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 forecasting with GARCH is done with the following formula:

\[\sigma_{l} ^{2} + (\sigma_{t} ^{2} - \sigma_{l} ^{2}) \cdot (\alpha + \beta) ^{t - 1}\]

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.

No programming experience? With the Finance Toolkit MCP server, AI assistants such as Claude and ChatGPT can calculate the GARCH Volatility Forecast for you. Just ask in plain English.

Calculate the GARCH Volatility Forecast in Python

The GARCH Volatility Forecast is available in the Risk module of the open-source Finance Toolkit. Install it with:

pip install financetoolkit -U

Then call get_garch_forecast as shown below.

from financetoolkit import Toolkit

toolkit = Toolkit(["AMZN", "TSLA"], api_key="FINANCIAL_MODELING_PREP_KEY")

toolkit.risk.get_garch_forecast(period="quarterly")

Which returns:

  AMZN TSLA Benchmark
2026Q4 0.0267 0.1703 0.0053
2027Q1 0.0267 0.1703 0.0053
2027Q2 0.0267 0.1738 0.0056
2027Q3 0.0267 0.1745 0.0058
2027Q4 0.0266 0.1747 0.006
2028Q1 0.0266 0.1747 0.0062
2028Q2 0.0266 0.1747 0.0063
2028Q3 0.0266 0.1747 0.0064
2028Q4 0.0266 0.1747 0.0065
2029Q1 0.0266 0.1747 0.0066

Parameters

get_garch_forecast accepts the following parameters:

  • period (str, optional): The data frequency for returns (daily, weekly, monthly, quarterly, or yearly). Defaults to “quarterly” if the Toolkit is initialised with quarterly=True, otherwise “yearly”.
  • time_steps (int, optional): Time steps to calculate GARCH and to forecast sigma_2 values for.
  • within_period (bool, optional): 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.
  • rounding (int | None, optional): The number of decimals to round the results to. Defaults to None.
  • growth (bool, optional): Whether to calculate the growth of the GARCH values over time. Defaults to False.
  • lag (int | list[int], optional): The lag to use for the growth calculation. Defaults to 1.
  • standardize (bool, optional): Whether to standardize (Z-Score) the result. When combined with growth=True, standardizes the growth values instead of the raw values. Defaults to False.
Tail Ratio Maximum Drawdown (MDD) Maximum Drawdown Duration Maximum Drawdown Recovery Time Ulcer Index (UI) GARCH Volatility Model Variance Volatility Excess Volatility Downside Deviation Skewness Kurtosis

The Risk module page introduces the module, and the sidebar lists all of its functions.

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