Search results

A time-varying grey Fourier model (TVGFM(1,1,N)) is proposed for the simulation of variable amplitude seasonal fluctuation time series, as the performance of traditional grey models can't catch the time-varying trend well.

The proposed model couples Fourier series and linear time-varying terms as the grey action, to describe the characteristics of variable amplitude and seasonality. The truncated Fourier order N is preselected from the alternative order set by Nyquist-Shannon sampling theorem and the principle of simplicity, then the optimal Fourier order is determined by hold-out method to improve the robustness of the proposed model. Initial value correction and the multiple transformation are also studied to improve the precision.

The new model has a broader applicability range as a result of the new grey action, attaining higher fitting and forecasting accuracy. The numerical experiment of a generated monthly time series indicates the proposed model can accurately fit the variable amplitude seasonal sequence, in which the mean absolute percentage error (MAPE) is only 0.01%, and the complex simulations based on Monte-Carlo method testify the validity of the proposed model. The results of monthly electricity consumption in China's primary industry, demonstrate the proposed model catches the time-varying trend and has good performances, where MAPE_F and MAPE_T are below 5%. Moreover, the proposed TVGFM(1,1,N) model is superior to the benchmark models, grey polynomial model (GMP(1,1,N)), grey Fourier model (GFM(1,1,N)), seasonal grey model (SGM(1,1)), seasonal ARIMA model seasonal autoregressive integrated moving average model (SARIMA) and support vector regression (SVR).

The parameter estimates and forecasting of the new proposed TVGFM are studied, and the good fitting and forecasting accuracy of time-varying amplitude seasonal fluctuation series are testified by numerical simulations and a case study.

The specific objective of the study is to investigate the presence of natural rate of crime rates in selected emerging economies by using panel unit roots. The majority of the literature examines the issue using conventional unit root tests in a country-specific context. Meanwhile, there is no panel unit root investigation has been undertaken considering both cross-sectional dependence (CD) and structural changes.

As a result, this study is to fill the aforementioned gap and validate the natural rate of crime rates for 10 countries by using a Fourier panel unit root test. The advantage of the test is that structural shifts are modelled as gradual or smooth changes with a Fourier approximation, and it also accounts cross-sectional dependency. Thus, the Fourier panel unit root test may have better performance in capturing potential changes in the nature of data.

The result of the conventional unit roots test shows evidence of the hysteresis effect in crime, as it stands does not adequately account for smooth transitions or breaks. On contrary, the Fourier panel unit root test confirms the natural rate hypothesis in crime rates. The present results highlight the detrimental effects of crime cannot be abated by short-run deterrence policies.

Contrary to previous studies, the theoretical implications of the study imply that the empirical models consider the dynamic nature of crime rates should account for natural rate properties instead of the hysteresis assumption.

In this paper, the authors take the first step in the study of constructive methods by using Sobolev polynomials.

To do that, the authors use the connection formulas between Sobolev polynomials and classical Laguerre polynomials, as well as the well-known Fourier coefficients for these latter.

Then, the authors compute explicit formulas for the Fourier coefficients of some families of Laguerre–Sobolev type orthogonal polynomials over a finite interval. The authors also describe an oscillatory region in each case as a reasonable choice for approximation purposes.

In order to take the first step in the study of constructive methods by using Sobolev polynomials, this paper deals with Fourier coefficients for certain families of polynomials orthogonal with respect to the Sobolev type inner product. As far as the authors know, this particular problem has not been addressed in the existing literature.

This investigation aims to determine the effect of trade uncertainty on domestic investment (DI) and foreign direct investment (FDI) for the Turkish economy from the first quarter of 2005 to the first quarter of 2020.

The authors adopt the vector autoregression (VAR) model augmented with Fourier terms. Using this methodology, the authors obtain the empirical results of the impulse-response functions and the variance decomposition analysis.

The empirical results demonstrate that a shock to trade uncertainty has a slight negative impact on DI for up to approximately 1.5 years, whereas its impact on FDI is negative but long-lasting. Moreover, the contribution of trade uncertainty to FDI is relatively higher than to DI in the error variance decomposition for the investigated period. These empirical results can be beneficial for shaping the Turkish authorities' trade policies in the following periods.

These findings have implications within the macroeconomic setting. Government authorities can provide tax exemptions for specified sectors and debureaucratize investment processes for both domestic and foreign entrepreneurs. Additionally, institutional quality and property rights should be protected strictly and developed gradually.

This study is the first to examine the impact of world trade uncertainty on Türkiye’s DI and FDI. Because trade uncertainty might act as fixed costs, this creates the option value of waiting and seeing the market, and firms hesitate to incur investment.

The purpose of this paper is to solve the local problem involving strong contrast heterogeneous conductive material, with application to gas-filled porous media with both perfect and imperfect Kapitza boundary conditions at the bi-material interface. The effective parameters like the dynamic conductivity and the thermal permeability in the acoustics of porous media are also derived from the cell solution.

The Fourier transform method is used to solve frequency-dependent heat transfer problems. The periodic Lippmann–Schwinger integral equation in Fourier space with source term is first formulated using discrete Green operators and modified wavevectors, which can then be solved by iteration schemes.

Numerical examples show that the schemes converge fast and yield accurate results when compared with analytical solution for benchmark problems.

The formulation of the method is constructed using static and dynamic Green operators and can be applied to pixelized microstructure issued from tomography images.

