Nonlinear Unit Research Articles

Is art market efficient? Evidence from non-linear quantile unit-root tests

ABSTRACT In this paper, we use quarterly stock price index data to test the weak form of the efficient market hypothesis for 13 art market indices. The fact that hypotheses can be efficiently tested by performing unit root tests is well known. The conventional unit root test results show that most art indices have unit roots, which means that these art markets are efficient. However, the results of the non-linear quantile unit root tests we conduct over a range of quantiles lead us to reject the null of the unit root test for several art markets. To acquire more information, we perform the test over sub-quantile intervals, finding asymmetric market efficiency between the low and high quantile intervals: we cannot reject the unit root null in upper quantile intervals for most art price indices.

Testing the efficiency of emerging markets: Evidence from nonlinear panel unit tests

In this study, we investigate market efficiency considering nonlinearities by testing the weak-form market efficiency of the stock markets of Brazil, China, Russia, Turkey, and South Africa using recently proposed nonlinear panel unit root tests. The stock markets of these emerging countries are deliberately selected for their market capitalization to form a homogenous panel. The results of nonlinear models indicate that the stock market indexes are stationary and weak-form inefficient. This finding contributes to the contradictory results of the prior research using linear and nonlinear models about the efficiency of emerging stock markets in favor of nonlinear ones. Furthermore, we propose that studies using financial variables consider such nonlinearity in order to achieve more accuracy in findings related to such studies.

Asymmetric Dynamics of Inflation Inertia in Some Selected Non-Eurozone European Countries

Relevance. Inflation inertia refers to the persistence of inflation over time and can be caused by a variety of factors, including expectations about future inflation, the structure of the economy, and the behavior of economic agents. Over the past two decades, the European economy has grappled with a range of challenges and currently seeks to mitigate the negative impacts of the global pandemic. Research objective. Persistent inflation can lead to uncertainty, decreased investment, and a loss of confidence in an economy. Non-eurozone economies can also face challenges in controlling inflation due to such factors as the lack of monetary integration with the eurozone, limited access to the European Central Bank's resources, and the lack of a unified currency. Hence, for a more effective monetary policy in these countries, it is necessary to measure and understand the inflation inertia. This paper offers a novel empirical study of the dynamics of inflation inertia for seven EU economies that are not part of the eurozone. Data and methods. To achieve the research objective, three non-linear unit root tests are employed to consider both structural changes and regime switching. These tests allowed for the inclusion of almost all non-linear dynamics observed in the inflation series. In addition, the tests involve the use of the dynamic rolling windows sample approach in order to provide more sensitive measurements of the effect of time-varying shocks on inflation inertia. Results. According to the static sample analysis of 200 observations, Bulgaria, Croatia, and the Czech Republic have inflation inertia. Sweden, Romania, Hungary, and Poland do not have inflation inertia when non-linear regime switching dynamics and structural change are considered. However, Croatia and the Czech Republic show a mostly non-stationary inflation in dynamic rolling windows sampling. Hungary has persistent inflation even though it was not detected in the static sample analysis. The shocks of inflation fade out in Bulgaria, Poland, Romania, and Sweden with non-linear dynamics. If non-linear dynamics is ignored, it can lead to misleading results in economic time series. Conclusions. Inflation inertia can be influenced by a variety of factors, including the global pandemic, global or regional conflicts and monetary policy preferences. The successful management of inflation inertia in Romania and Sweden may serve as a model for other economies that have demonstrated an ability to effectively address and mitigate the challenges posed by inflation inertia.

Get Used To Or Adapt. Adaptive Market Hypothesis Testing With Linear And Nonlinear Unit Root Tests

Get Used To Or Adapt. Adaptive Market Hypothesis Testing With Linear And Nonlinear Unit Root Tests

Impact of major global events on the Turkish stock market efficiency

Market efficiency is of great importance to many investors, policy makers, as well as researchers. It provides them with information regarding the market and acts as a guide in their decision-making process. For this reason, there have been extensive amount of research done through the years. However, the World has witnessed several major events in the last couple of decades, which has been of great importance for financial markets, having both direct and indirect impacts. The Global Financial Crisis of 2008 and the COVID-19 pandemic can be the two most important events the World has experienced. Although past research shows that the impact of both events on the efficiency of the stock markets were looked at in separate studies, there is lack of studies involving both major events and analysing how the efficiency of the stock market is changing between these periods. The aim of this study is to analyse the weak-form efficiency of the Turkish stock market and how it has evolved over time. There are 4 different data sets used to observe the changes in market efficiency, with full sample ranging from February 1988 to September 2022. Monthly closing prices of the BIST100 Index are analysed using both the traditional linear Augmented Dickey-Fuller unit root test and 5 different non-linear unit root tests. Results show that different tests have different strengths in capturing the stationarity and due to the LNV test Turkish Stock Market was found not to be weak form efficient.

