Empirical prediction intervals are constructed based on the distribution of previous out-of-sample forecast errors. Given historical data, a sample of such forecast errors is generated by successively applying a chosen point forecasting model to a sequence of fixed windows of past observations...

In this article, we investigated the multifractality and its underlying formation mechanisms in international crude oil markets, namely, Brent and WTI, which are the most important oil pricing benchmarks globally. We attempt to find the answers to the following questions: (1) Are those different...

There is a well-developed framework, the Black–Scholes theory, for the pricing of contracts based on the future prices of certain assets, called options. This theory assumes that the probability distribution of the returns of the underlying asset is a Gaussian distribution. However, it is...

One of the important issues in finance and economics for both scholars and practitioners is to describe the behavior of markets, especially during times of crises. In this paper, we analyze the behavior of some mature and emerging markets with a Tsallis entropy framework that is a non-extensive...

The Multifractal Embedded Branching Process (MEBP) process and Canonical Embedded Branching Process (CEBP) process were introduced by Decrouez and Jones (2012). The CEBP is a process in which the crossings of dyadic intervals constitute a branching process. An MEBP process is defined as a...

Electronic Cardiogram (ECG) data taken from healthy adult subjects are found to characterize multifractality. In order to quantitatively analyze multifractal spectrum, the area of the spectrum is computed. We have a comparison between the spectrum of the young subjects and that of the old ones....

A time series can be decomposed into two sub-series: a magnitude series and a sign series. Here we analyze separately the scaling properties of the magnitude series and the sign series using the increment time series of cardiac interbeat intervals as an example. We find that time series having...

This paper proposes the generalized use of fractional Brownian motion in a multifractal trading time framework to reveal variation in the index price diffusion process that appears before and after 'extreme' events of distinct origin. "Crashes" following internal self-organization and those...

We consider a self-similar phase space with specific fractal dimension d being distributed with spectrum function f(d). Related thermostatistics is shown to be governed by the Tsallis formalism of the non-extensive statistics, where the non-additivity parameter equals to τ̄(q)≡1/τ(q)1, and...