## What is/are Cointegration Analysis?

Cointegration Analysis - Cointegration analysis and VAR model are used in this paper to estimate the effects of the determinants of the credit spreads in the long-run and in the short-run respectively.^{[1]}We apply a novel approach, as we extend the cointegration analysis by combining it with structural break tests.

^{[2]}For the robustness of cointegration analysis, the authors also employ ARDL bound testing in the presence of structural break years.

^{[3]}By using cointegration analysis, our results suggest that there are both long-run and short-run relationships between loss of employment and lockdown measures in Malaysia.

^{[4]}This article explores the correlation between the two stages and different modes of transportation through coupling analysis, cointegration analysis, and gray correlation analysis based on the data from 1989 to 2018 of freight transportation volume and GDP.

^{[5]}Cointegration analysis was performed to test whether all variables are cointegrated in the long term.

^{[6]}The empirical design builds upon four well-known approaches to implement pairs trading, namely: correlation analysis, distance approach, stochastic return differential approach, and cointegration analysis, that use monthly closing prices of leading cryptocoins over the period January 1, 2018, – December 31, 2019.

^{[7]}This study investigates the association between economic growth and tourism in Sri Lanka using cointegration analysis for the period 1980 to 2019.

^{[8]}We establish that the index generates insights into time series dynamics which are complementary to those obtained from cointegration analysis.

^{[9]}Then, the cointegration analysis (CA), dynamic principal component analysis (DPCA) and dynamic independent component analysis (DICA) models are singled out to monitor the abnormities in the three subspaces, respectively.

^{[10]}This study’s principal objective was to examine the effect of railway lines on economic growth using annual data from 1980 to 2016 and cointegration analysis.

^{[11]}The authors relied on the cointegration analysis of time series using the Engle-Granger tests, the analysis of the stationarity of the Dickey-Fuller methods in order to determine cointegration, to assess the degree of interrelation between the values of mining and manufacturing production volumes on GDP indicators, as evidence of the presence of "Dutch disease".

^{[12]}The cointegration analysis, based on the ARDL, GregoryeHansen, and combined cointegration tests, confirms the existence of long-run relationships between mining and all sustainable development dimensions.

^{[13]}To assess if there a cyclic relationship between the daily number of molecular tests and daily COVID-19 cases in Colombia, we executed a cointegration analysis and evaluated the hypothesis with an augmented Dickey-Fuller (ADF) test.

^{[14]}Finally, we subject these global probability time paths to a cointegration analysis with CO2 concentration and run projections to year 2040 of the GPOD conditional on nine Shared Socioeconomic Pathways scenarios.

^{[15]}The fundamental innovation of the approach is that it offers an alternative to cointegration analysis, which reduces the implicit assumption of the singular adjustment in cointegration analysis.

^{[16]}We focus on the use of neural networks in combination with techniques of cointegration analysis to map swap rate projections derived from given scenarios (e.

^{[17]}The authors apply methods of cointegration analysis, scenario modeling, substantiation of the studied patterns by methods of regression analysis, etc.

^{[18]}Cointegration analysis and error correction modeling are used to determine the long run as well as short run dynamics, between real exchange rate and trade balance.

^{[19]}The adequacy of the time series econometric model was checked through cointegration analysis and found that there is no spurious regression.

^{[20]}The following methods were used: the unit root test—for checking the stationarity of data—and the Johansen test and VEC-modelling—for the cointegration analysis.

^{[21]}Complex models have been implemented to monitor the key CHS development indices based on the phase and cointegration analysis of the relationship between the following processes: investment and GDP; GDP and industrial production dynamics; GDP dynamics and import volumes dynamics; wages dynamics and industrial production dynamics; migration and natural population growth.

^{[22]}Despite the fact that the study employed data concerning a forty-year time period, the cycles of deviations from the balance path take too long to be able to demonstrate the stationarity of residuals in the cointegration analysis.