Weak EMH and Canadian stock markets: evidence from linear and nonlinear unit root tests

PurposeThe purpose of this paper is to test the weak form of the efficient market hypothesis (EMH) using monthly data from 2004M08 to 2018M04 for two Canadian stock indices: the Islamic (DJICPI) and the conventional (CCSI). This paper investigates whether Islamic and/or conventional stock market would be efficient through the non-stationarity test of the stock indices.Design/methodology/approachThe authors conduct the linearity test of Harvey et al. (2008) to identify whether the considered series has linear or nonlinear behavior. If the time series exhibits nonlinear evolution, then the authors apply nonlinear unit root tests (three KSS type tests and Sollis tests).FindingsLinearity test results say that LCCSI has nonlinear behavior, while Dow Jones Islamic Canadian Price Index, LDJICPI, is a linear process. Then, the findings of this paper show that only Canadian Islamic Price Index (DJICPI) has the characteristics of random walk indicating that only conventional stock markets are inefficient. The major implication is that in Canada, fund managers and investors can (cannot) enjoy excess returns to their investment in conventional (Islamic) stock market.Originality/valueNumerous empirical studies of the weak EMH are carried out within a linear framework. However, stock indices can show nonlinear behavior as a result of 2008 global financial crisis. To contribute to the existing literature on the Islamic and conventional stock market efficiency, the authors take into account both structural breaks and nonlinearity. Thus, as a testing strategy for weak EMH, the authors perform (Harvey et al., 2008) linearity test to examine the presence of nonlinear behavior and correct for outliers effect when it is needed.

Reconfigurable Low-Threshold All-Optical Nonlinear Activation Functions Based on an Add-Drop Silicon Microring Resonator

The realization of optical nonlinear activation functions (NAFs) is essential for integrated optical neural networks (ONNs). Here, we propose and experimentally demonstrate a photonic method to implement reconfigurable and low-threshold all-optical NAFs based on a compact and high-Q add-drop microring resonator (MRR) on silicon. In the experiment, four different NAFs including softplus, radial basis, clamped ReLU, and sigmoid functions are realized by exploiting the thermo-optical (TO) effect of the MRR. The threshold to implement NAFs is as low as 0.08 mW. As a demonstration, a handwritten digit classification benchmark task is simulated based on a convolutional neural network (CNN) using the obtained activation functions, where an accuracy of 98% is realized. Thanks to the unique advantages of ultra-compact footprint and ultralow threshold, the proposed nonlinear unit is promising to be widely used in large-scale integrated ONNs.

GAPCNN with HyPar: Global Average Pooling convolutional neural network with novel NNLU activation function and HYBRID parallelism.

With the increasing demand for deep learning in the last few years, CNNs have been widely used in many applications and have gained interest in classification, regression, and image recognition tasks. The training of these deep neural networks is compute-intensive and takes days or even weeks to train the model from scratch. The compute-intensive nature of these deep neural networks sometimes limits the practical implementation of CNNs in real-time applications. Therefore, the computational speedup in these networks is of utmost importance, which generates interest in CNN training acceleration. Much research is going on to meet the computational requirement and make it feasible for real-time applications. Because of its simplicity, data parallelism is used primarily, but it performs badly sometimes. In most cases, researchers prefer model parallelism to data parallelism, but it is not always the best choice. Therefore, in this study, we implement a hybrid of both data and model parallelism to improve the computational speed without compromising accuracy. There is only a 1.5% accuracy drop in our proposed study with an increased speed up of 3.62X. Also, a novel activation function Normalized Non-linear Activation Unit NNLU is proposed to introduce non-linearity in the model. The activation unit is non-saturated and helps avoid the model's over-fitting. The activation unit is free from the vanishing gradient problem. Also, the fully connected layer in the proposed CNN model is replaced by the Global Average Pooling layers (GAP) to enhance the model's accuracy and computational performance. When tested on a bio-medical image dataset, the model achieves an accuracy of 98.89% and requires a training time of only 1 s. The model categorizes medical images into different categories of glioma, meningioma, and pituitary tumor. The model is compared with existing state-of-art techniques, and it is observed that the proposed model outperforms others in classification accuracy and computational speed. Also, results are observed for different optimizers', different learning rates, and various epoch numbers.

