Title: Estimation of ARMA models with $t$-distributed innovations
Authors: Haruhisa Nishino - Hiroshima University (Japan) [presenting]
Abstract: The standard ARMA model assumes that its innovations are white noise processes with 0 mean and a constant variance. That is, the ARMA model is a second-order stationary process characterized by its autocovariance function. The white noise process has no information about its fourth-order moment. In general, assuming a Gaussian process and a Gaussian likelihood enables us to estimate the ARMA model. On the other hand, the literature of financial time series tells us that the financial returns have fatter tails than Gaussian ones. The student $t$-distribution is a typical example of fat-tailed distributions. The fat-tailed property is related to the fourth-order moment. We thus consider that estimation for ARMA models with $t$-distributed innovations, which is useful for analyzing financial time series. If we know degrees of freedom of the $t$-distribution of the model, is it possible to estimate the parameters of the ARMA model more efficiently than the Gaussian likelihood? Also, the talk proposes a preliminary estimate for degrees of freedom based on the method of moments, since estimating degrees of freedom of $t$-distribution by MLE causes a severe problem.