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This study re-examines the stationarity properties of per capita electricity consumption in 18 MENA countries from 1980–2021. We use a novel panel stationarity test with a Fourier approximation to capture structural breaks and nonlinearities in the data. This Fourier panel test accounts for cross-sectional dependence and allows heterogeneity across cross-sections in the panel. Moreover, we apply several new panel stationarity tests that complement the aforementioned Fourier test. The study finds strong empirical evidence supporting the stationarity of per capita electricity consumption in the MENA region when considering smooth structural breaks, and our results remain unchanged using sharp structural breaks panel stationarity test. Therefore, we conclude that policies to manage energy demand will have no long-run effect as per capita electricity consumption will, after a shock, return to its long-run trend path. [ABSTRACT FROM AUTHOR]

This study revisits income convergence among Turkish provinces for 1992-2019 and differs from most empirical literature due to its unique structural and methodological framework. Stochastic convergence is tested by employing a battery of panel stationarity tests that allow cross-sectional dependence and structural breaks. Breaks are further analyzed with respect to the nature of breaks as sharp and smooth. Sharp breaks are identified endogenously, while smooth breaks are accounted for using the Fournier approximation. Although due to its unique structural convergence is tested by employing a sectional dependence and respect to the nature of breaks endogenously, while smooth approximation. Although s-of stochastic convergence that at the provincial level, additional dimensions of procedure, outcomes about However, findings at the panel stochastic convergence. At the convergence is detected, there are no shreds of evidence of stochastic convergence at the panel level. Univariate test statistics demonstrate that at the provincial level, there is no single case that applies to all provinces. As additional dimensions of the data-generating process are evaluated in the testing procedure, outcomes about stochastic convergence slightly shift for provinces. However, findings at the panel level remain consistent and do not produce stochastic convergence. At the provincial level, mixed results are obtained. [ABSTRACT FROM AUTHOR]

In this paper we consider an orthonormal basis, generated by a tensor product of Fourier basis functions, half period cosine basis functions, and the Chebyshev basis functions. We deal with the approximation problem in high dimensions related to this basis and design a fast algorithm to multiply with the underlying matrix, consisting of rows of the non-equidistant Fourier matrix, the non-equidistant cosine matrix and the non-equidistant Chebyshev matrix, and its transposed. Using this, we derive the ANOVA (analysis of variance) decomposition for functions with partially periodic boundary conditions through using the Fourier basis in some dimensions and the half period cosine basis or the Chebyshev basis in others. We consider sensitivity analysis in this setting, in order to find an adapted basis for the underlying approximation problem. More precisely, we find the underlying index set of the multidimensional series expansion. Additionally, we test this ANOVA approximation with mixed basis at numerical experiments, and refer to the advantage of interpretable results. [ABSTRACT FROM AUTHOR]

This article focuses on developing classical surrogates for parametrized quantum circuits using interpolation via (trigonometric) polynomials. We develop two algorithms for the construction of such surrogates and prove performance guarantees. The constructions are based on circuit evaluations which are blackbox in the sense that no structural specifics of the circuits are exploited. While acknowledging the limitations of the blackbox approach compared to white-box evaluations, which exploit specific circuit properties, we demonstrate scenarios in which the blackbox approach might prove beneficial. Sample applications include but are not restricted to the approximation of variational quantum eigensolvers and the alleviaton of the barren plateau problem. [ABSTRACT FROM AUTHOR]

