V-Lab
S&P 500 Growth Index Spline-GARCH Volatility Analysis
Volatility prediction for Thursday, September 10th, 2026
1 Day
15.15%
decreased by 0.43%
1 Week
15.66%
increased by 0.08%
1 Month
17.23%
increased by 1.65%
Analysis last updated: Wednesday, September 9, 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 Sep 4, 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
Spline-GARCH Model
Tap to view equation
Time-varying baseline: volatility reverts to a slowly-shifting spline trend
| Param | Value | t-stat |
|---|---|---|
| ωconst | 0.7885 | 4.97*** |
| αARCH | 0.1027 | 10.27*** |
| βGARCH | 0.8645 | 72.22*** |
Spline Coefficients
K=7
| γ1 | 0.0974 | 3.39*** |
| γ2 | -0.2066 | -5.06*** |
| γ3 | 0.1908 | 7.50*** |
| γ4 | -0.1374 | -5.54*** |
| γ5 | 0.0917 | 3.09*** |
| γ6 | -0.0349 | -1.13 |
| γ7 | -0.0114 | -0.27 |
0.967
Persistence21d
Half-lifeτ
Spline-GARCH Model
Tap to view equation
| Parameter | Value | t-statistic |
|---|---|---|
ω const Unconditional variance weight | 0.7885 | 4.97*** |
α ARCH Response to squared shocks | 0.1027 | 10.27*** |
β GARCH Volatility persistence | 0.8645 | 72.22*** |
Spline Coefficients
K=7
| γ1 | 0.0974 | 3.39*** |
| γ2 | -0.2066 | -5.06*** |
| γ3 | 0.1908 | 7.50*** |
| γ4 | -0.1374 | -5.54*** |
| γ5 | 0.0917 | 3.09*** |
| γ6 | -0.0349 | -1.13 |
| γ7 | -0.0114 | -0.27 |
Persistence:
0.967
Half-life:
21 days
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