GARCH Volatility Forecast

Calculates sigma_2 forecasts.

GARCH (Generalized autoregressive conditional heteroskedasticity) is stochastic model for time series, which is for instance used to model volatility clusters, stock return and inflation. It is a generalisation of the ARCH models.

The formula is as follows:

\[\sigma_{n + h} ^{2} = \sigma_{L} ^{2} + (\sigma_{n + 1} ^{2} - \sigma_{L} ^{2}) \cdot (\text{Alpha} + \text{Beta}) ^{h - 1}\] \[\sigma_{L} ^{2} = \text{Omega} / (1 - \text{Alpha} - \text{Beta})\]

Where n is the last observation, h = 1, …, time_steps (10 by default) the forecast step, sigma_(n+1)^2 the one-step-ahead variance of the fitted GARCH(1, 1) recursion (see get_garch) and sigma_L^2 the long-run variance.

For more information about the method, see the following book:

Finance Compact Plus Band 1, by Yvonne Seler Zimmerman and Heinz Zimmerman; ISBN: 978-3-907291-31-1

Also known as: volatility forecast, predicted volatility.

GARCH Volatility Forecast in Python or via the MCP

Install the Finance Toolkit with:

pip install financetoolkit -U

Then call get_garch_forecast as shown below.

from financetoolkit import Toolkit

toolkit = Toolkit(
    ["^GSPC"],
    api_key="FINANCIAL_MODELING_PREP_KEY",
    start_date="2021-01-01",
    end_date="2025-12-31",
)

toolkit.risk.get_garch_forecast()

Or, after setting up the Finance Toolkit MCP, ask:

What variance does a GARCH(1,1) model of the S&P 500, fitted on its returns from 2021 to 2025, forecast for the first ten trading days of 2026?

Which returns:

	^GSPC	Benchmark
2026-01-01	0.0001	0
2026-01-02	0.0001	0.0001
2026-01-05	0.0001	0.0001
2026-01-06	0.0001	0.0001
2026-01-07	0.0001	0.0001
2026-01-08	0.0001	0.0001
2026-01-09	0.0001	0.0001
2026-01-12	0.0001	0.0001
2026-01-13	0.0001	0.0001
2026-01-14	0.0001	0.0001

Parameters

get_garch_forecast accepts the following parameters.

Parameter	Type	Description	Example
`period`	`str`	The data frequency for returns (daily, weekly, monthly, quarterly, or yearly). Defaults to “daily”.	`"weekly"`
`time_steps`	`int`	Time steps to calculate GARCH and to forecast sigma_2 values for. Defaults to 10.	`20`
`within_period`	`bool`	Whether to calculate GARCH within each specified period or all at once. Thus whether to look at the GARCH within each specific year (if period = ‘yearly’) or look at the entirety of all years. Defaults to False.	`True`
`rounding`	`int \| None`	The number of decimals to round the results to. Defaults to None.	`2`
`growth`	`bool`	Whether to calculate the growth of the GARCH values over time. Defaults to False.	`True`
`lag`	`int \| list[int]`	The lag to use for the growth calculation. Defaults to 1.	`4`
`standardize`	`bool`	Whether to standardize (Z-Score) the result. When combined with growth=True, standardizes the growth values instead of the raw values. Defaults to False.	`True`

GARCH Volatility Forecast in Python or via the MCP

Parameters

Related Volatility Models