Solution to Double Differencing in Nonstationary Data Using a Difference Transformation Mecha-nism
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Abstract
This study introduces a novel difference transformation mechanism (DTM) designed to address the problem of double differencing in persistent unit root problem common in nonstationary time series data. The DTM eliminates double differencing when the underlying data series is integrated of order two (I(2)). This study utilizes three empirical non-stationary datasets: monthly observations of the All Share Index (ASI) spanning January 1985 to December 2023; annual data on total exports and re-exports of oil and non-oil products (TEXP) and services sector output (SSO) spanned from 1981 to 2020 and from 1981 to 2023 respectively. The auxiliary AR(3) order of integration test, alongside the ADF and PP unit root tests, were conducted on the three datasets. The analysis indicated that ASI is integrated of order one (I(1)), whereas TEXP and SSO are integrated order two (I(2)) in their original forms. Subsequently, the DTM was implemented on these variables, followed by a repetition of the integration and unit root tests on their transformed series. The results showed that the transformed variables ASI*, TEXP*, and SSO* attained stationarity significant at 5% level regardless of their initial orders of integration. These outcomes confirm the efficacy of the proposed DTM in achieving stationarity in non-stationary time series, irrespective of the number of unit roots present in the data variable. Consequently, DTM is recommended in analytical contexts where data stationarity is a critical prerequisite for robust statistical inference.
Keywords
Difference transformation mechanism; Non-stationary data; Persistent unit root
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How to cite this paper
Solution to Double Differencing in Nonstationary Data Using a Difference Transformation Mechanism
How to cite this paper: Amaefula Chibuzo Gabriel, Eleje Chinwendu Best. (2025) Solution to Double Differencing in Nonstationary Data Using a Difference Transformation Mechanism, International Journal of Statistics and Data Science, 1(1), 38-48.
DOI: http://dx.doi.org/10.26855/ijsds.2025.12.004
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