Considering Africa's increasing electricity demands and the pivotal role of electricity in socioeconomic development, this study addresses a research gap in understanding the stochastic properties of per capita electricity consumption in African contexts. Through examining the integration properties of per capita electricity consumption across 19 African countries, the research determines whether 'shocks' yield transitory or permanent effects, aiding policy formulation and future demand forecasting. Annual electric power consumption data (1971 – 2014) (kWh per capita) from the WDI across 19 African countries are used. Our methodology starts with formally testing for cross-sectional dependence (CSD) using various tests to avoid potential size distortions. Subsequently, we employ the novel panel stationarity test of Nazlioglu and Karul (2017), a Fourier KPSS panel stationarity test. The robustness of the analysis is enriched by incorporating the Hadri and Kurozumi (2011) panel stationarity test and Nazlioglu et al. (2021) new panel stationary tests. The CSD test results reveal mutual dependency in electricity consumption among the sampled African countries, underscoring the need for a panel testing methodology that accommodates CSD. The results of the panel stationarity tests that allow CSD and structural breaks—specifically, the Nazlioglu and Karul (2017) test, which models structural breaks as a gradual process—reject the null hypothesis of trend stationarity for both single frequencies, i.e., k =1, and 2. Similarly, all new, complementary panel stationarity tests from Nazlioglu et al. (2021) reject the null hypothesis of stationarity for both frequencies. Collectively, the outcomes from various panel stationarity tests present strong evidence of nonstationary per capita electricity consumption within the sampled African countries. Additionally, the Nazlioglu and Karul panel stationarity test enables an analysis of the individual Fourier KPSS test for cross-sectional units in the panel. Of the 19 countries, only Togo does not reject the null hypothesis of stationarity for both frequencies. These individual country results align with the panel outcomes, providing compelling evidence for the nonstationarity of the per capita electricity consumption series across the investigated African nations. Accordingly, shocks to electricity consumption will have permanent effects, indicating that per capita electricity consumption will not return to its pre-shock equilibrium path. In this case, demand or consumption stabilizing policies will have long-run effects. [ABSTRACT FROM AUTHOR]

This paper suggests a new testing procedure to systematically examine the middle-income trap (MIT). To empirically demonstrate this procedure, one high income and 14 middle-income countries are examined using newly developed unit root tests — Fourier ADF with structural break (FADF-SB) and Seemingly Unrelated Regressions Fourier ADF (SUR-FADF). The FADF-SB test incorporates unknown nonlinearity and smooth break in the time-series, while the SUR-FADF test accounts for cross-sectional dependency. The empirical findings produced mixed results: 10 countries have a relatively high possibility of facing the MIT problem, while only one country has a relatively low possibility of facing the problem. For the remaining three countries, it is uncertain whether they will face the problem of MIT. These empirical findings have significant policy implications. [ABSTRACT FROM AUTHOR]

Structural breaks represent periods of turmoil that may influence how tourism affects economic growth. Current research on the tourism-led growth hypothesis (TLGH) measures the effect of structural breaks using dummy variables in regression models. However, the drawback of this approach is that there could be multiple structural breaks which result in an overfitting problem and reduce degrees of freedom in small samples. It also becomes difficult to isolate the effect of individual breaks when multiple structural breaks occur within the same year. We thus highlight the role of the Fourier ARDL model in addressing these shortcomings. We use three Pacific Island Countries: Fiji, Tonga, and Vanuatu as case studies to evaluate the efficacy of the Fourier ARDL model. Contrary to earlier research, our results indicate that tourism does not always lead to economic growth. Appropriate modelling of structural breaks also influences the outcome of asymmetric effects. These findings imply that future research should pay close attention to the effects of structural breaks in the TLGH. [ABSTRACT FROM AUTHOR]

This paper studies high-dimensional threshold models with a time-varying threshold approximated using a Fourier function. We develop a weighted LASSO estimator of regression coefficients as well as the threshold parameters. Our LASSO estimator can not only select covariates but also distinguish between linear and threshold models. We derive non-asymptotic oracle inequalities for the prediction risk, the l1 and l∞ bounds for regression coefficients, and provide an upper bound on the l1 estimation error of the time-varying threshold estimator. The bounds can be translated easily into asymptotic consistency for prediction and estimation. We also establish the variable selection consistency and threshold detection consistency based on the l∞ bounds. Through Monte Carlo simulations, we show that the thresholded LASSO works reasonably well in finite samples in terms of variable selection, and there is little harmness by the allowance for Fourier approximation in the estimation procedure even when there is no time-varying feature in the threshold. On the contrary, the estimation and variable selection are inconsistent when the threshold is time-varying but being misspecified as a constant. The model is illustrated with an empirical application to the famous debt-growth nexus. [ABSTRACT FROM AUTHOR]

This study investigates whether shocks to tourist arrivals in Indonesia, Malaysia, Philippines, Singapore, and Thailand (ASEAN‐5) are permanent or transitory, given the frequent and severe external shocks experienced by the tourism industry. Using monthly data from 2000 to 2019, we employ a novel panel unit‐root test that controls for cross‐correlations, multiple gradual structural breaks, and other nonlinearities present in the data to assess the stationarity properties of tourist arrivals. Additionally, we apply a panel unit‐root test that controls for cross‐correlations and allows for abrupt structural changes for robustness. The empirical findings reveal that shocks to tourist arrivals in the ASEAN‐5 countries exert persistent effects. Our results demonstrate nonstationarity within the series, illuminated by our careful consideration of both gradual and abrupt structural breaks. This finding underscores the necessity for policy interventions to mitigate the impact of adverse shocks on the tourism industry. [ABSTRACT FROM AUTHOR]