^{[23]}A cointegration analysis of panel time series was estab-lished by applying econometric tests and the cointegration equation for the period 1999–2018 was estimated using FMOLS (Fully Modified OLS) and DOLS (Dynamic OLS) estimators.

^{[24]}In fact, the first results of cointegration analysis show that there is no evidence that financial derivative instruments determine the fluctuation of wheat future price.

^{[25]}According to the results obtained from cointegration analysis and causality tests, the variables analyzed move together in the long-run.

^{[26]}PLS Test, Pesaran (2004) CD-Test, Pesaran (2007) Unit Root Test, Swamy S Homogeneity Test conducted before causality and cointegration analysis.

^{[27]}To base the analyses, the ADF test for unit root, cointegration analysis, and Granger causality have been employed.

^{[28]}Cointegration analysis-based fault detection model is built to investigate the relationship between nonstationary variables, which can effectively distinguish the incipient fault from the normal trend of the nonstationary variables.

^{[29]}The fault-common model is constructed by cointegration analysis to capture the common nonstationary fault variations, and fault-specific model is built to explain the specific fault variations of each fault.

^{[30]}To achieve this aim, cointegration analysis under the VECM approach is applied.

^{[31]}Cointegration analysis of Johansen-Juselius with daily data from January 2008 to December 2018 suggests that there is one cointegrating vector as per the Trace statistic.

^{[32]}In addition to causality relation, according the cointegration analysis, oil prices and GDP increase the CAD in the long run.

^{[33]}The dual adjustment approach provides an alternative to the cointegration analysis for some cases, e.

^{[34]}This article illustrates the dynamics of and tradeoff between inflation and output in Pakistan by utilizing data on 18 major trading partners in a cointegration analysis.

^{[35]}Principal components and cointegration analysis further suggest digitalization is a key driver of lower trend inflation.

^{[36]}The Heij coefficient was used to calculate the dynamic multipliers while the Engel & Granger two-step technique was used for cointegration analysis.

^{[37]}Then, empirical analysis carried out under the probabilistic approach to econometric modeling shows statistical evidence, estimated through cointegration analysis, that in the long run, in three very open economies—Mexico, France, and Korea—the wage share is positively associated with demand and output.

^{[38]}Before we estimated panel regression model, we did a stationarity and cointegration analysis of sample data.

^{[39]}We address the question of whether European electricity markets have experienced convergence patterns in recent years, using the stochastic definitions of convergence and common trend based on cointegration analysis.

^{[40]}Cointegration analysis and the vect.

^{[41]}Subsequently, the series purged of seasonality will be fed into a cointegration analysis, in order to produce a more stationary residual series (damage indicator series).

^{[42]}Empirical studies have been done using cointegration analysis and causality test to justify the relationship and causality of the variables.

^{[43]}Hence, this study examines the long run and short run effect of corruption on public debt in Nigeria over the period of 1996 to 2017 using ARDL bound test to cointegration analysis.

^{[44]}Both avenues analyse the mean-reverting behaviour of the current account balance using Fourier unit root and cointegration analysis which can scrutinise an unknown number of structural breaks, capture sharp breaks, and approximates them as smooth gradual processes.

^{[45]}For the cointegration analysis, an autoregressive distributive lag methodology and the recent novel Bayer and Hanck combined cointegration technique are employed.

^{[46]}The objective of this article is to examine the market integration among the BRICS (Brazil, Russia, India, China, and South Africa) emerging markets with respect to the global financial crisis of 2008 using cointegration analysis and factor analysis.

^{[47]}Since the series are not stationary, cross-dependence tests and Westerlund (2007) cointegration analysis are performed to the series and it is determined that the series are cross-dependent and cointegrated.

^{[48]}The cointegration analysis is used to evaluate the co-movement of a long-term equilibrium relationship among the four stock market indices.

^{[49]}Cointegration analysis is performed for aggregate, male and female time-series.

^{[50]}

## autoregressive distributed lag

We use a cointegration analysis and estimate an autoregressive distributed lag model using quarterly data (1973: q1-2020: q1).^{[1]}We use a panel cointegration analysis and compute an autoregressive distributed lag model.

