S&P 500 Index Spline-GARCH Volatility Analysis
Volatility prediction for Tuesday, July 21st, 2026
1 Day
11.56%
decreased by 0.48%
1 Week
11.81%
decreased by 0.23%
1 Month
12.57%
increased by 0.53%
Analysis last updated: Tuesday, July 21, 2026 at 12:21 AM UTC
News Impact Curve
How returns affect tomorrow's volatilityVolatility Forecast
How volatility evolves over timeParameter Estimates
Jan 1, 1990 to Jul 17, 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 20 trading days.
τ
Spline-GARCH Model
Tap to view equation
| Parameter | Value | t-statistic |
|---|---|---|
ω const Unconditional variance weight | 1.3627 | 7.92*** |
α ARCH Response to squared shocks | 0.1016 | 10.12*** |
β GARCH Volatility persistence | 0.8650 | 72.90*** |
Spline Coefficients
K=6
| γ1 | 0.0884 | 6.81*** |
| γ2 | -0.1404 | -6.68*** |
| γ3 | 0.0821 | 5.25*** |
| γ4 | -0.0549 | -3.83*** |
| γ5 | 0.0543 | 2.94*** |
| γ6 | -0.0591 | -2.01** |
Persistence:
0.967
Half-life:
20 days
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