Many numerical methods have been developed since 1961, but unresolved issues remain. This study developed a numerical method to address these issues and determine the coefficients and properties of rotational waves with a shear current in a finite water depth. The number of unknown constants was reduced significantly by introducing a wavelength-independent coordinate system. The reference depth was calculated independently using the shooting method. Therefore, there was no need for partial derivatives with respect to the wavelength and the reference depth, which simplified the numerical formulation. This method had less than half of the unknown constants of the other method because Newton's method only determines the coefficients. The breaking limit was calculated for verification, and the result agreed with the Miche formula. The water particle velocities were calculated, and the results were consistent with the experimental data. Dispersion relations were calculated, and the results are consistent with other numerical findings. The convergence of this method was examined. Although the required series order was reduced significantly, the total error was smaller, with a faster convergence speed.

Since Chappelear developed a Fourier approximation method, considerable research efforts have been made. On the other hand, Fourier approximations are unsuitable for deep water waves. The purpose of this study is to provide a Fourier approximation suitable even for deep water waves and a numerical method to determine the Fourier coefficients and the wave properties. In addition, the convergence of the solution was tested in terms of its order. This paper presents a velocity potential satisfying the Laplace equation and the bottom boundary condition (BBC) with a truncated Fourier series. Two wave profiles were derived by applying the potential to the kinematic free surface boundary condition (KFSBC) and the dynamic free surface boundary condition (DFSBC). A set of nonlinear equations was represented to determine the Fourier coefficients, which were derived so that the two profiles are identical at specified phases. The set of equations was solved using Newton’s method. This study proved that there is a limit to the series order, i.e., the maximum series order is N=12, and that there is a height limitation of this method which is slightly lower than the Michell theory. The reason why the other Fourier approximations are not suitable for deep water waves is discussed.

In this study, the relationship between electricity and growth of the economy is investigated by applying the newly-developed bootstrap autoregressive-distributed lag test with a Fourier function to examine both the causality and cointegration for China, India, and the United States (US). While it is not possible to detect a long-term cointegration relation among the economy's electricity and growth, the study findings demonstrate the contingency of the causality. The ensemble method in machine learning performs better than conventional methods as electricity is an independent indicator for forecast economics. Concerning the US, previous electricity consumption has a positive impact on the current nature of economic growth. In contrast, the consumption of electricity is negatively affected by the development of the economy. However, for China and India, positive and negative feedback can be observed, respectively. Due to the increased awareness of the environment's adverse effects, China should promote technologies that conserve energy and boost energy efficiency to achieve sustainable development in both environmental and economic terms. In India's context, broadening access to electricity has significance for residents in rural areas and enhances economic growth. It is recommended that policy-makers promote innovative technologies in the US, as the abundant natural and human resources can make valuable contributions to the society and development of the economy. [ABSTRACT FROM AUTHOR]

Anthropogenic emissions of carbon dioxide (CO2) are the most important greenhouse gas. However, until now, no research has investigated the persistence of global CO2 emissions over a very long period of time. This work aims to fill this gap by examining the persistence of shocks to global CO2 emissions with a dataset of more than 2000 years. To this end, the study applies a battery of unit root tests by considering sharp and smooth structural shifts as well as the frequency domain properties of the series. Lee-Strazicich method results reveal that sharp break dates relate to the influenza pandemic of 1557 and the invention of the steam engine in 1712, and these historical events led to changes in the trend function of CO2 emissions. The findings of the Fourier Lagrange Multiplier and Fourier wavelet unit root tests illustrate that global CO2 emissions contain a unit root and do not exhibit mean-reverting behavior, thus external shocks have permanent effects on CO2 emissions. The results suggest that a reduction in global CO2 emissions is possible if effective environmental and energy policies established in international meetings such as Rio Conference, Kyoto Protocol Paris Agreement, and the United Nations Sustainable Development Summit are properly implemented. [ABSTRACT FROM AUTHOR]