^{[2]}It examines the relationship between environmental sustainability, gender equality in education, energy consumption, and sub-Saharan Africa’s income by using cointegration analysis and autoregressive distributed lag (ARDL) method.

^{[3]}This study is positioned to explore the case of Nigeria by examining the impact of micro-credit lending to Small Scale Enterprises on economic advancement in Nigeria over the period 1992–2019, using the autoregressive distributed lag approach to cointegration analysis.

^{[4]}It employs panel cointegration analysis and estimate an autoregressive distributed lag model.

^{[5]}A panel cointegration analysis, specifically an autoregressive distributed lag model, is used to achieve the paper’s goal.

^{[6]}The research involves cointegration analysis to test the existence of a long-term equilibrium relationship between the variables included in tourism demand using the autoregressive distributed lag bounds testing approach.

^{[7]}Cointegration analysis is investigated using the autoregressive-distributed lag bounds (ARDL Bounds) test and vector autoregressive cointegration.

^{[8]}This study examines the effects of insurance activity on per capita income in the case of a southern Mediterranean country (Jordan) over the period 1990-2017 using an Autoregressive Distributed Lag (ARDL) cointegration analysis to describe the dynamic long relationship between per capita income and insurance activity.

^{[9]}(Journal of Applied Econometrics 16:289–326, 2001) to analyse the cointegration relationship and the autoregressive distributed lag (ARDL) modelling approach of Pesaran and Shin (An autoregressive distributed lag modeling approach to cointegration analysis.

^{[10]}

## vector error correction

The ARDL methodology approach to cointegration analysis and vector Error Correction model were adopted to examine the equilibrium relationship and direction of causality respectively.^{[1]}It makes use of panel cointegration analysis and long-run vector error correction model analysis in assessing both the short-run and the long-run relationship dynamics between NGC and economic growth.

^{[2]}Based on cointegration analysis, a vector error correction model (VECM), and the impulse response function method, this paper empirically analyses the interaction among urban expansion, economic development, and population growth in China from 1980 to 2016.

^{[3]}Methodology: We applied a cointegration analysis using Pedroni and Johansen test and vector error, correction models as well as causality Granger test.

^{[4]}Research Methodology: Secondary data from 1980 to 2017 were collected and analysed using the Johansen Cointegration analysis and vector error correction model.

^{[5]}Unit root tests were conducted, followed by cointegration analysis, leading to Granger causality test and vector error correction model.

^{[6]}We compiled annual data for the period from 1965 to 2016 and we adopted an empirical methodology based on the cointegration analysis and on Vector Error Correction Models.

^{[7]}

## error correction model

Econometrics estimations, including ARDLcointegration analysis, parsimonious error correction model, and other post estimation tests, were used to analyze the study data.^{[1]}This paper examines aggregate supply response of 19 selected crops in Algerian agriculture during the 1966-2018 period by employing cointegration analysis and error correction model (ECM).

^{[2]}We perform a cointegration analysis and empirical verification of the error correction model, where PRIBOR interest rates and the actual and expected development of the CZK/EUR spot rate act as endogenous variables.

^{[3]}The study used a variety of methods based on the cobb-Douglus production function, the Koyck geometrical lag model, cointegration analysis, error correction model and causality analysis.

^{[4]}The research analyzes the RTA projects that enable Dubai to include elements of the smart city which imply the potential technological aspects, as well as providing an econometrics analysis by using cointegration analysis and error correction model.

^{[5]}By means of an Error Correction Model (ECM), a cointegration analysis was conducted to visualize the stable, long-term relationship between the consumption of financial products and changes in the age structure of the population.

^{[6]}In our study, Johansen cointegration analysis and error correction model (VEC) were used and it was concluded that there was a statistically significant and positive relationship between the variables according to the findings.

