22,040 research outputs found
Long-memory recursive prediction error method for identification of continuous-time fractional models
This paper deals with recursive continuous-time system identification using fractional-order models. Long-memory recursive prediction error method is proposed for recursive estimation of all parameters of fractional-order models. When differentiation orders are assumed known, least squares and prediction error methods, being direct extensions to fractional-order models of the classic methods used for integer-order models, are compared to our new method, the long-memory recursive prediction error method. Given the long-memory property of fractional models, Monte Carlo simulations prove the efficiency of our proposed algorithm. Then, when the differentiation orders are unknown, two-stage algorithms are necessary for both parameter and differentiation-order estimation. The performances of the new proposed recursive algorithm are studied through Monte Carlo simulations. Finally, the proposed algorithm is validated on a biological example where heat transfers in lungs are modeled by using thermal two-port network formalism with fractional models
Long Run And Cyclical Dynamics In The Us Stock Market
This paper examines the long-run dynamics and the cyclical structure of the US stock market using fractional integration techniques. We implement a version of the tests of Robinson (1994a), which enables one to consider unit roots with possibly fractional orders of integration both at the zero (long-run) and the cyclical frequencies. We examine the following series: inflation, real risk-free rate, real stock returns, equity premium and price/dividend ratio, annually from 1871 to 1993. When focusing exclusively on the long-run or zero frequency, the estimated order of integration varies considerably, but nonstationarity is found only for the price/dividend ratio. When the cyclical component is also taken into account, the series appear to be stationary but to exhibit long memory with respect to both components in almost all cases. The exception is the price/dividend ratio, whose order of integration is higher than 0.5 but smaller than 1 for the long-run frequency, and is between 0 and 0.5 for the cyclical component. Also, mean reversion occurs in all cases. Finally, we use six different criteria to compare the forecasting performance of the fractional (at both zero and cyclical frequencies) models with others based on fractional and integer differentiation only at the zero frequency. The results show that the former outperform the others in a number of cases
Non-asymptotic fractional order differentiators via an algebraic parametric method
Recently, Mboup, Join and Fliess [27], [28] introduced non-asymptotic integer
order differentiators by using an algebraic parametric estimation method [7],
[8]. In this paper, in order to obtain non-asymptotic fractional order
differentiators we apply this algebraic parametric method to truncated
expansions of fractional Taylor series based on the Jumarie's modified
Riemann-Liouville derivative [14]. Exact and simple formulae for these
differentiators are given where a sliding integration window of a noisy signal
involving Jacobi polynomials is used without complex mathematical deduction.
The efficiency and the stability with respect to corrupting noises of the
proposed fractional order differentiators are shown in numerical simulations
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Modelling long-run trends and cycles in financial time series data
Copyright @ 2012 Wiley Publishing Ltd. This is the accepted version of the following article: "Modelling long-run trends and cycles in financial time series data", Journal of Time Series Analysis, 34(3), 405-421, 2013, which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1111/jtsa.12010/abstract.This article proposes a general time series framework to capture the long-run behaviour of financial series. The suggested approach includes linear and segmented time trends, and stationary and non-stationary processes based on integer and/or fractional degrees of differentiation. Moreover, the spectrum is allowed to contain more than a single pole or singularity, occurring at both zero but non-zero (cyclical) frequencies. This framework is used to analyse five annual time series with a long span, namely dividends, earnings, interest rates, stock prices and long-term government bond yields. The results based on several likelihood criteria indicate that the five series exhibit fractional integration with one or two poles in the spectrum, and are quite stable over the sample period examined.Ministerio de Ciencia y Tecnologia and Jeronimo de Ayanz project of the Government of Navarra
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Testing the Marshall-Lerner condition in Kenya
In this paper we examine the Marshall-Lerner (ML) condition for the Kenyan economy. In particular, we use quarterly data on the log of real exchange rates, export-import ratio and relative (US) income for the time period 1996q1 â 2011q4, and employ techniques based on the concept of long memory or long-range dependence. Specifically, we use fractional integration and cointegration methods, which are more general than standard approaches based exclusively on integer degrees of differentiation. The results indicate that there exists a well-defined cointegrating relationship linking the balance of payments to the real exchange rate and relative income, and that the ML condition is satisfied in the long run although the convergence process is relatively slow. They also imply that a moderate depreciation of the Kenyan shilling may have a stabilizing influence on the balance of payments through the current account without the need for high interest rates.This study is partly funded by the Ministry of Education of Spain (ECO2011-2014 ECON Y FINANZAS, Spain) and from a Jeronimo de Ayanz project of the Government of Navarra
Optimal control of a fractional order epidemic model with application to human respiratory syncytial virus infection
A human respiratory syncytial virus surveillance system was implemented in
Florida in 1999, to support clinical decision-making for prophylaxis of
premature newborns. Recently, a local periodic SEIRS mathematical model was
proposed in [Stat. Optim. Inf. Comput. 6 (2018), no.1, 139--149] to describe
real data collected by Florida's system. In contrast, here we propose a
non-local fractional (non-integer) order model. A fractional optimal control
problem is then formulated and solved, having treatment as the control.
Finally, a cost-effectiveness analysis is carried out to evaluate the cost and
the effectiveness of proposed control measures during the intervention period,
showing the superiority of obtained results with respect to previous ones.Comment: This is a preprint of a paper whose final and definite form is with
'Chaos, Solitons & Fractals', available from
[http://www.elsevier.com/locate/issn/09600779]. Submitted 23-July-2018;
Revised 14-Oct-2018; Accepted 15-Oct-2018. arXiv admin note: substantial text
overlap with arXiv:1801.0963
Fractional order differentiation by integration with Jacobi polynomials
The differentiation by integration method with Jacobi polynomials was
originally introduced by Mboup, Join and Fliess. This paper generalizes this
method from the integer order to the fractional order for estimating the
fractional order derivatives of noisy signals. The proposed fractional order
differentiator is deduced from the Jacobi orthogonal polynomial filter and the
Riemann-Liouville fractional order derivative definition. Exact and simple
formula for this differentiator is given where an integral formula involving
Jacobi polynomials and the noisy signal is used without complex mathematical
deduction. Hence, it can be used both for continuous-time and discrete-time
models. The comparison between our differentiator and the recently introduced
digital fractional order Savitzky-Golay differentiator is given in numerical
simulations so as to show its accuracy and robustness with respect to
corrupting noises
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