To achieve environmental sustainability, it is important to change the energy pattern from dirty fossil fuels to renewable-clean energy sources. For this transition, countries should use their financial resources effectively and efficiently. Against this background, this study aims to examine the impact of financial development on renewable energy consumption in the United States over the period 1980–2019, considering urbanization, economic structure, and economic growth as control variables. The study contributes to the existing literature by testing the effect of six sub-indicators, namely efficiency, depth, and accessibility of financial markets and institutions on renewable energy consumption. This is done using the novel Fourier quantile causality test with wavelet transforms. The empirical results show that financial development encourages renewable energy consumption at high quantiles in the medium- and long-run. Moreover, depth and access to financial markets are the two most important factors that promote renewable energy consumption. Based on the overall findings, the study suggests that the United States government should adopt policies that improve the depth and access to financial markets rather than financial institutions to support green growth. [Display omitted] • Is there any impact of financial sector on renewable energy consumption in the USA? • A Fourier and wavelet based quantile causality analysis is used. • Financial development stimulates renewable energy consumption at higher quantiles. • Improving financial depth and access is crucial for renewable energy consumption. [ABSTRACT FROM AUTHOR]

This study investigates the impact of renewable and non-renewable energy consumption on economic growth in the top ten renewable energy-consuming countries over the period 1970–2019 using newly developed Fourier panel cointegration and causality tests. The negligence of structural breaks can significantly alter causal relationships, leading to misinterpretation of renewable energy policies. This study eliminates the problem using Fourier-based techniques. The long-run estimates show that non-renewable energy supports economic growth in eight out of the ten countries, while renewable energy has a positive effect on economic growth in Brazil, the United Kingdom, and France. The Fourier causality test indicates that the energy-led growth hypothesis is valid for both types of energy in the United States, India, the United Kingdom, and Spain. While the non-renewable energy-led growth hypothesis is valid for Italy, the conservation hypothesis is valid for both energy variables for Germany and for renewable energy for China. The overall results show that renewable energy can also be an important driver of economic growth, although not as strong as non-renewable energy. Therefore, countries need to closely monitor economic development while pursuing policies to reduce fossil fuels and deploy renewables in a way that enables higher economic growth. • Advanced Fourier based cointegration and causality methods are employed. • Non-renewable energy supports economic growth more than renewables. • Renewable energy boosts economic growth in Brazil, the United Kingdom and France. • Renewable energy causes economic growth in the United Kingdom, the United States, India and Spain. • Energy conservation policies hurt economic growth in five out of ten countries. [ABSTRACT FROM AUTHOR]

Fourier approximation plays a key role in qualitative theory of deterministic and random differential equations. In this paper, we will develop a new approximation tool. For an mm-order differentiable function ff on [0,10,1], we will construct an mm-degree algebraic polynomial Pm{P}_{m} depending on values of ff and its derivatives at ends of [0,10,1] such that the Fourier coefficients of Rm=f−Pm{R}_{m}=f-{P}_{m} decay fast. Since the partial sum of Fourier series Rm{R}_{m} is a trigonometric polynomial, we can reconstruct the function ff well by the combination of a polynomial and a trigonometric polynomial. Moreover, we will extend these results to the case of random processes.

The biggest challenge of texture filtering is to smooth the strong gradient textures while maintaining the weak structures, which is difficult to achieve with current methods. Based on this, we propose a scale-adaptive texture filtering algorithm in this paper. First, the four-directional detection with gradient information is proposed for structure measurement. Second, the spatial kernel scale for each pixel is obtained based on the structure information; the larger spatial kernel is for pixels in textural regions to enhance the smoothness, while the smaller spatial kernel is for pixels on structures to maintain the edges. Finally, we adopt the Fourier approximation of range kernel, which reduces computational complexity without compromising the filtering visual quality. By subjective and objective analysis, our method outperforms the previous methods in eliminating the textures while preserving main structures and also has advantages in structure similarity and visual perception quality. [ABSTRACT FROM AUTHOR]

The biggest challenge of texture filtering is to smooth the strong gradient textures while maintaining the weak structures, which is difficult to achieve with current methods. Based on this, we propose a scale-adaptive texture filtering algorithm in this paper. First, the four-directional detection with gradient information is proposed for structure measurement. Second, the spatial kernel scale for each pixel is obtained based on the structure information; the larger spatial kernel is for pixels in textural regions to enhance the smoothness, while the smaller spatial kernel is for pixels on structures to maintain the edges. Finally, we adopt the Fourier approximation of range kernel, which reduces computational complexity without compromising the filtering visual quality. By subjective and objective analysis, our method outperforms the previous methods in eliminating the textures while preserving main structures and also has advantages in structure similarity and visual perception quality.

