarterly", "annual", "monthly"),
  max_lambda = 100000L,
  show_cycle = FALSE,
  fmhp = FALSE
)

Arguments

Value

A ggplot object.

Author(s)

Muhammad Yaseen (myaseen208@gmail.com)

Examples

data(us_macro)
plot_comparison(
    x          = log(us_macro$gdp)
  , frequency  = "quarterly"
  , max_lambda = 100000
  , show_cycle = TRUE
  , fmhp       = TRUE
  )

Print a filter result

Description

print() of a result of hp_filter(), mhp_filter() or fmhp_filter() (with as_dt = FALSE) shows the smoothing parameter, the criterion and summaries of the cycle, as in version 0.1.0, and the sources of the method.

Usage

## S3 method for class 'mhp'
print(x, ...)

Arguments

Value

x, invisibly.

Author(s)

Muhammad Yaseen (myaseen208@gmail.com)

Examples

data(us_macro)
m <-
  mhp_filter(
      x          = log(us_macro$gdp)
    , max_lambda = 100000
    , as_dt      = FALSE
    , log_scale  = FALSE
    , criterion  = c("approximate", "exact")
    )
print(x = m)

United States real GDP, consumption and investment, 1959 to 2009 (quarterly)

Description

Quarterly real gross domestic product, real personal consumption expenditures and real gross private domestic investment of the United States from the first quarter of 1959 to the third quarter of 2009: the three series (income, consumption and investment) of the empirical analysis of Hanif, Iqbal and Choudhary (2017), for one country.

Usage

us_macro

Format

A data frame with 203 rows and 5 columns:

year

year, 1959 to 2009.

quarter

quarter, 1 to 4.

gdp

real gross domestic product (billions of chained 2005 US dollars, seasonally adjusted annual rate).

consumption

real personal consumption expenditures (same units).

investment

real gross private domestic investment (same units).

Source

Federal Reserve Economic Data (FRED), Federal Reserve Bank of St. Louis, accessed 15 December 2009, as compiled in the data set macrodata of the Python library statsmodels (public domain).

References

Hanif, M. N., Iqbal, J. and Choudhary, M. A. (2017). Fully modified HP filter. SBP Working Paper Series, No. 88, State Bank of Pakistan.

Examples

data(us_macro)
head(us_macro)
gdp <- ts(data = us_macro$gdp, start = c(1959, 1), frequency = 4)
plot(log(gdp))