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Introductory Mathematics and Statistics for Islamic Finance, + Website by Noureddine Krichene, Abbas Mirakhor

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Chapter 16Nonstationary Time Series and Unit-Root Testing

Islamic finance deals with nonstationary time series such as share prices, sales, andcommodity prices. Often, financial time series, such as stock indices, tend to display a trend over time and do not have a constant mean or variance; they are nonstationary. If the first difference of a nonstationary variable yields a stationary variable img, we denote the nonstationary time series by img and we call it integrated time series of order one. A theoretical nonstationary time series img is the random walk. Many nonstationary time series resemble the behavior of a random walk and can be approximated by a random walk. We cover the definition of random walk with and without drift; we apply the random walk model to obtain a decomposition of nonstationary time series into trend component, called also permanent component, and a transitory, or cyclical component. The permanent component means that when a series is exposed to a shock, the impact of the shock will persist and does not vanish. An example of such shock is a technological shock such as the invention of automobiles, airplanes, computers, and the Internet. These shocks increase productivity ...

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