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The purpose of this study is to examine the accuracy of combined models with the individual models in terms of forecasting Euro against US dollar during COVID-19 era. During COVID, the euro shows sharp fluctuation in upward and downward trend; therefore, this study is keen to find out the best-fitted model which forecasts more accurately during the pandemic.

The descriptive design has been adopted in this research. The three univariate models, i.e. autoregressive integrated moving averages (ARIMA), Naïve, exponential smoothing (ES) model, and one multivariate model, i.e. nonlinear autoregressive distributive lags (NARDL), are selected to forecast the exchange rate of Euro against the US dollar during the COVID. The above models are combined via equal weights and var-cor methods to find out the accuracy of forecasting as Poon and Granger (2003) showed that combined models can forecast better than individual models.

NARDL outperforms all remaining individual models, i.e. ARIMA, Naïve and ES. By applying a combination of different models via different techniques, the combination of NARDL and Naïve models outperforms all combination of models by scoring the least mean absolute percentage error value, i.e. 1.588. The combined forecasting of NARDL and Naïve techniques under var-cor method also outperforms the forecasting accuracy of individual models other than NARDL. It means the euro exchange rate against the US dollar which is dependent upon the macroeconomic fundamentals and recent observations of the time series.

The findings could help the FOREX market, hedgers, traders, businessmen, policymakers, economists, financial managers, etc., to minimize the risk indulged in global trade. It also helps to produce more accurate results in different financial models, i.e. capital asset pricing model and arbitrage pricing theory, because their findings may not be useful if exchange rate fluctuations do not trace effectively.

The NARDL models have been applied previously in different time series and only limited to the asymmetric or symmetric relationships. This study is using it for the forecasting exchange rate which is almost abandoned in earlier literature. Furthermore, this study combined the NARDL with univariate models to produce the accuracy which itself is a novelty. Moreover, the findings help to enhance the effectiveness of different financial theories as well.

This paper aims to investigate the determinants of bilateral exports of India to the USA by taking the non-linearity issue in export demand equations which is neglected so far in the empirical work. The study tries to know the reaction of change in exports to exchange rate changes in a non-liner fashion. For this purpose, non-linear autoregressive distributed lag (NARDL) bounds testing approach of Shin et al. (2011) has been used. This approach allows testing for non-linearities both in the short and long run, which might give indications of strategic pricing and non-linearities in exchange rate. The empirical analysis is carried out for bilateral export demand relationships of India with the USA for the period from January 1993 until December 2013. The overall results show that exports are determined in the long run by foreign demand, exchange rates and relative prices. The assumed linearity in export demand functions might be too restrictive. Thereby, the one threshold model that distinguishes exchange rate effects between appreciations and depreciations delivers plausible results. If exchange rate non-linearities are detected, it would seem that exports respond stronger to appreciations than to depreciations. A reason for this might be that firms perform strategic pricing in international trade to gain or maintain market shares.

The paper uses the newly developed non-linear ARDL framework of Shin et al. (2011) to investigate whether there are non-linearities with respect to the exchange rate for India’s exports to the USA. One of the important features of this framework is that it is free from unit root pre-testing and can be applied regardless of whether variables are I(0) or I(1). In addition, ARDL and NARDL technique efficiently determines the cointegrating relation in small sample. The short-run and long-run parameters with appropriate asymptotic inferences can be obtained by applying OLS to NARDL with an appropriate lag length. Following is the NARDL representation of equation 4(a) and 4(b). For brevity, this is illustrated for 4(a) only, where is the first difference operator, P is the drift component and it is the white noise residual, the coefficients ?_1 to ?_4 represent the long-run relationship, whereas remaining expressions with summation sign represent the short-term dynamics of the model. This equation nests the linear ARDL model presented in Pesarean et al. (2001) for the case of d_k^+=d_k^-and ?_2=?_3for all k. Thus, equation is less restrictive than a linear model. For this test, as its distribution is non-standard, Pesarean et al. (2001) tabulate the critical values. The bound test is used to examine the existence of the long-run relationship among the variables in the system. This test is based on Wald/F-statistic and follows a non-standard distribution. To check whether a cointegrating relationship exists, one has to test the null hypothesis ?_1=?_2=?_3=?_4 = 0 in the equation. Pesarean et al. (2001) provide two sets of critical values in which lower critical bound assumes that all the variables in the ARDL are I(0) and upper critical bound assumes I(1). The null hypothesis of cointegration is rejected if the calculated F-statistics is greater than the upper bound critical values. If the F-statistics is below than the lower critical bound, then null hypothesis cannot be rejected; this indicates no cointegration among the variables. If it lies within the lower and upper bounds, the result is inconclusive. After examining the cointegration, long-run coefficients are calculated by estimating the model with the appropriate lag orders based on the Schwarz Information Criteria (SIC). Further, the short-run dynamics of the model is also analyzed by using unrestricted error correction model based on the assumption made by Pesarean et al. (2001). Thus, the error correction version of the NARDL model pertaining to the central export equation can be expressed as: 10; 10, where ? is the speed of adjustment parameter, and EC is the residuals that are obtained from the estimated cointegration model of equation 4(a). The EC term is expressed as 10; 10, where are the OLS estimators obtained from the equation (5a). The coefficients of the lagged variables provide the short-run dynamics of the model covering the equilibrium path. The error correction coefficient ( ) is expected to be less than zero, and its significant value implies the cointegration relation among the variables. Finally, various tests such as serial correlation, functional form, normality and heteroskedasticity have been conducted to check the performance of the model.