^{[7]}

## unit root test

Using ADF unit root test, cointegration analysis and Granger’s causality test, this paper empirically studies the relationship between the real effective exchange rate of RMB and the consumption trade imports, total trade imports and import trade structure from 1997 to 2019.^{[1]}Then, the following econometric tests were performed on the variables representing FDI inflows, exports, and GDP as proxies for FDI, trade, and economic growth: the unit root test; the unit root test with a structural break; Johansen cointegration analysis; the error correction model; and the Granger causality test.

^{[2]}In contributing to this ongoing debate, the study applied unit root tests, cointegration analysis, a dynamic vector error correction model and Toda-Yamamoto Granger-causality representation using annual time series data for Kenya from 1980 to 2016.

^{[3]}Before the cointegration analysis, the stationarities of the series were determined with Carrion-i Silvestre (2009) (CS) unit root test, which allowed up to five structural breaks.

^{[4]}Methodology: The study employs unit root tests, Johansen cointegration analysis, a dynamic vector error correction model and a multivariate Toda-Yamamoto Granger-causality representation.

^{[5]}Subsequently, the stationarity status of the study underlines series were examined with a conventional unit root test and the Pesaran’s bounds test for cointegration analysis.

^{[6]}

## cross sectional dependence

Design/methodology/approachThe main approach is panel cointegration analysis that allows to overcome certain data restrictions such as spatial heterogeneity, cross-sectional dependence, and non-stationary, but cointegrated data.^{[1]}This model consists of panel cointegration analysis considering the cross-sectional dependence, applied to quantify the effects of environmental taxes on environment-related technological innovation in high and middle-income 42 countries from 1995 to 2018.

^{[2]}For analysis purposes, this research considers cross-sectional dependence analysis, unit root test with and without structural break (Pesaran, 2007), slope heterogeneity analysis, Westerlund and Edgerton (2008) panel cointegration analysis, Banerjee and Carrion-i-Silvestre (2017) cointegration analysis, long-short run CS-ARDL results, as well as AMG and CCEMG for robustness check.

^{[3]}Using an updated set of quarterly data from 1975 to 2018, we perform panel cointegration analysis allowing for cross-sectional dependence.

^{[4]}

## long run relationship

Design/methodology/approach: By using time series data, this study employs Pedroni’s panel cointegration analysis to test the long run relationship between financial stability of conventional banks and Islamic banks as a dependent variable and independent variables including financial crisis under three periods; pre (2006-2007), during (2008-2009) and post (2010-2011) crisis.^{[1]}A multivariate cointegration analysis is developed and results reveal a potent and long run relationship exists, thus error correction model constructed to trace both the short and the long run behaviour among variables of the model.

^{[2]}

## Panel Cointegration Analysis

Current study is based on panel cointegration analysis, FGLS and FMOLS techniques, where the renewable energy consumption is given as a function of export diversification, economic growth, industrialization, trade openness and natural resources.^{[1]}Design/methodology/approachThe main approach is panel cointegration analysis that allows to overcome certain data restrictions such as spatial heterogeneity, cross-sectional dependence, and non-stationary, but cointegrated data.

^{[2]}Based on World Bank data, the panel cointegration analysis reveals that renewable energy consumption and economic growth are positively associated in the long run in CEE countries.

^{[3]}We use a panel cointegration analysis and compute an autoregressive distributed lag model.

^{[4]}Panel unit roots and panel cointegration analysis were conducted on the study.

^{[5]}This model consists of panel cointegration analysis considering the cross-sectional dependence, applied to quantify the effects of environmental taxes on environment-related technological innovation in high and middle-income 42 countries from 1995 to 2018.

^{[6]}It employs panel cointegration analysis and estimate an autoregressive distributed lag model.

^{[7]}Panel unit roots and panel cointegration analysis were conducted on the study.

^{[8]}First, the cross-sectional dependency, stationarity and the homogeneity of the series are examined; second, a panel cointegration analysis is implemented; third, long-term panel cointegration coefficients are analyzed with Dynamic Common Correlated Effects (DCCE) approach; and, finally, Dumitrescu and Hurlin’s (2012) Granger non-causality test is used to detect the causality.

