Sentence examples for orders of integration from inspiring English sources

Fractional calculus is the subject of studying fractional integrals and fractional derivatives, which means that the orders of integration and differentiation are not integers but non-integers, and even complex numbers.

Two methodologies, following the two orders of integration, lead to different governing equations for the statistical quantities.

To this end, we apply the widely-used ADF and PP unit root tests for establishing the variables' orders of integration.

As ARDL can be applied irrespective of the order of integration (Pesaran et al. 2001), Granger causality tests are applicable irrespective of the orders of integration of the underlying variables if it has been established that there exists a long-run equilibrium relationship between the underlying series (Groenewold and Tang 2007).

The order of integration is important, because variables with different orders of integration pose problems in setting the cointegration relationship.

Fubini theorems giving conditions for change of the order of integration in multiple integrals are useful in all forms of calculus.

Our new tests are wild bootstrap implementations of score-based tests for the order of integration of a fractionally integrated time series.

The convolution theorem is a good example of this – it makes use of switching the order of integration in a double integral.

(3.4) Multiplying both sides of (3.4) by (e^{frac{-x^{2}}{ 4gamma}}), we integrate the results with respect to x from 0 to ∞, and make a change of order of integration in the repeated integral.

This paper presents a simple and efficient method for the design of recursive digital fractional order integrator when the order of integration is a real number between 0 and 1.

The choice of the order of integration (D, d) parameters is based on the plot of integrated time series and based on comparison of their standard deviation; the series having the more stabilized mean is selected.