Anomalous wavefront control via nonlinear acoustic metasurface through second-harmonic tailoring and demultiplexing

We propose a nonlinear acoustic metasurface concept by exploiting the nonlinearity of locally resonant unit cells formed by curved beams. The analytical model is established to explore the nonlinear phenomenon, specifically the second-harmonic generation (SHG) of the nonlinear unit cell, and validated through numerical and experimental studies. By tailoring the phase gradient of the unit cells, nonlinear acoustic metasurfaces are developed to demultiplex different frequency components and achieve anomalous wavefront control of SHG in the transmitted region. To this end, we numerically demonstrate wave steering, wave focusing, and self-bending propagation. Our results show that the proposed nonlinear metasurface provides an effective and efficient platform to achieve significant SHG and separate different harmonic components for wavefront control of individual harmonics. Overall, this study offers an outlook to harness nonlinear effects for acoustic wavefront tailoring and develops potential toward advanced technologies to manipulate acoustic waves.

Nonlinear hierarchical unit cell for passive, amplitude-dependent filtering of acoustic waves

In this letter we propose a nonlinear hierarchical unit cell for use in passive, amplitude-dependent filtering of acoustic energy transmission. Analogous to unit cell designs which filter on frequency using bandgaps, the nonlinear hierarchical unit cell filters on amplitude with minimal waveform distortion. Numerical simulations of wave propagation in a mechanical chain employing the proposed unit cell predict nearly zero transmission of energy at low amplitudes, and nearly perfect energy transmission at large amplitudes. We hypothesize that the amplitude-dependent transmission behavior results from the nonlinear unit cell locking at high amplitudes, and thus acting as a single mass. When this single mass has the same weight as the other masses in the chain, near-perfect transmission is possible. We investigate this behavior further through a nonlinear analysis using a harmonic balance method to predict wave transmission through the nonlinear unit cell. The analysis confirms the transmission behavior and the rigid body hypothesis at large amplitudes. To validate the simulated and analysis results, we design and construct a monatomic chain using steel masses and additively-manufactured serpentine springs, to include a specially-designed nonlinear spring in the hierarchical unit cell. We then document amplitude-dependent filtering in the experiment for multiple frequencies, with strong agreement documented between measured results and simulation. In addition, high-speed camera images of the hierarchical cell verify the hypothesized locking behavior at large amplitudes. We believe the ability to passively select transmission based on a signal’s amplitude, with minimal resulting distortion, may open new opportunities in wave control and filtering, and new approaches for conceiving wave-based devices.

Fourier Nonlinear Quantile Unit Root Test of Purchasing Power Parity in cryptocurrencies

ABSTRACT The primary purpose of this article is to conduct the Fourier Nonlinear Unit Root Test to check Purchasing Power Parity (PPP) for seven cryptocurrencies traded in seventeen countries from 2010 to 2021. The unit root test supports the PPP hypothesis when we use each cryptocurrency separately for all the countries. However, the PPP hypothesis is strongly supported when we pool them together by countries and cryptocurrencies. This finding is in line with the power of the test issue of the PPP for regular PPP testing, which also holds good in cryptocurrencies.

A 2-DOF-IMC method for suppressing transmission chain vibration of wind power generation system with a clearance

To address the vibration problem caused by gear clearance in the wind drivetrain, a two-degree-of-freedom internal model control (2-DOF-IMC) method was proposed to suppress the clearance’s nonlinear vibration. The two-mass wind drivetrain with clearance is the object of this paper’s research. First, we discuss the nonlinear characteristics of gear clearance and the mechanism by which vibration occurs. The nonlinear clearance unit is then decomposed into a linear unit and a nonlinear bounded disturbance unit. A suppression disturbance method based on 2-DOF-IMC was proposed to address nonlinear bounded disturbances. The 2-DOF-IMC overcomes the shortcoming of the PID control and the common internal model control (1-DOF-IMC) by allowing for independent adjustment of the anti-disturbance performance, effectively suppressing the nonlinear disturbance caused by gear clearance. A 2-DOF-IMC scheme and an IMC controller are designed, and the method’s effectiveness is validated through simulation.

