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I want to Compare methods (Such as exponential smoothing methods, ARIMA models, artificial neural networks, grey-Markov model) to forecast short time series using a detailed simulation study.

How can I generate a simulated short time series data to compare the methods? OR, How can I get rid of the bias if using ARIMA models to generate simulated data?

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Write your own simulator ..there is no bias there as it is all you ! . I suggest that you inject anomalies (an example of a Gaussian Violation that needs attention ) to test the robustness of your candidate models.

Take a look at Commonly used example data sets for challenging ways to create realistic data that nearly often defeats simple model-based approaches as compared to data-based approaches which evolve the model from the data.

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