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V-Lab

S&P 500 Index Zero Slope Spline-GARCH Volatility Analysis

Volatility prediction for Friday, July 31st, 2026

1 Day

15.74%

increased by 1.80%

1 Week

15.86%

increased by 1.92%

1 Month

16.25%

increased by 2.31%

Analysis last updated: Friday, July 31, 2026 at 12:22 AM UTC

Date Range:

from

to

6M ·

1Y ·

2Y ·

5Y ·

10Y ·

All

graph of S&P 500 Index S0GARCH

News Impact Curve

How returns affect tomorrow's volatility

Volatility Forecast

How volatility evolves over time

Parameter Estimates

Jan 1, 1990 to Jul 24, 2026

Model 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

Zero Slope Spline-GARCH Model

Tap to view equation

ParameterValuet-statistic
ω

const

Unconditional variance weight

1.3569
7.70***
α

ARCH

Response to squared shocks

0.1019
10.24***
β

GARCH

Volatility persistence

0.8662
74.47***
γi Spline Coefficients
K=6
γ10.0857
6.48***
γ2-0.1359
-6.33***
γ30.0779
4.88***
γ4-0.0488
-3.42***
γ50.0425
2.62***
γ6-0.0311
-2.47**

Persistence:

0.968

Half-life:

21 days