THE PURCHASING POWER PARITY HYPOTHESIS TESTED -ONCE AGAIN-. NEW EMPIRICAL EVIDENCE FOR 28 OECD COUNTRIES

The present study is aimed to examine the validity of the purchasing power parity hypothesis for 28 OECD countries over the 1960q1-2021q4 period. To reach this goal, we apply three methods to evaluate whether the real exchange rates are stationary: the traditional unit root tests in time series, the panel unit root tests, and nonlinear unit root tests based on OLS and GLS detrending. The findings suggest that the purchasing power parity hypothesis does not hold even if the assessment considers nonlinear adjustment.

Persistence of CO2 emissions in G7 countries: a different outlook from wavelet-based linear and nonlinear unit root tests.

Today, environmental issues such as the inability to control rising carbon dioxide (CO2) emissions, climate change, and global warming are on the agenda of policy-makers and various organizations. The Paris Agreement, signed in 2016 and rejoined by the USA in 2021, emphasizes the need for decarbonization and the importance of CO2 reduction for sustainable development. Since environmental policies can have long-term effects on variables containing unit roots, it is important for policy-makers to understand the stochastic properties of CO2 emissions. In this context, we propose a new wavelet-based nonlinear unit root test to investigate the stationary properties of the per capita CO2 emissions for the G7 countries during the period 1868–2014. To compare results, we use eight different tests that take into account both the time–frequency domain difference, the nonlinear-linear difference, and smooth structural breaks. The results of the different linear tests illustrate that CO2 emissions have a unit root in the frequency domain for all countries. Moreover, nonlinear unit root test results indicate that the CO2 emissions for the UK are stationary in the time domain. Overall, we consider frequency domain test results, and conclude that CO2 emission policies have permanent effects for G7 countries. Based on the findings, we recommend that the G7 countries take long-term measures to reduce CO2 emissions, such as joint actions to improve environmental quality through fossil fuel conservation, renewable energy improvement, and environmental awareness programs.

Suppressing vibration of structures using nonlinear single unit impact dampers via Taguchi method

This paper investigates a vibratory system that employs Hertzian contact theory in terms of free vibration. Nonlinear impact dampers are created by using a spring, mass, and viscous damper model. The model is simulated in MATLAB software using the DAS method as a proper simulation framework. The Taguchi method is used to examine the efficacy of impact dampers for controlling structural vibrations of the structure. It is demonstrated that the optimal factors obtained can effectively suppress the structure’s unwanted vibrations. The analysis of variance is also used to indicate the most influential factor of dampers to demonstrate their ability to quench vibrations.

Examining the non-linear stochastic behavior of the European energy market: evidence from nonlinear unit root tests

ABSTRACT Stock market efficiency has been one of the most investigated topics of the last century. Knowing the efficiency of a market has major implications for both investors and policymakers, as a perfectly efficient market eliminates any arbitrage opportunity and the possibility of actually beating the market. For this reason, this study aims to examine the weak-form market efficiency of the European energy markets using linear and nonlinear unit root tests for the period covering February 2012 to April 2021. The results indicated that while the Augmented Dickey–Fuller test captured the stationarity in only Austria’s Oil, and Gas index, using nonlinear tests showed stationarity in 17 of the 20 indices tested. Overall, the European Energy Market can be considered inefficient under the weak form of the Efficient Market Hypothesis. Therefore, there is an indication of profitable arbitrage opportunities among energy stocks. Signs of stationarity also suggest that shocks to energy stocks will have temporary effects. Energy markets of Austria, Finland, France, Greece, Italy, Netherlands, Russia, Spain, Sweden, and the United Kingdom, for this reason, could benefit from policy changes to support increased information flow to achieve more transparency and utilize better trading technologies.

