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I am trying to predict a time series where every data point is a percentage value between 0 and 1. Most data points are either 1 and few below 0.5. In such a case what could be suitable data transformation or an algorithm that can be used for prediction purposes. The plot below shows the data that I have.

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This might help : Beta Regression for time series analysis of bounded data, with application to Canada Google® flu trends

From the abstract : Bounded time series consisting of rates or proportions are often encountered in applications. This manuscript proposes a practical approach to analyze bounded time series.

And it comes with the GCMR package.

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