Title: Estimation for 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 characterised by its autocovariance function. The white noise process has no information about its fourth-order moment. To estimate the ARMA model, we assume a Gaussian process and a Gaussian likelihood. On the other hand, the literature of financial time series tells that the financial returns have fatter tails than Gaussian ones. The Student $t$-distribution is a typical fat-tailed distribution. The fat-tailed property is related to the fourth order moment. We thus consider that the estimation for ARMA models with $t$-distributed innovations is useful for analysing financial time series. If we know the degrees of freedom of the $t$-distribution of the model, can we estimate the parameters of the ARMA model more efficiently than the Gaussian likelihood? Besides, the talk proposes a preliminary estimate for the degrees of freedom based on the method of moments, since the application of MLE for the degrees of freedom has a severe problem.