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The code you posted is wrong since you do not model the time series behavior of the up/down process (ie if you have 10 up move and consequently 10 down move it is not the same as the opposite ie 10 down and after 10 up..). I would recommend you to use standards Arma Garch models apply on returns instead of modeling the process of up/down. These are (at ...


HF data have a lot of auto correlation so common models to deal with this problems are ARFIMA, FIGARCH, Fractional Integrated GARCH. Engle recently propose the multiplicative components GARCH for high frequency data, which can include a mean model like and ARMA. In this post they explain how to implement it in R with the rugarch package, it takes some time ...

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