This study aims to analyze whether the effect of shocks on the ecological footprint and its sub-accounts in the Big Ten emerging economies is transitory or not. To this end, we employ the Fourier augmented Dickey–Fuller unit root test with a fractional frequency (FADF) and the recently developed fractional unit root test with a Fourier function (FUR) on annual data from 1961 to 2017. The results of the FADF unit root test suggest the validity of stationarity for about 30% of the series, while the FUR test indicates evidence of stationarity for almost all footprint series. These results imply that policy shocks to ecological footprints are temporary and policies to reduce environmental pollution in the Big Ten countries do not have the expected impact. Since shocks have temporary effects on ecological footprints, the Big Ten countries should not cause irreversible environmental degradation. The Big Ten governments need to implement permanent structural reforms to counteract the growth of the ecological footprint.Article Highlights: The persistence of the ecological footprint and its six subaccounts in the Big Ten emerging markets is investigated. Novel Fourier-based and fractional frequency unit root tests are performed. Almost all series are stationary. Policy shocks will have temporary effects on the ecological footprint. [ABSTRACT FROM AUTHOR]

[Display omitted] • Open loop optimal control for batch biodiesel production. • Fourier-based approach for control vector parameterization. • Minimum parameters to optimize. • Smooth optimal temperature profile. • Monte Carlo combined with genetic algorithms for parameters optimization. In this work, a novel methodology for the dynamic optimization of biodiesel batch production is developed. Two problem statements are carried out. In the first approach, only the final concentration of biodiesel is optimized. In the second, the signal energy is also considered, which is measured as the integral of the square reactor temperature over the reaction time and represents an indirect way to contemplate the energy employed. The proposed strategy to solve the optimal control problem is based on the Fourier series for the reactor temperature parameterization. The main advantage of this Fourier-based sequential approach over competing methods is that the obtained profiles are smooth and continuous, which is relevant since smoothing techniques are not required for implementation in real systems. Besides, a minimum number of parameters to optimize is required. The process is modeled and simulated in Matlab and Simulink. The results are compared with data reported in the literature. An improvement of over 5% in biodiesel production is achieved without energy contemplation. In the second case, an increase of 3% in the final biodiesel production is achieved with a 10% lower energy, in both cases employing only three parameters. [ABSTRACT FROM AUTHOR]

This paper examines the information transmission between Bitcoin derivatives and spot exchanges using 15-minute interval data over May 2016 - September 2020. We employ a novel econometric framework with Fourier approximation, taking structural shifts in causal linkages, on the prices, returns, and volatilities of BitMEX, the derivatives market, and five other major spot exchanges, Coinbase, Bitstamp, Kraken, CEX.io, and Poloniex. Overall, the results provide robust evidence of information flow between the derivatives and spot exchanges, implying the markets react to new information simultaneously. The results are of importance for investors conducting portfolio allocation exercises and risk management strategies. [ABSTRACT FROM AUTHOR]

In this paper we propose an approximation method for high-dimensional 1-periodic functions based on the multivariate ANOVA decomposition. We provide an analysis on the classical ANOVA decomposition on the torus and prove some important properties such as the inheritance of smoothness for Sobolev type spaces and the weighted Wiener algebra. We exploit special kinds of sparsity in the ANOVA decomposition with the aim to approximate a function in a scattered data or black-box approximation scenario. This method allows us to simultaneously achieve an importance ranking on dimensions and dimension interactions which is referred to as attribute ranking in some applications. In scattered data approximation we rely on a special algorithm based on the non-equispaced fast Fourier transform (or NFFT) for fast multiplication with arising Fourier matrices. For black-box approximation we choose the well-known rank-1 lattices as sampling schemes and show properties of the appearing special lattices [ABSTRACT FROM AUTHOR]

