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The purpose of this study is to suggest a new framework that we call the CIR#, which allows forecasting interest rates from observed financial market data even when rates are negative. In doing so, we have the objective is to maintain the market volatility structure as well as the analytical tractability of the original CIR model.

The novelty of the proposed methodology consists in using the CIR model to forecast the evolution of interest rates by an appropriate partitioning of the data sample and calibration. The latter is performed by replacing the standard Brownian motion process in the random term of the model with normally distributed standardized residuals of the “optimal” autoregressive integrated moving average (ARIMA) model.

The suggested model is quite powerful for the following reasons. First, the historical market data sample is partitioned into sub-groups to capture all the statistically significant changes of variance in the interest rates. An appropriate translation of market rates to positive values was included in the procedure to overcome the issue of negative/near-to-zero values. Second, this study has introduced a new way of calibrating the CIR model parameters to each sub-group partitioning the actual historical data. The standard Brownian motion process in the random part of the model is replaced with normally distributed standardized residuals of the “optimal” ARIMA model suitably chosen for each sub-group. As a result, exact CIR fitted values to the observed market data are calculated and the computational cost of the numerical procedure is considerably reduced. Third, this work shows that the CIR model is efficient and able to follow very closely the structure of market interest rates (especially for short maturities that, notoriously, are very difficult to handle) and to predict future interest rates better than the original CIR model. As a measure of goodness of fit, this study obtained high values of the statistics R² and small values of the root of the mean square error for each sub-group and the entire data sample.

A limitation is related to the specific dataset as we are examining the period around the 2008 financial crisis for about 5 years and by using monthly data. Future research will show the predictive power of the model by extending the dataset in terms of frequency and size.

Improved ability to model/forecast interest rates.

The original value consists in turning the CIR from modeling instantaneous spot rates to forecasting any rate of the yield curve.

The purpose of this paper is to compare the ability of popular temperature models, namely, the models given by Alaton et al., by Benth and Benth, by Campbell and Diebold and by Brody et al., to forecast the prices of heating/cooling degree days (HDD/CDD) futures for New York, Atlanta, and Chicago.

To verify the forecasting power of various temperature models, a statistical backtesting approach is utilised. The backtesting sample consists of the market data of daily settlement futures prices for New York, Atlanta, and Chicago. Settlement prices are separated into two groups, namely, “in‐period” and “out‐of‐period”.

The findings show that the models of Alaton et al. and Benth and Benth forecast the futures prices more accurately. The difference in the forecasting performance of models between “in‐period” and “out‐of‐period” valuation can be attributed to the meteorological temperature forecasts during the contract measurement periods.

In future studies, it may be useful to utilize the historical data for meteorological forecasts to assess the forecasting power of the new hybrid model considered.

Out‐of‐period backtesting helps reduce the effect of any meteorological forecast on the formation of futures prices. It is observed that the performance of models for out‐of‐period improves consistently. This indicates that the effects of available weather forecasts should be incorporated into the considered models.

To the best of the author's knowledge this is the first study to compare some of the popular temperature models in forecasting HDD/CDD futures. Furthermore, a new temperature modelling approach is proposed for incorporating available temperature forecasts into the considered dynamic models.

It is shown that if one assumes, as a consequence of biological cycles and cultural background, that human systems are subject to random time different from the standard physical time, then one comes across dynamical systems which are necessarily of fractal nature. Two illustrative examples are outlined: mathematical finance and prey‐predator systems.

Three kinds of observations are usually used in the modelling of general systems: Gallilean observation, observation with informational invariance and scaling observation. All these models presuppose the invariance of the dimension of the system under consideration. The purpose of the present paper is to examine what happens when the observation process increases this dimension. A 1‐D co‐ordinate switches to a 2‐D co‐ordinate. Complex‐valued random variables are used to describe this approach. Prospects of applications are outlined.

This purpose of this paper is to find the approximate analytical solutions of a multidimensional partial differential equation such as Helmholtz equation with space fractional derivatives α,β,γ (1<α,β,γ≤2). The fractional derivatives are described in the Caputo sense.

By using initial values, the explicit solutions of the equation are solved with powerful mathematical tools such as He's homotopy perturbation method (HPM).

This result reveals that the HPM demonstrates the effectiveness, validity, potentiality and reliability of the method in reality and gives the exact solution.

The most important part of this method is to introduce a homotopy parameter (p), which takes values from [0,1]. When p=0, the equation usually reduces to a sufficiently initial form, which normally admits a rather simple solution. When p→1, the system goes through a sequence of deformations, the solution for each of which is close to that at the previous stage of deformation. Here, we also discuss the approximate analytical solution of multidimensional fractional Helmholtz equation.

