V-Lab
S&P 500 Index Zero Slope Spline-GARCH Volatility Analysis
Volatility prediction for Friday, July 31st, 2026
1 Day
15.74%
increased by 1.80%
1 Week
15.86%
increased by 1.92%
1 Month
16.25%
increased by 2.31%
Analysis last updated: Friday, July 31, 2026 at 12:22 AM UTC
News Impact Curve
How returns affect tomorrow's volatilityVolatility Forecast
How volatility evolves over timeParameter Estimates
Jan 1, 1990 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 | 1.3569 | 7.70*** |
α ARCH Response to squared shocks | 0.1019 | 10.24*** |
β GARCH Volatility persistence | 0.8662 | 74.47*** |
Spline Coefficients
K=6
| γ1 | 0.0857 | 6.48*** |
| γ2 | -0.1359 | -6.33*** |
| γ3 | 0.0779 | 4.88*** |
| γ4 | -0.0488 | -3.42*** |
| γ5 | 0.0425 | 2.62*** |
| γ6 | -0.0311 | -2.47** |
Persistence:
0.968
Half-life:
21 days
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