In order to achieve sustainable development objectives, safeguard the ecosystem, combat global warming and preserve biodiversity for a more sustainable and secure future, the ecological footprint (EF) must be reduced. Therefore, embracing holistic methods, emphasizing renewable energy (RN) and environmental taxes (ET) is crucial. Therefore, the present study aims to capture the effect of ET and RN on EF in Germany.

To achieve this aim, the novel Fourier-based Autoregressive Distributive Lag (ADL) cointegration and the time and frequency-based connections among the variables are investigated in this work throughout the 1994–2021 time span using the wavelet analytic methods, including wavelet power spectrum (WPS) and wavelet coherence (WC) methods, respectively.

The study’s results express that (1) RN, ET and EF are cointegrated in the long run; (2) EF and RN have volatility; (3) RN use in Germany prevents environmental deterioration and (4) ET decreases EF.

The research findings imply that Germany needs rigorous environmental restrictions and enforcement of alternate energy sources for energy use plans and sustainable production objectives.

To the best of our knowledge, the effect of RN and ET on EF in Germany has not been comprehensively explored by using newly developed econometrics techniques and a single dataset. Therefore, the study provides important policy implementations for the German government and is also likely to open debate on the concept.

The author develops and extends the asymptotic F- and t-test theory in linear regression models where the regressors could be deterministic trends, unit-root processes, near-unit-root processes, among others. The author considers both the exogenous case where the regressors and the regression error are independent and the endogenous case where they are correlated. In the former case, the author designs a new set of basis functions that are invariant to the parameter estimation uncertainty and uses them to construct a new series long-run variance estimator. The author shows that the F-test version of the Wald statistic and the t-statistic are asymptotically F and t distributed, respectively. In the latter case, the author shows that the asymptotic F and t theory is still possible, but one has to develop it in a pseudo-frequency domain. The F and t approximations are more accurate than the more commonly used chi-squared and normal approximations. The resulting F and t tests are also easy to implement – they can be implemented in exactly the same way as the F and t tests in a classical normal linear regression.

The purpose of this paper is to exploit a new and robust method to forecast the long-term extreme dynamic responses for wave energy converters (WECs).

A new adaptive binned kernel density estimation (KDE) methodology is first proposed in this paper.

By examining the calculation results the authors has found that in the tail region the proposed new adaptive binned KDE distribution curve becomes very smooth and fits quite well with the histogram of the measured ocean wave dataset at the National Data Buoy Center (NDBC) station 46,059. Carefully studying the calculation results also reveals that the 50-year extreme power-take-off heaving force value forecasted based on the environmental contour derived using the new method is 3572600N, which is much larger than the value 2709100N forecasted via the Rosenblatt-inverse second-order reliability method (ISORM) contour method.

The proposed method overcomes the disadvantages of all the existing nonparametric and parametric methods for predicting the tail region probability density values of the sea state parameters.

It is concluded that the proposed new adaptive binned KDE method is robust and can forecast well the 50-year extreme dynamic responses for WECs.

The purpose of this study is to analyze heat transfer for solid–liquid phase change in two inclined cavities assisted with open cell and closed cell porous structures for enhancement of heat transfer and compare them.

The heat transfer analysis is done numerically. The set of conservation equations for mass, momentum and energy for phase change material (PCM) and conduction heat transfer equation for metal frame are solved. Furthermore, temperature and solid–liquid fraction distributions for a cavity filled only with PCM are also obtained for comparison. The porosity is 0.9 for both porous structures. Rayleigh number and inclination angle change from 1 to 10⁸, and from −90° to 90°, respectively.

The present study reveals that the use of closed cell structures not only can make phase change faster than open cell structure (except for Ra = 10⁸ and = 90°) but also provide more stable process. The use of a closed cell porous structure in a cavity with PCM can reduce melting period up to 55% more than a cavity with an open cell porous structure. The rate of this additional enhancement depends on Rayleigh number and inclination angle.

To the best of the authors’ knowledge, this is the first time that the comparison between closed cell and open cell porous structures for heat transfer enhancement in a solid/liquid phase change process is reported. Authors believe that the present study will lead more attentions on the use of closed cell porous structures.

The purpose of this study is to determine whether the Ottoman Empire’s net interest payments and foreign debt were sustainable or not in terms of their burden on budget revenues, using the method of historical econometric analysis.

In this study, the period between 1847 and 1882 of the Ottoman Empire is analyzed for sustainability analysis. Within the framework of the study, unit root tests and econometric analysis methods frequently used in the literature were used to analyze the sustainability of public debt. In the econometric analysis, in addition to various unit root tests, current econometric analysis methods, in particular Fourier expansion, were also used.

The results of econometric analyses showed that the burden of interest payments and foreign debt on the budget of the Ottoman state was unsustainable. This situation clearly shows the reason for the official bankruptcy of the Ottoman Empire, which was declared in 1875.

Although this study reveals the bankruptcy process of an important structure such as the Ottoman Empire in the historical process through econometric analyses, it also gives a very important message to today’s states. Accordingly, today’s state policies and decision-making mechanisms should take these results into account and strive to make the burden of public interest payments sustainable. It is believed that the study will shed light on the public finance policies of today’s states by drawing lessons from the collapse process of the Ottoman state.

Unlike the historical assessments in the literature on the decline of the Ottoman Empire, this study presents a cliometric approach by applying current econometric analysis techniques to past historical data. The study explains the unsustainability of the Ottoman Empire’s interest payments and external debt burden in the period under consideration in a way that, to the best of the authors’ knowledge, has not been done before.