# Modelling Skew when using ARMA Time Series

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?

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.