Many empirical studies have estimated the elasticities of different final export demand components with respect to the exports because of their importance in trade policy formulation. But all the work has accounted only linearity in the exchange rate in export demand equation. Hence, in this paper, we tried to estimate non-linearities in export demand equation. The study fills the gap in the literature by improving on existing literature with the incorporation of the newly developed NARDL approach of Shin et al. (2011). This approach allows testing for non-linearities both in the short- and in the long run which might give indications of strategic pricing and non-linearities in exchange rate. The empirical analysis is carried out for bilateral export demand relationships of India with the USA for the period from January 1993 until December 2013. The bound test shows that there exists cointegration among the variables. Results show that exports are determined in the long run by foreign demand, exchange rates and relative prices. The long-run coefficients have got the expected sign and are of reasonable magnitude and statistically significant. Regarding non-linearities, the results show that assuming linearity in export demand functions might be too restrictive. Thereby, the one threshold model that distinguishes exchange rate effects between appreciations and depreciations deliver plausible results. If exchange rate non-linearities are detected, it seems that exports respond stronger to appreciations than to depreciations. A reason for this might be that firms perform strategic pricing in international trade to gain or maintain market shares.

The originality of this paper lies in the fact that it applies NARDL approach to Indian trade data (export demand) and analyzes the asymmetrical and non-linear impact of exchange rate changes on Indian exports.

The COVID-19 pandemic and the onset of the conflict in Ukraine led to a sustained downturn in tourist arrivals (TA) in Russia. This paper aims to explore the influence of geopolitical risk (GPR) and other indices on TA over 1995–2023.

We employ a nonlinear autoregressive distributed lag (NARDL) model to analyze the effects, capturing both the positive and negative shocks of these variables on TA.

Our research demonstrates that the NARDL model is more effective in elucidating the complex dynamics between macroeconomic factors and TA. Both an increase and a decrease in GPR lead to an increase in TA. A 1% negative shock in GPR leads to an increase in TA by 1.68%, whereas a 1% positive shock in GPR also leads to an increase in TA by 0.5%. In other words, despite the increase in GPR, the number of tourists coming to Russia increases by 0.5% for every 1% increase in that risk. Several explanations could account for this phenomenon: (1) risk-tolerant tourists: some tourists might be less sensitive to GPR or they might find the associated risks acceptable; (2) economic incentives: increased risk might lead to a depreciation in the local currency and lower costs, making travel to Russia more affordable for international tourists; (3) niche tourism: some tourists might be attracted to destinations experiencing turmoil, either for the thrill or to gain firsthand experience of the situation; (4) lagged effects: there might be a time lag between the increase in risk and the actual impact on tourist behavior, meaning the effects might be observed differently over a longer period.

Our study, employing the NARDL model and utilizing a dataset spanning from 1995 to 2023, investigates the impact of GPR, gross domestic product (GDP), real effective exchange rate (REER) and economic policy uncertainty (EPU) on TA in Russia. This research is unique because the dataset was compiled by the authors. The results show a complex relationship between GPR and TA, indicating that factors influencing TA can be multifaceted and not always intuitive.

This study aims to analyze the effect of cryptocurrency capitalization market development on bank deposits variability in the United Arab Emirates (UAE) spanning the period 2005M1–2020M4 using the novel nonlinear autoregressive distributive lag (NARDL).

