The Fourier approximation and testing for the null of cointegration

Tsong, Ching-Chuan; Lee, Cheng-Feng; Tsai, Li-Ju; Hu, Te-Chung

doi:10.1007/s00181-015-1028-6

Cited by 107 publications

(98 citation statements)

References 44 publications

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“…Since Tsong et al () conducted a conventional unit root test developed by Ng and Perron () in their seminal work on Fourier cointegration test, we employ ADF and PP tests which do not consider structural breaks and non‐linearities in the series. Following the unit root analysis, we investigate the long‐run relationship between crude oil import, crude oil price and income level through Fourier SHIN (hereafter, FSHIN) cointegration test.…”

Section: Data Model and Methodologymentioning

confidence: 99%

“…Tsong et al () proposed a cointegration test with a Fourier form which allows for structural breaks of unknown form of deterministic trend. We consider the following cointegration regression:

y_{t} = d_{t} + x_{i}^{^{'}} β + η_{t}, t = 1, 2, 3, \dots, T,

where

η_{t} = γ_{t} + v_{1 t}

γ_{t} = γ_{t - 1} + u_{t}

with

γ_{0} = 0

, and

x_{t} = x_{t - 1} + v_{2 t}

.…”

Section: Data Model and Methodologymentioning

confidence: 99%

“…Besides,

{\overset{false^}{ω}}_{1}^{2}

shows the consistent estimator of the long‐term variance of

v_{1 t}

. The null of cointegration is tested against the alternative hypothesis of non‐cointegration (Tsong et al , ; Yılancı et al , ).…”

Section: Data Model and Methodologymentioning

confidence: 99%

“…To examine the price and income elasticities of crude oil import demand and the causal linkages between variables in Turkey between 1996:1 and 2017:9, this study employs the recently developed cointegration and causality techniques proposed by Tsong et al () and Nazlioglu et al () in order. We choose Turkey, one of the world’s largest economies, as a sample to our empirical analysis with the aim to make inferences that could be further useful for the analysis of other large and energy‐dependent economies such as most of the Organisation for Economic Co‐operation and Development (OECD) and the Asia‐Pacific countries.…”

Section: Introductionmentioning

confidence: 99%

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The relationship between oil prices, oil imports and income level in Turkey: evidence from Fourier approximation

2019

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The study aims at examining possible impacts of the changes in oil prices and income on crude oil import demand in Turkey using monthly data between 1996:1 and 2017:9. To this end, the study uses a recently introduced Fourier Shin cointegration test of Tsong et al. (2016) and Fourier Toda–Yamamoto approach of Nazlioglu et al. (2016). The study also constructs error correction model to estimate the short‐run parameters. Our empirical findings detect that oil imports are more sensitive to changes in income relative to changes in oil price in the long‐run. Furthermore, 81.4 per cent of the disequilibrium of the shocks converges back to the equilibrium level within the next month. Also, the causality test results provide an evidence for conservation hypothesis in Turkey. Thus, energy conservative policies do not have adverse effects on real economic activity. These results include policy implications for future prospects.

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Section: Data Model and Methodologymentioning

confidence: 99%

“…Tsong et al () proposed a cointegration test with a Fourier form which allows for structural breaks of unknown form of deterministic trend. We consider the following cointegration regression:

y_{t} = d_{t} + x_{i}^{^{'}} β + η_{t}, t = 1, 2, 3, \dots, T,

where

η_{t} = γ_{t} + v_{1 t}

γ_{t} = γ_{t - 1} + u_{t}

with

γ_{0} = 0

, and

x_{t} = x_{t - 1} + v_{2 t}

.…”

Section: Data Model and Methodologymentioning

confidence: 99%

“…Besides,

{\overset{false^}{ω}}_{1}^{2}

shows the consistent estimator of the long‐term variance of

v_{1 t}

. The null of cointegration is tested against the alternative hypothesis of non‐cointegration (Tsong et al , ; Yılancı et al , ).…”

Section: Data Model and Methodologymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The relationship between oil prices, oil imports and income level in Turkey: evidence from Fourier approximation

2019

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“…The main problem with these tests is that the number and form of structural changes has been priorly determined. The test which has been developed by Tsong et al (2016) using Fourier functions, tests the existence of co-integration under the null hypothesis, rather than the absence of it unlike many tests in the literature. The Fourier cointegration test which could be regarded as a generalization of the counterpart in Shin (1994) yields strong results against the form and number of structural changes.…”

Section: Analysis Resultsmentioning

confidence: 99%

Türkiye’de Merkez Bankacılığı’nda Yeni Trendler: Rezerve Opsiyon Mekanizması ve Asimetrik Faiz Koridoru Üzerine Bir Çalışma

Kılcı¹

2019

Muhasebe Ve Finansman Dergisi

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After 2008-09 Global Financial Crisis, central banks in many emerging market economies including the Central Bank of the Republic of Turkey adopted unconventional monetary policy tools to ensure financial stability in addition to the price stability. In this study, after giving a brief review of reserve option mechanism and asymmetric interest rate corridor practise, we tried to investigate the impact of the CBRT average funding interest rate, which is a component of assymmetric interest rate corridor, on the banking sector credit volume and foreign exchange rates by using monthly dataset covering the period of 2010:01-2019:02 and by empoloying the Fourier ADF unit root test, FourierSHIN conitegration test and Fourier Granger causality test. These techniques have the great advantage of permitting us to test for unit root, cointegration and causality while allowing for multiple structural breaks in the series. The results supported the cointegration and causality relationship between the CBRT average funding interest rate and banking sector credit volume and foreign exchange rates.

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The resilience of green firms in the twirl of COVID‐19: Evidence from S&P500 Carbon Efficiency Index with a Fourier approach

2021

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This paper investigates the resilience of environmentally friendly companies in an overwhelming economic and social environment that has been generated after the outbreak of the novel coronavirus disease (COVID‐19) pandemic. To this respect, we have investigated the cointegration between the Standard & Poor's (S&P) 500 Carbon Efficiency Index (CEI) with COVID‐19 cases, supplemented with covariates such as government response stringency to the pandemic, economic policy uncertainty, oil prices and global markets fluctuations. We have used daily data from 2nd January to 5th October 2020 and have employed a robust estimator within a Fourier approach to accommodate both sharp and smooth breaks. Our results suggest that green companies have been positively affected by the outbreak of COVID‐19. Our paper provides practical implications for companies that wish to furnish themselves with resilience during rough times and stakeholders who wish to invest in safe, long‐lasting returns.

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The Fourier approximation and testing for the null of cointegration

Cited by 107 publications

References 44 publications

The relationship between oil prices, oil imports and income level in Turkey: evidence from Fourier approximation

The relationship between oil prices, oil imports and income level in Turkey: evidence from Fourier approximation

Türkiye’de Merkez Bankacılığı’nda Yeni Trendler: Rezerve Opsiyon Mekanizması ve Asimetrik Faiz Koridoru Üzerine Bir Çalışma

The resilience of green firms in the twirl of COVID‐19: Evidence from S&P500 Carbon Efficiency Index with a Fourier approach

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