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This study seeks to explore the nature of a data‐generating process for four dollar exchange rates.

Using a discrete parametric modeling approach, an efficient test statistic was computed for nonlinearity in terms of variance of the residuals of the linear and nonlinear autoregressive models by Akaike Information Criterion, and a surrogate data analysis was conducted.

It shows that a nonlinear autoregressive model outperforms a linear stochastic model in certain subsamples of baht, pound, ringgit, and yen dollar exchange rates. However, when the test statistics using different model orders and the data for the entire samples are estimated, it appears that the nonlinear model has a better performance than the linear model in fitting Thai and Malaysian currencies. The nonlinear model performs better than the linear model in the case of the UK pound in two thirds of the models, but the linear models completely outperform the nonlinear models for the yen data.

More financial and economic time series will be explored to employ the methodology used in the study, and tests for possible presence of nonlinear deterministic dynamics (chaos) in the exchange rates series will be conducted based on the present findings in further study.

These findings suggest that the assumption of linear stochastic process as the underlying dynamics for all currencies examined in this study may not be justifiable.

To the best of the authors' knowledge, this study is the first attempt to use the test statistic based on the information‐theoretical method in testing nonlinearity in financial and economic time series.

This survey focuses on two families of nonlinear vector time series models, the family of vector threshold regression (VTR) models and that of vector smooth transition regression (VSTR) models. These two model classes contain incomplete models in the sense that strongly exogeneous variables are allowed in the equations. The emphasis is on stationary models, but the considerations also include nonstationary VTR and VSTR models with cointegrated variables. Model specification, estimation and evaluation is considered, and the use of the models illustrated by macroeconomic examples from the literature.

The recent unprecedented levels reached by financial ratios have led to a re‐examination of their time‐series properties, with evidence of long memory and nonlinearity reported. The purpose of this paper is to re‐examine the nature of these series in the light of potential time‐variation in the unconditional mean.

The paper uses econometric techniques designed to capture fractional integration, nonlinearity and time‐variation in the unconditional mean level of a series.

Reported results support such time‐variation, with cyclical behaviour evident in the unconditional mean of each ratio. Evidence of nonlinearity is still apparent in the mean‐adjusted series.

A key result that arises is that accounting for this time‐variation appears to provide improved long horizon returns predictability.

The paper demonstrates that a nonlinear model incorporating a time‐varying mean improves returns predictability. This is of interest to market participants.

The present study is intended to develop an effective approach to the real-time modeling of general dynamic nonlinear systems based on the multidimensional Taylor network (MTN).

The authors present a detailed explanation for modeling the general discrete nonlinear dynamic system by the MTN. The weight coefficients of the network can be obtained by sampling data learning. Specifically, the least square (LS) method is adopted herein due to its desirable real-time performance and robustness.

Compared with the existing mainstream nonlinear time series analysis methods, the least square method-based multidimensional Taylor network (LSMTN) features its more desirable prediction accuracy and real-time performance. Model metric results confirm the satisfaction of modeling and identification for the generalized nonlinear system. In addition, the MTN is of simpler structure and lower computational complexity than neural networks.

Once models of general nonlinear dynamical systems are formulated based on MTNs and their weight coefficients are identified using the data from the systems of ecosystems, society, organizations, businesses or human behavior, the forecasting, optimizing and controlling of the systems can be further studied by means of the MTN analytical models.

MTNs can be used as controllers, identifiers, filters, predictors, compensators and equation solvers (solving nonlinear differential equations or approximating nonlinear functions) of the systems of ecosystems, society, organizations, businesses or human behavior.

The operating efficiency and benefits of social systems can be prominently enhanced, and their operating costs can be significantly reduced.

Nonlinear systems are typically impacted by a variety of factors, which makes it a challenge to build correct mathematical models for various tasks. As a result, existing modeling approaches necessitate a large number of limitations as preconditions, severely limiting their applicability. The proposed MTN methodology is believed to contribute much to the data-based modeling and identification of the general nonlinear dynamical system with no need for its prior knowledge.

In order to accurately forecast nonlinear and complex characteristics of solar power generation in China, a novel discrete grey model with time-delayed power term (abbreviated as TDDGM(1,1,tα) is proposed in this paper.

Firstly, the time response function is deduced by using mathematical induction, which overcomes the defects of the traditional grey model. Then, the genetic algorithm is employed to determine the optimal nonlinear parameter to improve the flexibility and adaptability of the model. Finally, two real cases of installed solar capacity forecasting are given to verify the proposed model, showing its remarkable superiority over seven existing grey models.

Given the reliability and superiority of the model, the model TDDGM(1,1,tα) is applied to forecast the development trend of China's solar power generation in the coming years. The results show that the proposed model has higher prediction accuracy than the comparison models.

This paper provides a scientific and efficient method for forecasting solar power generation in China with nonlinear and complex characteristics. The forecast results can provide data support for government departments to formulate solar industry development policies.

The main contribution of this paper is to propose a novel discrete grey model with time-delayed power term, which can handle nonlinear and complex time series more effectively. In addition, the genetic algorithm is employed to search for optimal parameters, which improves the prediction accuracy of the model.

