In this paper, instead of the usual Gaussian noise assumption, t-distribution noise is assumed. AMaximum Likelihood Estimator using the most recent N measurements is proposed for the Auto-Regressive-Moving-Average with eXogenous input (ARMAX) process with this assumption. The proposed estimator is robust to outliers because the ‘thick tail’ of the t-distribution reduces the effect of large erro...

1. BASIC PROBABILITY THEORY 1.1 Measure-theoretical foundation of probability theory 1.2 Independence 1.3 Borel measurable functions 1.4 Mathematical expectatlon 1.5 Characteristic functions 1.6 Random functions 2. CONVERGENCE 2.1 Heak and strong convergence of random variables 2.2 Convergence of mathematical expectations 2.3 Convergence of distributions 2.4 Central limit theoreras 2.5 Further ...

This paper investigates the relationship between Bitcoin returns and frequency of daily abnormal over period from June 2013 to February 2020 using a number regression techniques model specifications including standard OLS, weighted least squares (WLS), ARMA ARMAX models, quantile regressions, Logit Probit piecewise linear non-linear regressions. Both in sample out-of-sample performance various ...