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 analyze low frequency volatility in financial markets and its macroeconomic determinants. The model combines macroeconomic factors with time series dynamics to explain equity volatility. High frequency volatility is modeled as the product of a slow-moving component, represented by an exponential spline, and a unit GARCH. This slow-moving component, which coincides with the unconditional volatility, is estimated for nearly 50 countries over various sample periods of daily data. Low frequency volatility is modeled as a function of macroeconomic and financial variables in an unbalanced panel with various dependence structures. It is found to vary over time and across countries. The low frequency component of 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. Volatility is higher for emerging markets and for markets with small numbers of listed companies and market capitalization relative to GDP, but also for large economies. The Spline-GARCH 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. The model relaxes the assumption that volatility is mean-reverting to a constant level, which underlies almost all GARCH and SV models estimated over the last 25 years. The paper introduces the Spline-GARCH model to link high frequency financial data with low frequency macro data, enabling forecasts of the effect of potential macroeconomic events on equity volatility and volatility in a new market. The model is applied to explain financial volatility in nearly 50 markets over time. The model is estimated using time series of returns in a global context and shows that low frequency volatility is influenced by macroeconomic variables such as GDP, inflation, and short-term interest rates. The results suggest that emerging markets and markets with small numbers of listed companies and market capitalization relative to GDP have higher volatility, but also large economies. The model also shows that volatility is higher for markets with more persistent macroeconomic shocks. The paper concludes that the Spline-GARCH model provides a more flexible and accurate way to model volatility and its macroeconomic determinants.This paper proposes a new model, the Spline-GARCH, to analyze low frequency volatility in financial markets and its macroeconomic determinants. The model combines macroeconomic factors with time series dynamics to explain equity volatility. High frequency volatility is modeled as the product of a slow-moving component, represented by an exponential spline, and a unit GARCH. This slow-moving component, which coincides with the unconditional volatility, is estimated for nearly 50 countries over various sample periods of daily data. Low frequency volatility is modeled as a function of macroeconomic and financial variables in an unbalanced panel with various dependence structures. It is found to vary over time and across countries. The low frequency component of 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. Volatility is higher for emerging markets and for markets with small numbers of listed companies and market capitalization relative to GDP, but also for large economies. The Spline-GARCH 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. The model relaxes the assumption that volatility is mean-reverting to a constant level, which underlies almost all GARCH and SV models estimated over the last 25 years. The paper introduces the Spline-GARCH model to link high frequency financial data with low frequency macro data, enabling forecasts of the effect of potential macroeconomic events on equity volatility and volatility in a new market. The model is applied to explain financial volatility in nearly 50 markets over time. The model is estimated using time series of returns in a global context and shows that low frequency volatility is influenced by macroeconomic variables such as GDP, inflation, and short-term interest rates. The results suggest that emerging markets and markets with small numbers of listed companies and market capitalization relative to GDP have higher volatility, but also large economies. The model also shows that volatility is higher for markets with more persistent macroeconomic shocks. The paper concludes that the Spline-GARCH model provides a more flexible and accurate way to model volatility and its macroeconomic determinants.
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Understanding The Spline-Garch Model for Low Frequency Volatility and its Global Macroeconomic Causes