The purpose of this paper is to present a new quantum‐inspired evolutionary hybrid intelligent (QIEHI) approach, in order to overcome the random walk dilemma for stock market prediction.

The proposed QIEHI method is inspired by the Takens' theorem and performs a quantum‐inspired evolutionary search for the minimum necessary dimension (time lags) embedded in the problem for determining the characteristic phase space that generates the financial time series phenomenon. The approach presented in this paper consists of a quantum‐inspired intelligent model composed of an artificial neural network (ANN) with a modified quantum‐inspired evolutionary algorithm (MQIEA), which is able to evolve the complete ANN architecture and parameters (pruning process), the ANN training algorithm (used to further improve the ANN parameters supplied by the MQIEA), and the most suitable time lags, to better describe the time series phenomenon.

This paper finds that, initially, the proposed QIEHI method chooses the better prediction model, then it performs a behavioral statistical test to adjust time phase distortions that appear in financial time series. Also, an experimental analysis is conducted with the proposed approach using six real‐word stock market times series, and the obtained results are discussed and compared, according to a group of relevant performance metrics, to results found with multilayer perceptron networks and the previously introduced time‐delay added evolutionary forecasting method.

The paper usefully demonstrates how the proposed QIEHI method chooses the best prediction model for the times series representation and performs a behavioral statistical test to adjust time phase distortions that frequently appear in financial time series.

I review the burgeoning literature on applications of Markov regime switching models in empirical finance. In particular, distinct attention is devoted to the ability of Markov Switching models to fit the data, filter unknown regimes and states on the basis of the data, to allow a powerful tool to test hypotheses formulated in light of financial theories, and to their forecasting performance with reference to both point and density predictions. The review covers papers concerning a multiplicity of sub-fields in financial economics, ranging from empirical analyses of stock returns, the term structure of default-free interest rates, the dynamics of exchange rates, as well as the joint process of stock and bond returns.

In this study, the performance of ordinal GA-based trading strategies is evaluated under six classes of time series model, namely, the linear ARMA model, the bilinear model, the ARCH model, the GARCH model, the threshold model and the chaotic model. The performance criteria employed are the winning probability, accumulated returns, Sharpe ratio and luck coefficient. Asymptotic test statistics for these criteria are derived. The hypothesis as to the superiority of GA over a benchmark, say, buy-and-hold, can then be tested using Monte Carlo simulation. From this rigorously-established evaluation process, we find that simple genetic algorithms can work very well in linear stochastic environments, and that they also work very well in nonlinear deterministic (chaotic) environments. However, they may perform much worse in pure nonlinear stochastic cases. These results shed light on the superior performance of GA when it is applied to the two tick-by-tick time series of foreign exchange rates: EUR/USD and USD/JPY.

The 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.

The 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).

Linearity 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.

Numerous 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.

The purpose of this paper is to propose a comprehensive version of a hybrid autoregressive integrated moving average (ARIMA), and artificial neural networks (ANNs) in order to yield a more general and more accurate hybrid model for exchange rates forecasting. For this purpose, the Kalman filter technique is used in the proposed model to preprocess and detect the trend of raw data. It is basically done to reduce the existing noise in the underlying data and better modeling, respectively.

In this paper, ARIMA models are applied to construct a new hybrid model to overcome the above-mentioned limitations of ANNs and to yield a more general and more accurate model than traditional hybrid ARIMA and ANNs models. In our proposed model, a time series is considered as a function of a linear and nonlinear component, so, in the first phase, an ARIMA model is first used to identify and magnify the existing linear structures in data. In the second phase, a multilayer perceptron is used as a nonlinear neural network to model the preprocessed data, in which the existing linear structures are identified and magnified by ARIMA and to predict the future value of time series.

In this paper, a new Kalman filter based hybrid artificial neural network and ARIMA model are proposed as an alternate forecasting technique to the traditional hybrid ARIMA/ANNs models. In the proposed model, similar to the traditional hybrid ARIMA/ANNs models, the unique strengths of ARIMA and ANN in linear and nonlinear modeling are jointly used, aiming to capture different forms of relationship in the data; especially, in complex problems that have both linear and nonlinear correlation structures. However, there are no aforementioned assumptions in the modeling process of the proposed model. Therefore, in the proposed model, in contrast to the traditional hybrid ARIMA/ANNs, it can be generally guaranteed that the performance of the proposed model will not be worse than either of their components used separately. In addition, empirical results in both weekly and daily exchange rate forecasting indicate that the proposed model can be an effective way to improve forecasting accuracy achieved by traditional hybrid ARIMA/ANNs models.

In the proposed model, in contrast to the traditional hybrid ARIMA/ANNs, it can be guaranteed that the performance of the proposed model will not be worse than either of the components used separately. In addition, empirical results in exchange rate forecasting indicate that the proposed model can be an effective way to improve forecasting accuracy achieved by traditional hybrid ARIMA/ANNs models. Therefore, it can be used as an appropriate alternate model for forecasting in exchange ratemarkets, especially when higher forecasting accuracy is needed.