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The purpose of this paper is to report on a sequential three-stage analysis of inflation persistence using monthly data from 11 inflation targeting (IT) countries and, for comparison, the USA, a non-IT country with a history of credible monetary policy.

First, the authors estimate inflation persistence in a rolling-window fractional-integration setting using the semiparametric estimator suggested by Phillips (2007). Second, the authors use tests for unknown structural breaks as a means to identify effects of the regime switch and the global financial crisis on inflation persistence. The authors use the sequences of estimated persistence measures from the first stage as dependent variables in the Bai and Perron (2003) structural break tests. Finally, the authors reapply the Phillips (2007) estimator to the subsamples defined by the breaks.

Four countries (Canada, Iceland, Mexico, and South Korea) experience a structural break in inflation persistence that coincide with the implementation of the IT regime, and three IT countries (Sweden, Switzerland, and the UK), as well as the USA experience a structural break in inflation persistence that coincides with the global financial crisis.

The authors find that in most cases the estimates of inflation persistence switch from mean-reversion nonstationarity to mean-reversion stationarity.

Monetary policy implications differ between pre- and post-global financial crisis.

Global financial crisis affected the persistence of inflation rates.

First paper to consider the effect of the global financial crisis on inflation persistence.

This paper's aim is to test for the presence of fractional integration, or long memory, in the daily returns of the Portuguese stock market using autoregressive fractionally integrated moving average (ARFIMA), generalised autoregressive conditional heteroskedasticity (GARCH) and ARFIMA‐FIGARCH models.

The data cover two periods: 4 January 1993‐13 January 2006 (full sample), and 1 February 2002‐13 January 2006 (that is, data are considered after the merger of the Portuguese Stock Exchange with Euronext).

The results from the full sample show strong evidence of long memory in stock returns. When data after the merger are considered, weaker evidence of long memory is found. It is concluded that the Portuguese stock market is more efficient after the merger with Euronext.

The findings of this paper are helpful to financial managers and investors dealing with Portuguese stock indices.

Recently, a new formulation has been introduced for non-local mechanics in terms of fractional calculus. Fractional calculus is a branch of mathematical analysis that studies the differential operators of an arbitrary (real or complex) order and is used successfully in various fields such as mathematics, science and engineering. The purpose of this paper is to introduce a new fractional non-local theory which may be applicable in various simple or complex mechanical problems.

In this paper (by using fractional calculus), a fractional non-local theory based on the conformable fractional derivative (CFD) definition is presented, which is a generalized form of the Eringen non-local theory (ENT). The theory contains two free parameters: the fractional parameter which controls the stress gradient order in the constitutive relation and could be an integer and a non-integer and the non-local parameter to consider the small-scale effect in the micron and the sub-micron scales. The non-linear governing equation is solved by the Galerkin and the parameter expansion methods. The non-linearity of the governing equation is due to the presence of von-Kármán non-linearity and CFD definition.

The theory has been used to study linear and non-linear free vibration of the simply-supported (S-S) and the clamped-free (C-F) nano beams and then the influence of the fractional and the non-local parameters has been shown on the linear and non-linear frequency ratio.

A new parameter of the theory (the fractional parameter) makes the modeling more fixable – this model can conclude all of integer and non-integer operators and is not limited to special operators such as ENT. In other words, it allows us to use more sophisticated mathematics to model physical phenomena. On the other hand, in the comparison of classic fractional non-local theory, the theory applicable in various simple or complex mechanical problems may be used because of simpler forms of the governing equation owing to the use of CFD definition.

The purpose of this paper is to introduce a new class of fractional positive continuous‐time and discrete‐time linear systems.

Solutions to the state equations of the fractional systems are given.

Necessary and sufficient conditions are established for the internal and external positivity and of the reachability and controllability to zero of the fractional systems.

A method for analysis of the fractional positive linear systems is proposed.

This paper aims to apply fractional variational iteration method using He's polynomials (FVIMHP) to obtain exact solutions for variable-coefficient fractional heat-like and wave-like equations with fractional order initial and boundary conditions.

The approach is based on FVIMHP. The authors choose as some examples to illustrate the validity and the advantages of the method.