The purpose of this paper is to present a proportional-integral (PI) observer design on a linear system with stochastic noises.

The noised disturbances are modeled as independent Brownian motions for various affections, such as radiation, heat, and material fatigue. These phenomena are common in applications, such as biomolecules, nonlinear control, and biochemical networks. Under this framework, this paper proposes a new approach on a PI observer in terms of four crucial theorems, and an illustrative numerical example is given to verify the proposed design.

The results provide potential solutions for system fault tolerance and isolation.

This paper proposes a design, solvability, and controllability analysis on a PI observer in terms of four crucial theorems.

The purpose of this paper is to introduce a continuous time version of the speculative storage model of Deaton and Laroque (1992) and to use for pricing derivatives, in particular insurances on agricultural prices.

The methodology of financial engineering is used in order to find the partial differential equations that the dynamics of derivative prices have to satisfy. Furthermore, by using the Monte-Carlo method (and Feynman-Kac theorem) the insurance prices is computed.

Results of this paper show that insurance prices (and derivative prices in general) are heavily influenced by market structure, in particular, the demand function specifications. Furthermore, through an empirical analysis, the performance of the continuous time speculative storage model is compared with the geometric Brownian motion model. It is shown that the speculative storage model outperforms the actual data.

Since the agricultural insurances in many countries are subsidised by government, the results of this paper can be used by policy makers to measure changes in agricultural insurance premiums in scenarios that market experiences changes in demand. In the same manner, insurance companies and investors can use the results of this paper to better price agricultural derivatives.

The issue of agricultural insurance pricing (in general derivative pricing) is of great concern to policy makers, investors and insurance companies. To the author’s knowledge, an approach which uses the methodology of financial engineering to compute the insurance prices (in general derivatives) is new within the literature.

Academic and industrial researches on nanoscale flows and heat transfers are an area of increasing global interest, where fascinating phenomena are always observed, e.g. admirable water or air permeation and remarkable thermal conductivity. The purpose of this paper is to reveal the phenomena by the fractional calculus.

This paper begins with the continuum assumption in conventional theories, and then the fractional Gauss’ divergence theorems are used to derive fractional differential equations in fractal media. Fractional derivatives are introduced heuristically by the variational iteration method, and fractal derivatives are explained geometrically. Some effective analytical approaches to fractional differential equations, e.g. the variational iteration method, the homotopy perturbation method and the fractional complex transform, are outlined and the main solution processes are given.

Heat conduction in silk cocoon and ground water flow are modeled by the local fractional calculus, the solutions can explain well experimental observations.

Particular attention is paid throughout the paper to giving an intuitive grasp for fractional calculus. Most cited references are within last five years, catching the most frontier of the research. Some ideas on this review paper are first appeared.

The purpose of this paper is to develop a new method based on operational matrices of Bernoulli wavelet for solving linear stochastic Itô-Volterra integral equations, numerically.

For this aim, Bernoulli polynomials and Bernoulli wavelet are introduced, and their properties are expressed. Then, the operational matrix and the stochastic operational matrix of integration based on Bernoulli wavelet are calculated for the first time.

By applying these matrices, the main problem would be transformed into a linear system of algebraic equations which can be solved by using a suitable numerical method. Also, a few results related to error estimate and convergence analysis of the proposed scheme are investigated.

Two numerical examples are included to demonstrate the accuracy and efficiency of the proposed method. All of the numerical calculation is performed on a personal computer by running some codes written in MATLAB software.

The purpose of this paper is to test the efficient market hypothesis for major Indian sectoral indices by means of long memory approach in both time domain and frequency domain. This paper also tests the accuracy of the detrended fluctuation analysis (DFA) approach and the local Whittle (LW) approach by means of Monte Carlo simulation experiments.

The author applies the DFA approach for the computation of the scaling exponent in the time domain. The robustness of the results is tested by the computation of the scaling exponent in the frequency domain by means of the LW estimator. The author applies moving sub-sample approach on DFA to study the evolution of market efficiency in Indian sectoral indices.

The Monte Carlo simulation experiments indicate that the DFA approach and the LW approach provides good estimates of the scaling exponent as the sample size increases. The author also finds that the efficiency characteristics of Indian sectoral indices and their stages of development are dynamic in nature.

This paper has both methodological and empirical originality. On the methodological side, the author tests the small sample properties of the DFA and the LW approaches by using simulated series of fractional Gaussian noise and find that both the approach possesses superior properties in terms of capturing the scaling behavior of asset prices. On the empirical side, the author studies the evolution of long-range dependence characteristics in Indian sectoral indices.