This paper uncovers the link between economic development and environmental degradation in Turkey by employing two distinct methods. We test the so-called EKC hypothesis for four various outcomes, including carbon dioxide emissions, wastewater, sulfur dioxide, and particulate matter by implementing time-series and panel data models. Fully modified ordinary least squares provide an N-shaped linkage between environmental degradation, such as carbon dioxide emissions and economic growth between 1961 and 2014. The random- and fixed-effects models indicate that there exists an N-shaped connection between wastewater and particulate matter quality indicators and economic growth spanning 1992 and 2013. However, we find inverted N-shaped relationship between SO2 and economic growth over the same period. Our findings urge policymakers in Turkey to take precautions by implementing national policies to fight against pollution to increase environmental quality. [ABSTRACT FROM AUTHOR]

Sustainable development and reducing environmental pressure are major issues that concern developed as well as developing countries. Although researchers widely use carbon dioxide emissions and ecological footprint within the scope of environmental degradation, a more comprehensive ecological indicator is needed to assess environmental sustainability. In this context, the load capacity factor enables a comprehensive environmental sustainability assessment through the simultaneous analysis of biocapacity and ecological footprint. However, there are few studies analyzing the determinants of load capacity factor and this study aims to fill this gap for Indonesia. Using the recently developed Fourier quantile causality test, this study investigates the impact of income, export diversification, non-renewable and renewable energy consumption on the load capacity factor for Indonesia during 1965Q1–2014Q4. The results show unidirectional causality from non-renewable energy consumption to the load capacity factor at all quantiles, while income, export diversification, and renewable energy are the causes of environmental quality at middle and higher quantiles (within 0.5, 0.7, and 0.9). Most importantly, renewable energy and export diversification increase the load capacity factor and thus support environmental quality. In contrast, an increase in income and consumption of non-renewable energy reduces the load capacity factor. These results highlight the importance of renewable energy and export diversification for the sustainable development of Indonesia.

From the empirical energy literature, it is observed that studies focusing on the energy-economic growth nexus ignore the possible existence of gradual breaks as they employ methods without or with sharp structural breaks. Therefore, one can argue that they may yield biased and inefficient output in the presence of gradual breaks. The goal of this paper is to investigate the impact of solar energy consumption on GDP utilizing quarterly data over the period 1984–2018 for the USA. For this purpose, the paper performs a unit root test and a cointegration test that are based on the Fourier approximation to take gradual breaks into account. The paper also performs the dynamic ordinary least squares estimator to estimate long-run parameters. The findings document that there exists cointegration in the empirical model and that GDP is positively associated with solar energy consumption. Some implications based on the empirical findings are presented in the paper. [ABSTRACT FROM AUTHOR]

Classical threshold models assume that threshold values are constant and stable, which appears overly restrictive and unrealistic. In this article, we extend Hansen's (2000) constant threshold regression model by allowing for a time‐varying threshold which is approximated by a Fourier function. Least‐square estimation of regression slopes and the time‐varying threshold is proposed, and test statistics for the existence of threshold effect and threshold constancy are constructed. We also develop the asymptotic distribution theory for the time‐varying threshold estimator. Through Monte Carlo simulations, we show that the proposed estimation and testing procedures work reasonably well in finite samples, and there is little efficiency loss by the allowance for Fourier approximation in the estimation procedure even when there is no time‐varying feature in the threshold. On the contrary, the slope estimates are seriously biased when the threshold is time‐varying but being treated as a constant. The model is illustrated with an empirical application to a nonlinear Taylor rule for the United States. [ABSTRACT FROM AUTHOR]

The purpose of this study is to examine the weak-form market efficiency hypothesis (EMH) for 8 African Frontier markets between 2001 and 2017. To achieve this purpose, we employ unit root testing procedures which are robust to both nonlinearities and smooth structural breaks, making this study the first of its kind for African markets. Our empirical findings suggest that, regardless of whether daily or weekly series are employed, most African frontier markets are not market efficient, in the weak sense form, with the exception of the Kenyan stock market and to a very much lesser extent the Botswana and South African stock series. Important policy and investor implications are drawn in our study.

Each combustion chamber of the Fourier engine is open to multiple cylinders, which have pistons connected to crankshafts that rotate at different rates. The displacements of the individual cylinders and the relative phases of the pistons are selected according to a Fourier approximation of a prescribed time dependence of the volume of the combustion chamber. The parameters are selected so that the duration of the intake and ignition strokes is greater than the duration of the compression and exhaust strokes. As the speed of an engine increases, the power curve initially climbs approximately linearly, but it levels off as intake and ignition become less efficient at high rpm. By increasing the duration of these strokes relative to the duration of the other strokes, it may be possible to allow the power curve to climb higher before leveling off.

