The Spline-GARCH Model for Low-Frequency Volatility and Its Global Macroeconomic Causes

Abstract

Twenty-five years of volatility research has left the macroeconomic environment playing a minor role. This paper proposes modeling equity volatilities as a combination of macro- economic effects and time series dynamics. High-frequency return volatility is specified to be the product of a slow-moving component, represented by an exponential spline, and a unit GARCH. This slow-moving component is the low-frequency volatility, which in this model coincides with the unconditional volatility. This component is estimated for nearly 50 countries over various sample periods of daily data. Low-frequency volatility is then modeled as a function of macroeconomic and financial variables in an unbalanced panel with a variety of dependence structures. It is found to vary over time and across countries. The low-frequency component of volatility is greater when the macroeconomic factors of GDP, inflation, and short-term interest rates are more volatile or when inflation is high and output growth is low. Volatility is higher not only for emerging markets and markets with small numbers of listed companies and market capitalization relative to GDP, but also for large economies. The model allows long horizon forecasts of volatility to depend on macroeconomic developments, and delivers estimates of the volatility to be anticipated in a newly opened market.