---
title: "Generalized AutoRegressive Conditional Heteroscedasticity (GARCH(1,1)) Value At Risk"
method: POST
path: "/portfolios/analysis/value-at-risk/forecast/arma-garch"
tags: ["Portfolio Analysis / Risk Measures / Value At Risk Forecast"]
---

# Generalized AutoRegressive Conditional Heteroscedasticity (GARCH(1,1)) Value At Risk

`POST /portfolios/analysis/value-at-risk/forecast/arma-garch`

Forecast the value at risk of a portfolio, assuming the portfolio logarithmic returns follow a Generalized AutoRegressive Heteroscedasticity (GARCH(1,1)) conditional variance model, coupled with an AutoRegressive Moving Average (ARMA(1,1)) conditional mean model.

References
* [Christoph Hartz, Stefan Mittnik, Marc Paolella, Accurate value-at-risk forecasting based on the normal-GARCH model, Computational Statistics & Data Analysis, Volume 51, Issue 4, 2006, Pages 2295-2312](https://www.sciencedirect.com/science/article/abs/pii/S0167947306003367)
* [Bollerslev, Tim, 1987. A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return, The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-547](https://www.jstor.org/stable/1925546)

## Request body

- object
  - `confidenceLevel` number — The confidence level
  - `portfolios` object[], required
    - `portfolioValues` number[], required — portfolioValues[t] is the value of the portfolio at the time t
    - `portfolioReturnsConditionalMeanModel` 'zeroMean' | 'constantMean' | 'ar1Mean' | 'arma11Mean' — The conditional mean model for the portfolio logarithmic returns
    - `portfolioReturnsStandardizedResidualsDistribution` 'normal' | 'student' — The assumed distribution for the portfolio logarithmic returns standardized residuals

## Response `200`

OK

- object
  - `portfolios` object[], required
    - `portfolioValueAtRisk` number, required — The empirical value at risk of the portfolio, in (logarithmic return) percentage
    - `portfolioArithmeticValueAtRisk` number, required — The empirical value at risk of the portfolio, converted from logarithmic return percentage to arithmetic return percentage

---

[API](https://skmtc.net/portfoliooptimizer/apis/portfolio-optimizer.md) · [All operations](https://skmtc.net/portfoliooptimizer/apis/portfolio-optimizer/llms.txt) · [OpenAPI document](https://skmtc-service-staging.skmtc.workers.dev/v1/apis/portfoliooptimizer/portfolio-optimizer/versions/479fd4ac44aa/schema)