V-Lab
ProShares UltraPro S&P 500 Zero Slope Spline-GARCH Volatility Analysis
Volatility prediction for Monday, September 14th, 2026
1 Day
36.68%
increased by 1.45%
1 Week
38.33%
increased by 3.10%
1 Month
42.42%
increased by 7.19%
Analysis last updated: Saturday, September 12, 2026 at 12:01 AM UTC
News Impact Curve
How returns affect tomorrow's volatilityVolatility Forecast
How volatility evolves over timeParameter Estimates
Jun 25, 2009 to Sep 11, 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 11 trading days.
τ
Zero Slope Spline-GARCH Model
Tap to view equation
Time-varying baseline: volatility reverts to a slowly-shifting spline trend
| Param | Value | t-stat |
|---|---|---|
| ωconst | 1.1588 | 4.54*** |
| αARCH | 0.1489 | 7.16*** |
| βGARCH | 0.7876 | 29.41*** |
Spline Coefficients
K=8
| γ1 | -0.0670 | -0.40 |
| γ2 | 0.3269 | 1.15 |
| γ3 | -0.6690 | -1.73* |
| γ4 | 0.7440 | 1.71* |
| γ5 | -0.4043 | -1.25 |
| γ6 | 0.0196 | 0.09 |
| γ7 | 0.0700 | 0.44 |
| γ8 | -0.0217 | -0.20 |
0.936
Persistence11d
Half-lifeτ
Zero Slope Spline-GARCH Model
Tap to view equation
| Parameter | Value | t-statistic |
|---|---|---|
ω const Unconditional variance weight | 1.1588 | 4.54*** |
α ARCH Response to squared shocks | 0.1489 | 7.16*** |
β GARCH Volatility persistence | 0.7876 | 29.41*** |
Spline Coefficients
K=8
| γ1 | -0.0670 | -0.40 |
| γ2 | 0.3269 | 1.15 |
| γ3 | -0.6690 | -1.73* |
| γ4 | 0.7440 | 1.71* |
| γ5 | -0.4043 | -1.25 |
| γ6 | 0.0196 | 0.09 |
| γ7 | 0.0700 | 0.44 |
| γ8 | -0.0217 | -0.20 |
Persistence:
0.936
Half-life:
11 days
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