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

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

December 7, 2006 | Robert F. Engle, Jose Gonzalo Rangel
This paper proposes a new model, the Spline-GARCH, to capture the relationship between macroeconomic factors and equity volatility. The model combines high-frequency return volatility, which is specified as a product of a slow-moving component (low-frequency volatility) and a unit GARCH process, with low-frequency volatility modeled as a function of macroeconomic and financial variables. The study estimates the low-frequency volatility for nearly 50 countries over various sample periods of daily data and finds that it varies over time and across countries. The low-frequency volatility is greater when macroeconomic factors such as GDP, inflation, and short-term interest rates are more volatile, or when inflation is high and output growth is low. The model also allows for long-horizon forecasts of volatility, which depend on macroeconomic developments, and provides estimates of the volatility expected in a newly opened market. The paper relaxes the assumption that volatility reverts to a constant level, a common assumption in GARCH and SV models, by allowing the low-frequency volatility to vary over time. The empirical analysis covers developed and emerging markets, and the results are robust to different specifications and data proxies.This paper proposes a new model, the Spline-GARCH, to capture the relationship between macroeconomic factors and equity volatility. The model combines high-frequency return volatility, which is specified as a product of a slow-moving component (low-frequency volatility) and a unit GARCH process, with low-frequency volatility modeled as a function of macroeconomic and financial variables. The study estimates the low-frequency volatility for nearly 50 countries over various sample periods of daily data and finds that it varies over time and across countries. The low-frequency volatility is greater when macroeconomic factors such as GDP, inflation, and short-term interest rates are more volatile, or when inflation is high and output growth is low. The model also allows for long-horizon forecasts of volatility, which depend on macroeconomic developments, and provides estimates of the volatility expected in a newly opened market. The paper relaxes the assumption that volatility reverts to a constant level, a common assumption in GARCH and SV models, by allowing the low-frequency volatility to vary over time. The empirical analysis covers developed and emerging markets, and the results are robust to different specifications and data proxies.
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