^{[9]}For analysis purposes, this research considers cross-sectional dependence analysis, unit root test with and without structural break (Pesaran, 2007), slope heterogeneity analysis, Westerlund and Edgerton (2008) panel cointegration analysis, Banerjee and Carrion-i-Silvestre (2017) cointegration analysis, long-short run CS-ARDL results, as well as AMG and CCEMG for robustness check.

^{[10]}A panel cointegration analysis, specifically an autoregressive distributed lag model, is used to achieve the paper’s goal.

^{[11]}Using an updated set of quarterly data from 1975 to 2018, we perform panel cointegration analysis allowing for cross-sectional dependence.

^{[12]}Panel unit roots and panel cointegration analysis were conducted on the study.

^{[13]}It makes use of panel cointegration analysis and long-run vector error correction model analysis in assessing both the short-run and the long-run relationship dynamics between NGC and economic growth.

^{[14]}With the assumption of a Harrod-neutral technological progress and panel cointegration analysis, the results give evidence to suggest that capital accumulation contributes more than productivity growth to economic growth in six MENA countries.

^{[15]}This study examines how the relationship between renewable energy consumption and carbon emissions is associated with the development stage by applying a panel cointegration analysis to 107 countries during the period from 1990 to 2013.

^{[16]}Design/methodology/approach: By using time series data, this study employs Pedroni’s panel cointegration analysis to test the long run relationship between financial stability of conventional banks and Islamic banks as a dependent variable and independent variables including financial crisis under three periods; pre (2006-2007), during (2008-2009) and post (2010-2011) crisis.

^{[17]}Using a heterogeneous panel cointegration analysis, this study examines the long-run impacts of income, trade, and energy use on carbon dioxide emissions (CO2), in Argentina, Brazil, Paraguay and Uruguay between 1970 − 2008.

^{[18]}Design/methodology/approach This study used the Pedroni panel cointegration analysis and full modified ordinary least square method.

^{[19]}

## Johansen Cointegration Analysis

Then, the following econometric tests were performed on the variables representing FDI inflows, exports, and GDP as proxies for FDI, trade, and economic growth: the unit root test; the unit root test with a structural break; Johansen cointegration analysis; the error correction model; and the Granger causality test.^{[1]}Methodology: The study employs unit root tests, Johansen cointegration analysis, a dynamic vector error correction model and a multivariate Toda-Yamamoto Granger-causality representation.

^{[2]}Employing Johansen Cointegration analysis, the results of the study suggest that exchange rate and treasury bill rate are positive whereas interest rate and inflation rate are negatively associated with better stock market performance.

^{[3]}Findings – The results of panel Johansen cointegration analysis show that cointegration exists between the stock prices, the changes in stock prices due to inflation rates and the changes in stock prices due to real interest rates.

^{[4]}In the long term, the cointegration relationship between R&D expenditures and growth is determined by Johansen Cointegration Analysis.

^{[5]}The ARMA model and Johansen cointegration analysis theory of grid investment are used to analyze the relationship between power grid and various influencing factors, and the relationship between influencing factors and grid investment is obtained.

^{[6]}Results from Johansen cointegration analysis show that New Zealand and Australia bilateral real exchange rates with Japan as the base country share a common stochastic trend, which can be interpreted in terms of an optimum currency area.

^{[7]}Research Methodology: Secondary data from 1980 to 2017 were collected and analysed using the Johansen Cointegration analysis and vector error correction model.

^{[8]}The Johansen cointegration analysis was used to test for the relationship between markets price and the results indicated that the rural and urban markets price were cointegrated.

^{[9]}In our study, Johansen cointegration analysis and error correction model (VEC) were used and it was concluded that there was a statistically significant and positive relationship between the variables according to the findings.

^{[10]}

## Granger Cointegration Analysis

However, the study was tested by Engle–Granger Cointegration analysis.^{[1]}The results of Engle–Granger cointegration analysis indicates that there is a relationship between trade war and oil prices.

