hpfj_fix: HP filter with automatic jumps detection and fixed smoothing...

In jumps: Hodrick-Prescott Filter with Jumps

HP filter with automatic jumps detection and fixed smoothing constant

Description

This is the lower-level function for the HP filter with jumps with fixed smoothing parameter. The user should use the hpj function instead, unless in need of more control and speed. The function estimates the HP filter with jumps. Jumps happen contextually in the level and in the slope: the standard deviation of the slope disturbance is \gamma times the standard deviation of the level disturbance at time t. In this case the HP smoothing parameter \lambda is fixed by the user and so that \sigma^2_\varepsilon = \lambda\sigma^2_\zeta.

Usage

hpfj_fix(y, lambda, maxsum = sd(y), edf = TRUE, parinit = NULL)

Arguments

y	vector with the time series
lambda	either a numeric scalar with the smoothing constant or a string with the frequency of the time series to be selected among c("daily", "weekly", "monthly", "quarterly", "annual"); in this case the values of the smoothing constant are computed according to Ravn and Uhlig (2002), that is, 6.25 s^4, where $s$ is the number of observations per year.
maxsum	maximum sum of additional level standard deviations;
edf	boolean if TRUE computes effective degrees of freedom otherwise computes the number of degrees of freedom in the LASSO-regression way.
parinit	either NULL or vector of 3+n parameters with starting values for the optimizer; the order of the parameters is sd(slope disturbnce), sd(observatio noise), square root of gamma, n additional std deviations for the slope

Value

list with the following slots:

• opt: the output of the optimization function (nloptr)

• nobs: number of observations

• df: number of estimated parameters (model's degrees of freedom)

• loglik: value of the log-likelihood at maximum

• ic: vector of information criteria (aic, aicc, bic, hq)

• smoothed_level: vector with smoothed level with jumps (hp filter with jumps)

• var_smoothed_level: variance of the smoothed level

Examples

set.seed(202311)
n <- 100
mu <- 100*cos(3*pi/n*(1:n)) - ((1:n) > 50)*n - c(rep(0, 50), 1:50)*10
y <- mu + rnorm(n, sd = 20)
plot(y, type = "l")
lines(mu, col = "blue")
hp <- hpfj_fix(y, 60, 60)
lines(hp$smoothed_level, col = "red")

jumps documentation built on April 4, 2025, 2:22 a.m.