A widely used filter to extract a signal in a time series, in particular in the business cycle analysis, is the Hodrick-Prescott filter. The model that underlies the filter considers the data series as the sum of two unobserved component (signal and non signal) and a smoothing parameter which for quarterly series is set to a specified value. This paper proposes a generalization of the Hodrick-P...

Abstract Hodrick–Prescott (HP) filter is a popular trend filtering method for univariate macroeconomic time series such as real gross domestic product. This paper considers the quantile regression version of HP (qHP filter), which defined by replacing quadratic loss function with function. One essential properties that if includes intercept, then ratio negative residuals can be almost controlle...

Hodrick and Prescott (1997) proposed a smoothing method for economic time series that is very similar to graduation, it is usually known as the H-P method. They acknowledged that this method is equivalent to graduation methods and that it had been in use among actuaries. The literature on smoothing methods based on their approach grew separately from the graduation literature, due to the useful...

The irregular and slope disturbances, εt and ζt, respectively, are mutually independent and the notation NID(0, σ2) denotes normally and independently distributed with mean zero and variance σ2. The signal-noise ratio, q = σ2 ζ/σ 2 ε , plays the key role in determining how observations should be weighted for prediction and signal extraction. The higher is q, the more past observations are disco...

As part of the new macroeconomic modelling project at the Reserve Bank of New Zealand, considerable effort has been directed towards constructing an historical estimate of the productive capacity of the New Zealand economy. The technique documented in this paper augments the stochastic-trend estimation approach of the Hodrick-Prescott (1997) filter with information from broad macroeconomic rela...

On purpose to extract trend and cycle from a time series many competing techniques have been developed. The probably most prevalent is the Hodrick Prescott filter. However this filter suffers from diverse shortcomings, especially the subjective choice of its penalization parameter. To this point penalized splines within a mixed model framework offer the advantage of a data driven derivation of ...