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V-Lab

S&P 500 Index Spline-GARCH Volatility Analysis

Volatility prediction for Tuesday, July 21st, 2026

1 Day

11.56%

decreased by 0.48%

1 Week

11.81%

decreased by 0.23%

1 Month

12.57%

increased by 0.53%

Analysis last updated: Tuesday, July 21, 2026 at 12:21 AM UTC

Date Range:

from

to

6M ·

1Y ·

2Y ·

5Y ·

10Y ·

All

graph of S&P 500 Index SGARCH

News Impact Curve

How returns affect tomorrow's volatility

Volatility Forecast

How volatility evolves over time

Parameter Estimates

Jan 1, 1990 to Jul 17, 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 20 trading days.

τ

Spline-GARCH Model

Tap to view equation

ParameterValuet-statistic
ω

const

Unconditional variance weight

1.3627
7.92***
α

ARCH

Response to squared shocks

0.1016
10.12***
β

GARCH

Volatility persistence

0.8650
72.90***
γi Spline Coefficients
K=6
γ10.0884
6.81***
γ2-0.1404
-6.68***
γ30.0821
5.25***
γ4-0.0549
-3.83***
γ50.0543
2.94***
γ6-0.0591
-2.01**

Persistence:

0.967

Half-life:

20 days