V-Lab
ProShares UltraPro S&P 500 Zero Slope Spline-GARCH Volatility Analysis
Volatility prediction for Monday, July 27th, 2026
1 Day
38.79%
decreased by 2.58%
1 Week
40.25%
decreased by 1.12%
1 Month
43.95%
increased by 2.58%
Analysis last updated: Friday, July 24, 2026 at 10:53 PM UTC
News Impact Curve
How returns affect tomorrow's volatilityVolatility Forecast
How volatility evolves over timeParameter Estimates
Jun 25, 2009 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 11 trading days.
τ
Zero Slope Spline-GARCH Model
Tap to view equation
| Parameter | Value | t-statistic |
|---|---|---|
ω const Unconditional variance weight | 1.1543 | 4.45*** |
α ARCH Response to squared shocks | 0.1492 | 7.16*** |
β GARCH Volatility persistence | 0.7887 | 29.79*** |
Spline Coefficients
K=8
| γ1 | -0.0784 | -0.44 |
| γ2 | 0.3527 | 1.13 |
| γ3 | -0.6928 | -1.66* |
| γ4 | 0.7477 | 1.63 |
| γ5 | -0.3856 | -1.13 |
| γ6 | 0.0004 | 0.00 |
| γ7 | 0.0801 | 0.47 |
| γ8 | -0.0292 | -0.24 |
Persistence:
0.938
Half-life:
11 days
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