Testing GARCH and RV Exchange Rate Volatility Models using Hinich Tricorrelations

Abstract

The aim of this paper is to enlighten a need to test the two most popular volatility models: the
GARCH-ARMA model, based on a daily returns and the RV and the ARMA model, based on 30
min intraday high frequency (HF) data, in terms of non Gaussian Time Series Analysis. The
ability of the models to perform a digital whitening and to produce independent innovations is
tested on seven foreign exchange rates (FX) including Jpy/Eur, Usd/Eur, Cad/Usd, Chf/Eur,
Chf/Usd, Usd/Gbp and Gbp/Eur, taken from Bloomberg. In the first step, stationary ARMAGARCH
models of different orders were built and the best model was chosen by using AIC and
Box-Pierce test based on the innovations of daily squared returns. In the second step, realized
daily volatilities (RV), defined as the sum of intraday squared 30 min returns, are used to
estimate the RV-ARMA volatility model parameter and to calculate forecasting errors. In the
third step, the higher order cumulants (HOC) are calculated for 20 lags for all currencies and
used to perform the Hinich test. Finally, it was not shown that whitening of squared returns,
neither by using GARCH-ARMA nor by using RV ARMA model, is efficient. The finding of
serial dependence in innovations signifies the presence of structure in the data that cannot be
modeled by ARCH or GARCH or RV volatility models that assume a pure noise input. A further
improvement is suggested in the stage of parameter estimation by using Higher Order Cumulant
function , prior to the model testing based on Hinich test.