^{[2]}In the first stage of the research, the stationarity analysis of the variables was carried out using the ADF test, then, for the further stage of research, variables characterized by non-stationarity were selected and an Engle– Granger cointegration analysis was used.

^{[3]}METHODS The data for work-related fatalities in housing and civil engineering in China from 1996 to 2016 were tested for fluctuation and trends of both general economic and industry-specific indicators using the Engle-Granger cointegration analysis and the augmented Granger Causality test the with modified Wald method.

^{[4]}On the other hand, Engle-Granger cointegration analysis is considered in this study in order to reach this objective.

^{[5]}

## Conducted Cointegration Analysis

We conducted cointegration analysis within the VAR framework on monthly data spanning from 2007 to 2018.^{[1]}Using annual trade data during the period of 1976-2016, this study conducted cointegration analysis of the Korean trade pattern in the imports of agricultural manufactures.

^{[2]}We conducted cointegration analysis between search index data and incidence rates to examine whether a stable equilibrium existed between them.

^{[3]}

## Multivariate Cointegration Analysis

To capture the long-run association between major GCC stock markets and foreign exchange reserves of Saudi Arabia, UAE, and Qatar at post-international financial crisis of 2008, we employed multivariate cointegration analysis (As there is no foreign debts payable by these countries, change in foreign exchange reserves of these countries can be a good proxy for change in their sovereign wealth funds (SWFs)).^{[1]}A multivariate cointegration analysis is developed and results reveal a potent and long run relationship exists, thus error correction model constructed to trace both the short and the long run behaviour among variables of the model.

^{[2]}The group of I(1) variables were found to be cointegrated after testing for cointegration following a multivariate cointegration analysis proposed by Johansen and Juselius [20].

^{[3]}

## Using Cointegration Analysis

Using cointegration analysis, we also explore the long-term dynamics between the two longevity measures in some selected developed countries.^{[1]},Using cointegration analysis, our empirical evidence reveals that foreign aid, labor remittances, exports and human capital have had a robust positive long-run impact on economic growth.

^{[2]}

## cointegration analysis indicate

The results of Engle–Granger cointegration analysis indicates that there is a relationship between trade war and oil prices.^{[1]}Dynamic cointegration analysis indicates that the recent market-oriented reforms in China have boosted the price discovery function of soybean and corn futures markets, whereas price stabilization policies tend to weaken the price discovery function of futures markets.

^{[2]}The results of the cointegration analysis indicate a significant positive long-run relation between stock transactions in Belgium (as a percentage of GDP) and the real effective exchange rate.

^{[3]}In addition, the cointegration analysis indicates that the property price and its factors are cointegrated for all property market segments across states.

^{[4]}

## cointegration analysis indicated

Furthermore, the cointegration analysis indicated that both environmental stringency policies and human development had a decreasing impact on the CO2 emissions.^{[1]}A cointegration analysis indicated that tree-growth release from cold limitation significantly reduced the degree and spatial extent of synchronous growth at short- (annual) and long-term (decadal) scales, most likely by exposing forests to endogenous (local) factors (e.

^{[2]}

## cointegration analysis suggest

Results from Pedroni cointegration analysis suggest no evidence of long-run relationships among the variables.^{[1]}Cointegration analysis suggests that a long-term relationship exists among the relevant variables.

^{[2]}

## cointegration analysis within

We conducted cointegration analysis within the VAR framework on monthly data spanning from 2007 to 2018.^{[1]}Thus, this paper examines the extent to which exchange rate changes have an asymmetric effect on tourism demand in ten European countries by using hidden cointegration analysis within a likelihood-based panel framework.

^{[2]}

## cointegration analysis reveal

Based on World Bank data, the panel cointegration analysis reveals that renewable energy consumption and economic growth are positively associated in the long run in CEE countries.^{[1]}Cointegration analysis reveals that over the long term, the impacts of economic growth and population density on natural capital levels are significant.

^{[2]}