A first econometric analysis of the CRIX family

TL;DR

This paper conducts the first econometric analysis of the CRIX index family, modeling their dynamics with ARIMA and GARCH processes to understand volatility and interactions for pricing financial claims.

Contribution

It introduces a novel econometric framework applying ARIMA and GARCH models to the CRIX indices, capturing volatility clustering and fat-tail features.

Findings

ARIMA(2,0,2) model fits the data well

Volatility clustering observed in residuals

Multivariate GARCH models reveal index interactions

Abstract

In order to price contingent claims one needs to first understand the dynamics of these indices. Here we provide a first econometric analysis of the CRIX family within a time-series framework. The key steps of our analysis include model selection, estimation and testing. Linear dependence is removed by an ARIMA model, the diagnostic checking resulted in an ARIMA(2,0,2) model for the available sample period from Aug 1st, 2014 to April 6th, 2016. The model residuals showed the well known phenomenon of volatility clustering. Therefore a further refinement lead us to an ARIMA(2,0,2)-t-GARCH(1,1) process. This specification conveniently takes care of fat-tail properties that are typical for financial markets. The multivariate GARCH models are implemented on the CRIX index family to explore the interaction.