The Hodrick-Prescott (HP) filter is widely used in the field of economics to estimate trends and cycles from time series data. For certain applications – such as deriving implied trend and cycle models and obtaining filter weights – it is desirable to express the frequency response of the HP as the spectral density of an ARMA model; in other words, to accomplish the spectral factorization of th...

The Hodrick–Prescott (HP) filter is a commonly used tool in macroeconomics to obtain the HP trend of macroeconomic variable. In macroeconomics, difference between original series and this called ‘cyclical component’. article, we derive autocovariance function spectrum cyclical component that consists constant, linear time trend, unit root process, weakly stationary process. We show such depends...

The Hodrick-Prescott filter represents one of the most popular method for trendcycle extraction in macroeconomic time series. In this paper we provide a multivariate generalization of the Hodrick-Prescott filter, based on the seemingly unrelated time series approach. We first derive closed-form expressions linking the signal-noise matrix ratio to the parameters of the VARMA representation of th...

This paper aims to analyze the effectiveness of detrending policies in Turkey using Hodrick- Prescott (HP) filter, country’s Gross Domestic Product (GDP), and selected indicators from 2010 2021. The HP filter is a commonly used statistical tool for time series data by separating trend component cyclical series. discussion section shows observable physical impact overlooking components over comp...