Financial market integration of emerging markets: Heavy tails, structural shifts, nonlinearity, and asymmetric persistence

This study examines the financial market integration of emerging markets into international financial markets with regards to the real interest rate parity hypothesis. We focus on accounting for heavy-tailed (non-normal) distributions, structural shifts, nonlinearity, and asymmetric adjustment by utilizing recent methodological developments in unit root analysis. With data from January 2000 to May 2020 for 21 emerging markets, we find that considering heavy-tailed distributions in an asymmetric persistence framework with nonlinearity and structural shifts appears to be crucial in analyzing the financial market integrations of emerging markets. The nonlinear quantile unit root test with smooth structural breaks supports the real interest rate parity hypothesis in 18 out of 21 countries. An interesting result is that the conventional and quantile approaches are unable to support the validity of real interest parity in China. Our findings provide sound implications, which are discussed.

THE TWIN DEFICITS OR NEGATIVE REVERSE CAUSALITY? A NONLINEAR APPROACH TO THE TURKISH BUDGET AND CURRENT ACCOUNT BALANCES

The budget deficit causing an increase in the current account deficit is named twin deficits. In addition, the budget and current account balances represent the internal and external balance of the economy. As in many developed and developing countries, revealing the relationship between internal and external imbalances in the Turkish economy in terms of determining economic policies is very important. Most of the studies on twin deficits in the literature are based on analyzes with linear models. The aim of this study, unlike other studies in the literature, is to examine the relationship between the budget and current account balance in the Turkish economy with non-linear time series analysis. For this purpose, nonlinear unit root and cointegration tests were applied to the data covering the period 1994-2021. The findings show that the negative reverse causality hypothesis is valid instead of the twin deficits hypothesis in the Turkish economy in the analyzed period. Accordingly, there is a negative relationship from the current account balance to the budget balance in both the long and short run.

High-Speed Multi-Layer Convolutional Neural Network Based on Free-Space Optics

Convolutional neural networks (CNNs) are at the heart of several machine learning applications, while they suffer from computational complexity due to their large number of parameters and operations. Recently, all-optical implementation of the CNNs has achieved many attentions, however, the recently proposed optical architectures for CNNs cannot fully utilize the tremendous capabilities of optical processing, due to the required electro-optical conversions in-between successive layers. To implement an all-optical multi-layer CNN, it is essential to optically implement all required operations, namely convolution, summation of channels’ output for each convolutional kernel feeding the nonlinear unit, nonlinear activation function, and finally, pooling operations. Considering the lack of multi-layer photonic CNN implementation, in this paper, we explore a fully-optical design for implementing successive convolutional layers in an optical CNN. As a proof of concept, and without loss of generality, we considered two successive optical layers in the proposed network, named as 2L-OPCNN, for comparative studies against electrical counterpart and single optical layer CNN. Our simulation results confirm nearly the same accuracies for classifying images of Kaggle Cats and Dogs challenge, CIFAR-10, and MNIST datasets, compared to the electrical counterpart, as well as improved accuracies compared to single optical layer CNN.

PDNet: Progressive denoising network via stochastic supervision on reaction-diffusion–advection equation

Recent works on residual network and its variants help us to advance our understanding of deep neural networks as differential equations. Specifically, when taking convolution operator as the combinations of differential operators, deep convolutional neural network (DCNN) can be regarded as partial differential equation (PDE). Learn such PDEs have become popular in image restoration especially for image denoising. While current methods for learning the denoising PDEs face two critical issues. On the one hand, the learned PDEs are not guaranteed to behave as progressive denoising as traditional denoising PDEs. On the other hand, the low level feature may diminish with time increases in PDE. To resolve these issues, this paper designs to learn a specialized PDE network (PDNet) which depicts the information propagation in the network as a reaction-diffusion–advection process. Specifically, a reaction-term is introduced to prevent the low-level features from diminishing in the PDE network, and a decreasing residual gain strategy with stochastic supervision is adopted to facilitate the progressive denoising property. The progressive denoising property not only reveals the semantic of the network path but also regularizes the network training. Compared to vanilla DCNNs, the PDNet has clear physical meaning. Meanwhile PDNet simplifies the ResNet in that batch normalization is removed from the residual blocks and there is only one nonlinear unit in a residual block (2 for ResNet). Extensive experimental results on benchmark datasets verified that PDNet is not only efficient but also effective.