Over the past decades, scientific visualization became a fundamental aspect of modern scientific data analysis. Across all data-intensive research fields, ranging from structural biology to cosmology, data sizes increase rapidly. Dealing with the growing large-scale data is one of the top research challenges of this century. For the visual exploratory data analysis, interactivity, a view-dependent visibility optimization and frame coherence are indispensable. In this work, we extend the recent decoupled opacity optimization framework to enable a navigation without occlusion of important features through large geometric data. By expressing the accumulation of importance and optical depth in Fourier basis, the computation, evaluation and rendering of optimized transparent geometry become not only order-independent, but also operate within a fixed memory bound. We study the quality of our Fourier approximation in terms of accuracy, memory requirements and efficiency for both the opacity computation, as well as the order-independent compositing. We apply the method to different point, line and surface data sets originating from various research fields, including meteorology, health science, astrophysics and organic chemistry. [ABSTRACT FROM AUTHOR]

It is a popular method to deal with structural breaks using Fourier transformation, in which an integer frequency and a fractional frequency are respectively associated with transitory and permanent breaks, and hence is important in empirical applications. However, we still do not know how the integer and fractional frequencies affect the theoretical properties of unit root tests. This paper examines the properties of Dickey-Fuller tests when the true datagenerating process contains fractional Fourier-form breaks but ignored in testing procedures. We derive the limiting distributions by reparameterization, discuss the theoretical predictions of the limiting results on the properties of Dickey-Fuller tests, and give the conditions under which spurious rejection occurs. We use Monte Carlos simulations to confirm the predictions, finding that the theory is consistent with the simulation evidence. Our results imply that permanent breaks could more easily lead to spurious rejections than temporary breaks. Thus, ignoring a fractional frequency or specifying it as integer would cause misleading results. [ABSTRACT FROM AUTHOR]

The purpose of this study is to examine the weak-form market efficiency hypothesis (EMH) for 8 African Frontier markets between 2001 and 2017. To achieve this purpose, we employ unit root testing procedures which are robust to both nonlinearities and smooth structural breaks, making this study the first of its kind for African markets. Our empirical findings suggest that, regardless of whether daily or weekly series are employed, most African frontier markets are not market efficient, in the weak sense form, with the exception of the Kenyan stock market and to a very much lesser extent the Botswana and South African stock series. Important policy and investor implications are drawn in our study. [ABSTRACT FROM AUTHOR]

[Display omitted] • Causality between renewable energy, income and load capacity factor. • A Fourier- and wavelet-based causality test employed. • Bidirectional links between REC and GDP at short, medium and long run. • Bidirectional causality between REC and load capacity factor defined. • Renewable energy is ecologically and economically feasible. Stimulating renewable energy consumption is a major focus of the Sustainable Development Goals in combating climate change and global warming. The International Energy Agency estimates that renewable energy consumption should be doubled to achieve the COP21 targets. In this context, the question is whether renewable energy types promote the improvement of ecological quality and economic growth. Most studies have investigated the influence of renewable energy on ecological pollution using carbon dioxide emissions or ecological footprint indicators, which only represent the pollution caused by human consumption patterns, and these indicators neglect the supply side. Motivated by this point, this study uses the LCF (Load Capacity Factor) as an environmental indicator and examines the causality relationship among different types of renewable energy, income, and environmental quality in the USA, while also incorporating employment and capital stock into the analysis. Through using the Fourier causality test with the wavelet-decomposed series, the study explores for the validity of the renewable energy-based growth hypothesis and answers to the question of whether there is a causal effect of renewable energy types on environmental quality. The results demonstrate that there is a bidirectional causality between total renewable energy, wood, biomass, and economic growth as well as between these renewable energy types and the LCF. [ABSTRACT FROM AUTHOR]

This paper studies stationarity and cointegration of healthcare expenditure (HE) and GDP for a sample of OECD countries. In particular, we employ newly developed unit root and cointegration tests which approximate an unknown number of smooth structural shifts in the low-frequency components of a Fourier expansion. The new unit root test indicates that HE and GDP are non-stationary. In the presence of a number of smooth shifts in the cointegration regression, our empirical results support the existence of stochastic comovement between HE and GDP in 14 out of 20 OECD countries. In addition, we examine the income elasticity of HE for the countries that we found cointegration relationship between HE and GDP. We found 13 out of 14 countries with income elasticity of HE higher than 1, which implies that health care is a luxury good. [ABSTRACT FROM AUTHOR]

