The sum of squared intraday returns provides an unbiased and almost error-free measure of ex-post volatility. In this paper we develop a nonlinear Autoregressive Fractionally Integrated Moving Average (ARFIMA) model for realized volatility, which accommodates level shifts, day-of-the-week...

We simulate a simplified version of the price process including bubbles and crashes proposed in Kreuser and Sornette (2018). The price process is defined as a geometric random walk combined with jumps modelled by separate, discrete distributions associated with positive (and negative) bubbles....

We show that the presence of short-term overreaction in a stock price could make estimates of the conditional moments of stock returns be strongly affected by the frequency of time series. This conclusion implies that the other measures of stock returns, such as the conditional Sharpe ratio, its...

In this study, we examine bootstrap methods to construct a generalized KPSS test for functional time series. Bootstrap-based functional testing provides an intuitive and efficient estimation of the distribution of the generalized KPSS test statistic and is capable of achieving non-trivial powers...

Representation of continuous-time ARMA, CARMA, models is reviewed. Computational aspects of simulating and calculating the likelihood-function of CARMA are summarized. Some numerical properties are illustrated by simulations. Some real data applications are shown. -- CARMA ; maximum-likelihood ;...

Representation of continuous-time ARMA, CARMA, models is reviewed. Computational aspects of simulating and calculating the likelihood-function of CARMA are summarized. Some numerical properties are illustrated by simulations. Some real data applications are shown.

Infra-monthly economic time series have become increasingly popular in official statistics in recent years. This evolution has been largely fostered by official statistics’ digital transformation during the last decade. The COVID-19 pandemic outbreak in 2020 has added fuel to the fire as many...

This paper studies the behaviour of crypto-currencies financial time-series of which Bitcoin is the most prominent example. The dynamic of those series is quite complex displaying extreme observations, asymmetries and several nonlinear characteristics which are difficult to model. We develop a...