The study employs the NARDL recently developed by Shin et al. (2014) to estimate the long and short-run relationships between the variables rather than the widely known ARDL (Pesaran et al., 2001), which suffers from a complex structure in the estimation equation that usually includes lags and differences in both short and long terms. The implementation of NARDL required several proceedings after plotting the descriptive data, commencing with unit root tests, selection of lag length, estimating the long-and-short variables coefficients, heteroscedasticity test and Wald test for symmetries.

The long-run estimations of the positive and negative asymmetric coefficients indicate that cryptocurrencies capitalization has a negative impact on bank deposits in the UAE. Further, the short-run estimations coefficients exhibit that both significant positive and negative partial sum squares of cryptocurrencies decrease bank deposits.

The study has applied to the UAE spanning the period 2005M1–2020M4 using the NARDL.

The short-run estimations coefficients exhibit that both significant positive and negative partial sum squares of cryptocurrencies decreases bank deposits, which means that the increase in the magnitude of cryptocurrencies capitalization stimulates depositors and speculators to adjust their portfolios towards contracting their deposits in banks to invest partially in cryptocurrencies, on the other hand, the decline in cryptocurrencies capitalization process spur depositors and speculators to reduce their deposits for purchasing cryptocurrencies at lower prices.

The study infers that individuals and businesses are cautious when investing in cryptocurrencies, and they need more certainty and trust to include these types of assets in their portfolios. The fluctuation in cryptocurrencies capitalization prompts speculators to change their deposits according to the cryptocurrencies' prices.

This study explores the short-and long-run asymmetric impacts of cryptocurrencies capitalization development on bank deposits volatility in the UAE, based on a NARDL, for providing a manifest depiction of whether the cryptocurrencies industry might be a threat to conventional banking system performance in the potential future.

This study aims to examine the impact of some real variables such as real effective exchange rates, real mortgage rates, real money supply, real construction cost index and housing sales on the real housing prices.

This study uses a nonlinear autoregressive distributed lag (NARDL) model in the monthly period of 2010:1–2021:10.

The real effective exchange rate has a positive and symmetric effect. The decreasing effect of negative changes in real money supply on real housing prices is higher than the increasing effect of positive changes. Only positive changes in the real construction cost index have an increasing and statistically significant effect on real house prices, while only negative changes in housing sales have a small negative sign and a small increasing effect on housing prices. The fact that the positive and negative changes in real mortgage rates are negative and positive, respectively, indicates that both have a reducing effect on real housing prices.

This study suggests the first NARDL model that investigates the asymmetric effects on real housing prices instead of nominal housing prices for Turkey. In addition, the study is the first, to the best of the authors’ knowledge, to examine the effects of the five real variables on real housing prices.

Effective agricultural product price regulation policies depend on market integration and the degree of symmetry in the transmission of agricultural product price signals. This study analyzes the transmission and asymmetry of the price series between the Ouagadougou consumer market and assembly markets considering three primary cereal products in Burkina Faso.

This study applies the nonlinear autoregressive distributed lag (NARDL) econometric model, which is an asymmetric extension of the ARDL cointegration model. The price series examined covers the period extending from January 2005 to December 2020.

Our analysis provides novel insights regarding short- and long-term asymmetric effects in the transmission of price signals between assembly markets and the consumer market. We also determine that the effects of negative shocks are more persistent than those of positive shocks in several markets.

For markets that exhibit symmetrical responses of assembly market prices to consumer market prices, the results could reflect the continuous efforts of market players, particularly the government, to eliminate market failures and ensure the long-term efficiency of cereal markets. To this end, an agricultural market information system can have a crucial role in easing information access for all market players.

This study provides new evidence regarding the nature of the transmission and asymmetry of price information on primary cereal products in the largest markets in Burkina Faso. Applying the NARDL model makes it possible to simultaneously estimate short- and long-term asymmetry.

This study aims to critically examine the pricing of Islamic financial assets (Sharīʿah-compliant assets, Sharīʿah-compliant securities, Sharīʿah-compliant financing and Sukuk) in the three South-East Asia countries such as Malaysia, Indonesia and Brunei to provide necessary information to the policymakers and Islamic finance investors for making a sound decision.

This study used secondary data and used the nonlinear autoregressive distributed lags (NARDL) model to estimate the reaction of Islamic financial assets in South-East Asia towards price changes. Wald-test was used to diagnose the final model.