This study aims to test the long-run validity of the purchasing power parity with the Fourier stationarity analysis for real exchange rates. With Fourier approach, structural breaks are modelled as a gradual and smooth process. From the World Bank country classification, analyzes were applied for 92 countries, including 23 high income, 30 upper-middle income, 30 lower-middle income and 9 low income countries over the period 1995:1-2017:2 using quarterly data. The findings show that the purchasing power parity is valid for 8 high income countries, 5 upper middle income countries, 8 lower middle income countries and 3 low income countries. [ABSTRACT FROM AUTHOR]

Field monitoring strategy is critical for disaster preparedness and watershed emergency environmental management. However, development of such is also highly challenging. Despite the efforts and progress thus far, no definitive guidelines or solutions are available worldwide for quantitatively designing a monitoring network in response to river chemical spill incidents, except general rules based on administrative divisions or arbitrary interpolation on routine monitoring sections. To address this gap, a novel framework for spatial-temporal network design was proposed in this study. The framework combines contaminant transport modelling with discrete entropy theory and spectral analysis. The water quality model was applied to forecast the spatio-temporal distribution of contaminant after spills and then corresponding information transfer indexes (ITIs) and Fourier approximation periodic functions were estimated as critical measures for setting sampling locations and times. The results indicate that the framework can produce scientific preparedness plans of emergency monitoring based on scenario analysis of spill risks as well as rapid design as soon as the incident happened but not prepared. The framework was applied to a hypothetical spill case based on tracer experiment and a real nitrobenzene spill incident case to demonstrate its suitability and effectiveness. The newly-designed temporal-spatial monitoring network captured major pollution information at relatively low costs. It showed obvious benefits for follow-up early-warning and treatment as well as for aftermath recovery and assessment. The underlying drivers of ITIs as well as the limitations and uncertainty of the approach were analyzed based on the case studies. Comparison with existing monitoring network design approaches, management implications, and generalized applicability were also discussed. [ABSTRACT FROM AUTHOR]

This article examines the quality of China’s preliminary announcements of the quarterly GDP. We modify the tests for unbiasedness and efficiency by incorporating the Fourier approximation to capture the effect of the state of the economy, and employing the Kiefer, Vogelsang and Bunzel (KVB) approach, developed by KVB in 2000 to reconstruct the tests to improve the finite sample properties. The results show that: (1) there is no enough evidence to support that the preliminary and first revised data are unbiased and efficient; (2) there exist systematic errors related to the state of the economy, and hence information about the state of the economy was not incorporated into the GDP data. Furthermore, we find that there is a possibility that these systematic errors associated with the stages of the business cycle may offset each other, and there is also a possibility that there exist offsetting errors in the underlying components of GDP. [ABSTRACT FROM AUTHOR]

Terrestrial laser scanning (TLS) is an effective tool for retrieving forest attributes. For example, stem diameters can be estimated from the TLS point cloud by applying automatic algorithms, which often approximate the stem cross section by using a circle or a cylinder. However, the cross section of a tree stem is never exactly a circle. Moreover, the cross section provides other economically important attributes related to, for example, the wood quality and growth environment. Thus, advanced curve fitting and other geometric fitting methods should be explored further. In this letter, a Fourier series curve approximation approach is proposed for modeling stem cross section shapes. The routine uses iterative Fourier series approximation in polar coordinates to remove gross errors. Three different diameter approximations are tested: circle fitting, Fourier series fitting, and combined Fourier series and circle fitting. The proposed approach is tested for approximating the diameter at breast height (DBH) with the use of two data sets: the first from an Alpine mixed and landslide-affected forest with multiscan TLS, and the second from a mature Scots pine forest in Finland with single-scan TLS. The results showed that for the multiscan data, the use of the combined Fourier series and circle fitting improved the root mean square error of DBH by 12.4% compared with direct circle fitting. The DBH accuracy for the single-scan data resulted in similar accuracy compared with that of the circle fitting. The results imply that the new approach is able to accurately reconstruct stem cross sections, especially for multiscan data. [ABSTRACT FROM PUBLISHER]