Principle of Parsimony in Econometric Modeling

About

A fundamental principle in statistical and econometric modeling that advocates for concise model specification and objects to overparameterization.

Parsimony (Merriam-Webster):

1. The quality of being careful with money or resources
2. The quality or state of being stingy

In econometric modeling, parsimony means:

• Use the simplest model that adequately captures the data-generating process
• Avoid including unnecessary parameters
• Prefer models with fewer parameters when they fit equally well

The Problem with ARCH Models

ARCH(m) models require estimating many parameters to fully capture higher-order autoregressive relationships in $a_t^2$. An ARCH(m) model has $m+1$ parameters (${\alpha }_0,{\alpha }_1,...,{\alpha }_m$).

For example, if you need an ARCH(5) to capture the volatility dynamics, that’s 6 parameters just for the volatility equation—quite a lot!

The GARCH Solution

This is exactly why GARCH models were developed. A high-order ARCH model may have a more parsimonious GARCH representation:

• A GARCH(1,1) with only 3 parameters can often replace a high-order ARCH(m)
• This is analogous to how an ARMA(1,1) can replace a high-order AR process

Related

• ARCH(m) Model
• GARCH(m,s) Model