The results reveal that the FVIMHP method provides a very effective, convenient and powerful mathematical tool for solving fractional differential equations.

The variable-coefficient fractional heat-like and wave-like equations with fractional order initial and boundary conditions are solved first. Illustrative examples are included to demonstrate the validity and applicability of the method.

The purpose of this paper is to introduce a new class of positive two‐dimensional (2D) fractional linear systems.

A notion (concept) of order 2D difference is proposed and the solution to the state equations is given.

The classical Cayley‐Hamilton theorem is extended to the positive 2D fractional linear systems. Necessary and sufficient conditions for the positivity of 2D fractional linear systems, reachability and controllability to zero are established.

A method for analysis of positive 2D fractional linear systems is proposed.

In this article, the authors aim to present the homotopy analysis method (HAM) for obtaining the approximate solutions of space‐time fractional differential equations with initial conditions.

The series solution is developed and the recurrence relations are given explicitly. The initial approximation can be determined by imposing the initial conditions.

The comparison of the HAM results with the exact solutions is made; the results reveal that the HAM is very effective and simple. The HAM contains the auxiliary parameter h, which provides a simple way to adjust and control the convergence region of series solution. Numerical examples demonstrate the effect of changing homotopy auxiliary parameter h on the convergence of the approximate solution. Also, they illustrate the effect of the fractional derivative orders a and b on the solution behavior.

The idea can be used to find the numerical solutions of other fractional differential equations.

The purpose of this paper is to obtain a numerical scheme for finding numerical solutions of linear and nonlinear fractional differential equations involving ψ-Caputo derivative.

An operational matrix to find numerical approximation of ψ-fractional differential equations (FDEs) is derived. This study extends the method to nonlinear FDEs by using quasi linearization technique to linearize the nonlinear problems.

The error analysis of the proposed method is discussed in-depth. Accuracy and efficiency of the method are verified through numerical examples.

The method is simple and a good mathematical tool for finding solutions of nonlinear ψ-FDEs. The operational matrix approach offers less computational complexity.

Engineers and applied scientists may use the present method for solving fractional models appearing in applications.

The purpose of this paper is to focus on whether the deviations from the cointegrating relationship possess long memory and the fractional cointegration analyses may capture a wider range of mean-reversion behaviour than standard cointegration analyses.

This paper uses a fractional cointegration technique to test the purchasing power parity (PPP).

The authors found that PPP held, but very weakly, in the long run between the Argentine, Brazil, Chile, Colombia, Indonesia, Korea, Mexico, Thailand and Venezuela and US exchange rate during our floating exchange rate period but that the deviations from it did not follow a stationary process. Nevertheless, it is also found that the deviations from PPP exists and can be characterized by a fractionally integrated process in nine out of 13 countries studied.

The findings are consistent with the consensus of the empirical literature, reviewed earlier in this paper, on PPP between Argentine, Brazil, Chile, Colombia, Indonesia, Korea, Mexico, Thailand and Venezuela and the USA.

The purpose of this paper is to examine the existence of rational speculative bubbles in the Middle East and North African (MENA) stock markets.

To complement shortcomings of the traditional bubble tests, such as unit root tests and cointegration tests, mainly relying on expectations of future steams of dividends, the authors employ fractional integration tests and duration dependence tests.

Despite recent extreme fluctuations of MENA stock markets, fractional integration tests built on autoregressive fractionally integrated moving average models do not support the possibility of bubbles in the MENA stock markets. Similarly, duration dependence tests based on nonparametric Nelson‐Aalen hazard functions not only reject the existence of bubbles but also support equality of hazard functions between domestic and the US‐based investors without regard to the rapid financial liberalization and integration in the MENA stock markets.

The reliable results of bubble tests of the MENA stock markets provide domestic and international investors as well as policy makers with invaluable benchmark to better understand the irregular and highly fluctuating stock market behaviors of the MENA stock markets compared to other developed and emerging stock markets. For domestic and international investors, the formal analysis of MENA stock markets behavior including rational speculative bubbles will help them in their portfolio decisions and hedging purposes. Similarly, the empirical results of bubble tests in the paper will be also helpful to policymakers in MENA countries to take actions to improve the functioning of these dynamic markets.