hpconf: Confidence Bands for the Hodrick-Prescott Filter

In franzmohr/hpconf: Confidence Bands for the Hodrick-Prescott Filter

Description

A function for the calculation of confidence bands for the trend component of the Hodrick-Prescott (HP) filter as proposed by Giles (2013).

Usage

hpconf(data, V_y = NULL, ci = 0.95)

Arguments

data	an object of class "mFilter" containing the output of the function hpfilter.
V_y	a numeric specifying the variance of the cyclical component. If V_y = NULL (default), the sample variance of the original time series will be used.
ci	numeric between 0 and 1 specifying the confidence interval. Defaults to 0.95.

Details

The function uses the filter matrix F from an "mFilter" object to obtain the matrix Q = ≤ft[I_T + λ K' K]^{-1}\right]. Since Q y provides an estimate of the trend \hat{tau} and F y yields the cyclical component of the process \hat{c} and the time series y is decomposed only into those two components so that y = \hat{tau} + \hat{c}, Q can be obtained from I_T y - Fy = Q y so that Q = I_T - F.

The confidence band is then derived from the covariance matrix V(\hat{tau}) = Q V(y) Q.

By default V_y = NULL so that the sample variance of the original time series is used for the construction of V(y). This can be chanced by providing a numeric value, for example from the output of an esitmated ARIMA model.

Value

A time-series object of four variables

• trend: The estimated trend component

• ci_lower: The lower bound of the confidence band

• ci_upper: The upper bound of the confidence band

• y: The actual series

References

Giles, D. E. (2013). Constructing confidence bands for the Hodrick-Prescott filter. Applied Economics Letters, 20(5), 480–484. https://doi.org/10.1080/13504851.2012.714057

Examples

library(mFilter)
library(hpconf)

# Load data
data("unemp")

# Run HP-filter
hp_unemp <- hpfilter(unemp)

# Obtain confidence bands
hp_conf <- hpconf(hp_unemp)

# Plot
plot(hp_conf)

franzmohr/hpconf documentation built on Nov. 5, 2021, 10:17 p.m.