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V-Lab
V-Lab

S&P 500 Growth Index Spline-GARCH Volatility Analysis

Volatility prediction for Thursday, September 10th, 2026

1 Day

15.15%

decreased by 0.43%

1 Week

15.66%

increased by 0.08%

1 Month

17.23%

increased by 1.65%

Analysis last updated: Wednesday, September 9, 2026 at 11:06 PM UTC

Date Range:

from

to

6M ·

1Y ·

2Y ·

5Y ·

10Y ·

All

graph of S&P 500 Growth Index SGARCH

News Impact Curve

How returns affect tomorrow's volatility

Volatility Forecast

How volatility evolves over time

Parameter Estimates

Oct 29, 1992 to Sep 4, 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

Spline-GARCH Model

Tap to view equation

Time-varying baseline: volatility reverts to a slowly-shifting spline trend
ParamValuet-stat
ωconst0.7885
4.97***
αARCH0.1027
10.27***
βGARCH0.8645
72.22***
γi Spline Coefficients
K=7
γ10.0974
3.39***
γ2-0.2066
-5.06***
γ30.1908
7.50***
γ4-0.1374
-5.54***
γ50.0917
3.09***
γ6-0.0349
-1.13
γ7-0.0114
-0.27

0.967

Persistence

21d

Half-life
τ

Spline-GARCH Model

Tap to view equation

ParameterValuet-statistic
ω

const

Unconditional variance weight

0.7885
4.97***
α

ARCH

Response to squared shocks

0.1027
10.27***
β

GARCH

Volatility persistence

0.8645
72.22***
γi Spline Coefficients
K=7
γ10.0974
3.39***
γ2-0.2066
-5.06***
γ30.1908
7.50***
γ4-0.1374
-5.54***
γ50.0917
3.09***
γ6-0.0349
-1.13
γ7-0.0114
-0.27

Persistence:

0.967

Half-life:

21 days