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I am currently modelling financial time series via ARMA processes, but I have reason to believe that in addition to significant autocorrelation, the time series also exhibit skewness. Is there a way to estimate them jointly?

I am aware of Simulation of Non-normal Autocorrelated Variables, but it only talks about how to combine AR and MA models to achieve a desired skew and kurtosis. There is also this paper Looking for skewness in financial time series analyzing time series to show that they exhibit time-varying conditional skewness instead of unconditional skewness.

There is also this paper Time series models based on the unrestricted skew-normal process, which models skew innovations.

Does a general approach for modelling skewness with ARMA models exist that I am overlooking here? Do heuristics exist?

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Conceptually, if you want constant conditional skewness, you could simply choose an error distribution that is skewed for your ARMA model. ARMA only restricts the conditional mean of the time series to vary in a certain way, but all the other parameters such as skewness or kurtosis can be chosen freely.

In practice, you need a way to estimate such a model. If I needed to do this myself, I would use the rugarch package in R. It has a wide variety of distributions, including multiple skewed ones, to be used in AR(FI)MA-GARCH models. ARMA is a restricted version of ARFIMA-GARCH, and vis made feasible in rugarch. You can specify and fit an ARMA model with unconditional skenwness by using functions arfimaspec and arfimafit, respectively.

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