S&P Total Market Index Zero Slope Spline-GARCH Volatility Analysis
Volatility prediction for Friday, October 23rd, 2026
1 Day
13.83%
increased by 1.20%
1 Week
14.24%
increased by 1.61%
1 Month
15.48%
increased by 2.85%
Analysis last updated: Thursday, October 22, 2026 at 11:08 PM UTC
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News Impact Curve
How returns affect tomorrow's volatilityVolatility Forecast
How volatility evolves over timeParameter Estimates
Mar 30, 2006 to Oct 16, 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
Zero Slope Spline-GARCH Model
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Time-varying baseline: volatility reverts to a slowly-shifting spline trend
| Param | Value | t-stat |
|---|---|---|
| ωconst | 0.9004 | 5.82*** |
| αARCH | 0.1302 | 8.86*** |
| βGARCH | 0.8358 | 49.88*** |
Spline Coefficients
K=3
| γ1 | -0.0258 | -2.20** |
| γ2 | 0.0472 | 2.67*** |
| γ3 | -0.0294 | -3.00*** |
0.966
Persistence20d
Half-lifeτ
Zero Slope Spline-GARCH Model
Tap to view equation
| Parameter | Value | t-statistic |
|---|---|---|
ω const Unconditional variance weight | 0.9004 | 5.82*** |
α ARCH Response to squared shocks | 0.1302 | 8.86*** |
β GARCH Volatility persistence | 0.8358 | 49.88*** |
Spline Coefficients
K=3
| γ1 | -0.0258 | -2.20** |
| γ2 | 0.0472 | 2.67*** |
| γ3 | -0.0294 | -3.00*** |
Persistence:
0.966
Half-life:
20 days
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