Time Series Detrending for Macroeconomic Analysis

This skill provides guidance on decomposing economic time series into trend and cyclical components, a fundamental technique in business cycle analysis.

Overview

Economic time series like GDP, consumption, and investment contain both long-term trends and short-term fluctuations (business cycles). Separating these components is essential for:

• Analyzing business cycle correlations
• Comparing volatility across variables
• Identifying leading/lagging indicators

The Hodrick-Prescott (HP) Filter

The HP filter is the most widely used method for detrending macroeconomic data. It decomposes a time series into a trend component and a cyclical component.

Mathematical Foundation

Given a time series $y_t$, the HP filter finds the trend $\tau_t$ that minimizes: