Optimal Multi-Step-Ahead Prediction of ARCH/GARCH Models and NoVaS Transformation

• Main Authors: Jie Chen, Dimitris N. Politis
• Format: Article
• Language: English
• Published: MDPI AG 2019-08-01
• Series: Econometrics
• Subjects: bootstrap; <i>L</i>₁ and <i>L</i>₂ measures; GARCH(1,1); NoVaS transformation; multi-step prediction; Monte Carlo simulation
• Online Access: https://www.mdpi.com/2225-1146/7/3/34
• ISSN: 2225-1146

This paper gives a computer-intensive approach to multi-step-ahead prediction of volatility in financial returns series under an ARCH/GARCH model and also under a model-free setting, namely employing the NoVaS transformation. Our model-based approach only assumes <inline-formula> <math display="inline"> <semantics> <mrow> <mi>i</mi> <mo>.</mo> <mi>i</mi> <mo>.</mo> <mi>d</mi> </mrow> </semantics> </math> </inline-formula> innovations without requiring knowledge/assumption of the error distribution and is computationally straightforward. The model-free approach is formally quite similar, albeit a GARCH model is not assumed. We conducted a number of simulations to show that the proposed approach works well for both point prediction (under <inline-formula> <math display="inline"> <semantics> <msub> <mi>L</mi> <mn>1</mn> </msub> </semantics> </math> </inline-formula> and/or <inline-formula> <math display="inline"> <semantics> <msub> <mi>L</mi> <mn>2</mn> </msub> </semantics> </math> </inline-formula> measures) and prediction intervals that were constructed using bootstrapping. The performance of GARCH models and the model-free approach for multi-step ahead prediction was also compared under different data generating processes.