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CPS1297 Chin W.C. et al.

High frequency value-at-risk analysis: An
empirical study for IPC Mexican Index
1
2
Chin Wen Cheong , Liu ChengZhi , Jing ShengZhe & Ye ZhiQing 2
2
1 Department of Mathematics, Xiamen University Malaysia
2 School of Economics and Management, Xiamen University Malaysia

Abstract
This study investigates the dynamic volatility movements and market risk of
the high frequency Mexican IPC (Indice de Precios y Cotizaciones) index. Based
on the heterogeneous market hypothesis framework, the high frequency 5-
minute interval data have been utilized to examine the return and volatility of
IPC index. Using high frequency realized volatility and bi-power volatility
estimators in the heterogeneous autoregressive model, the IPC Mexican
market is found to be in concordance with the investment structure suggested
by the heterogeneous market hypothesis. Besides various volatility estimators,
the heterogeneous autoregressive model is improved with the enhancement
of autoregressive conditional heteroscedasticity effect in order to capture the
volatility of the realized volatility. In order to obtain a better forecast, the
combination forecasts have been applied using various averaging methods
and the forecast evaluations are examined using various forecast loss
functions. Finally, the forecasted results are utilized in determining the
Mexican IPC stock market risk via the value-at-risk based on normal and
heavy-tailed distributions.

Keywords
Heterogeneous market hypothesis; high frequency volatility; value at risk

1. Introduction
Over the last couple of decades, the efficient market hypothesis (Fama,
1998; Malkiel, 2003) in term of market information, has been rigorously
investigated using the financial markets data which include closed daily and
high-frequency data. Based on the traditional efficient market hypothesis
(EMH), new proposed hypotheses such as the heterogeneous market
hypothesis (HMH) has been introduced to complement the EMH. The relevant
studies for HMH are commonly conducted using high-frequency data which
normally included 1-minute or 5-minute interval data. This hypothesis
suggested that the financial markets consist of market participants with
various duration of investment strategies. The results of combining various
investment time horizons have generated the ‘seemingly’ like long-range

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