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# GARCH Model

#### What is a GARCH Model?

The Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model is an econometric term that describes an approach to estimate volatility in financial markets. The method was developed by Danish economist Tim Bollerslev in 1986.

The goal of GARCH is to provide volatility measures for heteroscedastic time series data, by considering the previous periods’ error terms. Heteroskedasticity is a term that describes an irregular variation pattern in an error term or variable.

Mathematically, GARCH models consider an autoregressive moving average model (ARMA) for the error variance:

y_{t} = x^{’}_{t}b + ε_{t}

ε_{t}|ψ_{t-s} ~ N(0,σ_{t}^{2})

σ_{t}^{2} = ω + α_{1}ε_{t-1}^{2} + … + α_{q}ε_{t-q}^{2} + β_{1}σ_{t-1}^{2} + … + β_{p}σ_{t-p}^{2}

where

ε: error term

α, β: coefficients

σ: variance

q: order of ARCH terms.

p: order of GARCH term.

In general, a GARCH model creation requires three steps:

- Estimate the best fit autoregressive (AR) model.
- Calculate the autocorrelations of the error term.
- Test for statistical significance.

These three steps are usually done with the aid of software.

#### Why are GARCH Models Important?

GARCH models aim to minimize errors by considering the errors in previous predictions. Thus, because they are autoregressive, they depend on past squared observations and past variances to calculate current variances. As a result, they provide more realistic results than other models.

Due to their higher accuracy, they are widely used in finance to predict prices and rates of financial instruments – such as bonds, market indices, and stocks – particularly during periods of high volatility.

#### GARCH Models + LogicPlum

Finding the most accurate GARCH model may require long and complex calculations. LogicPlum’s platform solves this problem through automation. This feature permits its users to estimate and compare hundreds of different possibilities in a short time and without the need for human intervention.

This is particularly useful in finance, as it frees financial analysts from having to learn mathematics and software programming at expert levels. As a result, analysts need only to concentrate on what matters to them, which is reading the markets.

##### Additional Resources

For those interested in Bollerslev’s paper:

Bollerslev, T. *Generalized autoregressive conditional heteroskedasticity*. Journal of Econometrics 31 (1986) 307-327. North-Holland. Available at https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.468.2892