jumps (version 1.0)

hpj: Hodrick-Prescott filter with jumps

Description

This function is a wrapper for the various Hodrick-Prescott filters with jumps functions. The end user should use this: it is simpler and more flexible than the other functions.

Usage

hpj(
  y,
  maxsum = NULL,
  lambda = NULL,
  xreg = NULL,
  ic = c("bic", "hq", "aic", "aicc"),
  scl = 1000
)

Value

S3 object of class hpj with the following slots:

• y: the input time series;

• maxsum: the maximum sum of additional standard deviations;

• lambda: the smoothing constant of the HP filter;

• pars: vector of estimated parameters (sigma_slope, sigma_noise, gamma);

• hpj: the time series of the HP filter with jumps;

• hpj_std: the time series of the HP filter with jumps standard deviations;

• std_devs: vector of additional standard deviations of the level disturbance;

• breaks: vector of indices of the breaks;

• xreg: matrix of regressors;

• df: model's degrees of freedom;

• loglik: value of the log-likelihood at maximum;

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

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

• call: the call to the function.

Arguments

y

either a numeric vector or a time series object containing the time series to filter;

maxsum

maximum sum of additional level standard deviations, if NULL the value is selected automatically on a grid using the specified information criterion (ic);

lambda

smoothing constant of the HP filter, if NULL the value is estimated by maximum likelihood;

xreg

matrix of regressors;

ic

string with information criterion for the automatic choice of maxsum: the default is "bic" (simulations show this is the best choice), but also "hq", "aic" and "aicc" are available.

scl

scaling factor for the time series (default is 1000): the time series is rescaled as (y-min(y))/(max(y)-min(y))*scl. This is done since the default starting values for the optimization seem to work well in this scale); If `scl` is set equal to the string `"original"` the time series is not rescaled.

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)
hp <- hpj(y, 50)
plot(hp)