The result of this study shows that the majority of Islamic financial assets in the three South-East Asia countries exhibit positive and negative long-run effects. The findings reveal a long-run asymmetric relationship that supports rockets and feathers effects. The indication is that Islamic financial assets pricing deviates from weak form EMH. Pricing of Islamic financial assets reveals unfair pricing.

Price adjustment of Islamic financial assets requires urgent attention of policymakers to prevent Sharīʿah non-compliant risk. Therefore, the Shariah advisory board in those countries, Accounting and Auditing Organization for Islamic Financial Institutions and Islamic Financial Services Board are hereby advised to act on the factors that might enable rockets and feathers effects on the pricing of Islamic financial assets, as the long-run asymmetric relationship is established.

This study is novel as it critically and simultaneously examines the pricing behaviour of Islamic financial assets in the three South-East Asian countries. The findings from the study provide vital information on the pricing behaviour of Islamic financial assets to the policymakers and investors.

Oil is crucial for industrial development. This paper investigates the impacts of oil price changes on China's industrial growth and examines whether the impacts are asymmetric. The estimations can help determine how oil price shocks are transmitted throughout the economy.

This paper adopts West Texas Intermediate (WTI) crude oil price and industrial sector output and uses monthly data. The recently developed nonlinear autoregressive distributed lag (NARDL) model is employed to illustrate the effects in both the short term and long term. Importantly, under NARDL framework, this paper examines whether the impacts are asymmetric by decomposing oil price shocks into their positive and negative partial sums.

The empirical results prove clear evidence of asymmetries in the short term, long term or both terms. Specifically, some sectors benefit from, rather than suffer from higher oil prices, even some energy-intensive sectors, i.e. C31 (Smelting and Pressing of Ferrous Metals) and C32 (Smelting and Pressing of Non-ferrous Metals). However, the effects on some other energy-intensive sectors appear insignificant. Additionally, the results prove significantly negative responses in some sectors in the long term, and most of these sectors are in the top half of the ranking by energy consumptions.

This paper studies the economic responses at a disaggregated level by employing industry-level data. NARDL method is used to decompose oil price changes into their increases and decreases and investigate the asymmetries in the impacts of oil price changes.

Within a multivariate framework, this study examines the asymmetric and threshold impact of external debt on economic growth in Egypt during the period 1980–2019.

The paper uses a nonlinear autoregressive distributed lag (NARDL) bounds testing approach to cointegration and a vector error-correction model to estimate the short- and long-run parameters of equilibrium dynamics. A multiple structural breaks model is estimated to test nonlinearity in the relationship between external debt and economic growth.

Results of the NARDL model show a robust statistically significant negative long-run impact on economic growth stemming from both positive and negative external-debt-induced shocks. In terms of magnitude, on the one hand, the impact of external-debt-induced negative shocks exceeds that of the positive. In the short and long run, on the other hand, the growth impact of external debt in Egypt is symmetric. There is also support for the nonlinearity hypothesis in which a negative impact on growth of external debt obtains once the threshold level of external debt-to-GDP ratio equals or exceeds 96.7%.

Identifying the threshold level after which external debt becomes harmful to economic growth would help inform policymakers in Egypt about maximum external debt levels that can be sustained without impairing economic growth.

The current study makes a substantial contribution to the extant literature on the debt-growth tradeoffs. It breaks ground by being the first tract that examines, using a NARDL model, asymmetry and nonlinearity of debt-growth tradeoffs in Egypt.

The primary purpose of the study is to analyse the asymmetric effects of public debt on economic growth, using secondary data over the period 1980–2018 in South Africa.

This study estimated a Smooth Transition Regression (STAR) and Nonlinear Autoregressive Distributed Lag (NARDL) approach, using time series data to analyse the asymmetric effect of public debt on economic growth in South Africa.

The findings revealed a significant nonlinear relationship between public debt and economic growth in South Africa. The results showed an inverted U-Shape relationship, implying a significant positive influence of public debt on economic growth during the low-debt regime. While during a high-debt regime, public debt exerted a significant negative effect on economic growth. The study proposes that policymakers ought to consider targeting a sustainable debt threshold that would enhance efficient use of public finances consistent with long-term economic prosperity.

This paper asymmetries and threshold effects between public debt and economic growth in South Africa, through the application of dynamic nonlinear models namely, Smooth Transition Regression (STAR) and Nonlinear Autoregressive Distributed Lag (NARDL) approach. Studies on the relationship under examination have predominantly been confined in advanced economies. This study provides rigorous empirical evidence from the South African perspective.