V-Lab
S&P 500 Growth Index Zero Slope Spline-GARCH Volatility Analysis
Volatility prediction for Friday, July 31st, 2026
1 Day
24.63%
increased by 4.91%
1 Week
24.46%
increased by 4.74%
1 Month
23.87%
increased by 4.15%
Analysis last updated: Thursday, July 30, 2026 at 11:06 PM UTC
News Impact Curve
How returns affect tomorrow's volatilityVolatility Forecast
How volatility evolves over timeParameter Estimates
Oct 29, 1992 to Jul 24, 2026Model Insight
This model fits a time-varying baseline (a spline), so volatility mean-reverts toward a slowly-shifting long-run level rather than a constant. Short-run deviations decay with a half-life of 21 trading days.
τ
Zero Slope Spline-GARCH Model
Tap to view equation
| Parameter | Value | t-statistic |
|---|---|---|
ω const Unconditional variance weight | 0.7793 | 4.89*** |
α ARCH Response to squared shocks | 0.1024 | 10.24*** |
β GARCH Volatility persistence | 0.8651 | 72.35*** |
Spline Coefficients
K=7
| γ1 | 0.0949 | 3.26*** |
| γ2 | -0.2026 | -4.89*** |
| γ3 | 0.1876 | 7.31*** |
| γ4 | -0.1331 | -5.30*** |
| γ5 | 0.0861 | 2.93*** |
| γ6 | -0.0289 | -1.02 |
| γ7 | -0.0164 | -0.83 |
Persistence:
0.967
Half-life:
21 days
Other S&P 500 Growth Index Analyses
Other Zero Slope Spline-GARCH Analyses on Equity Indices