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Contemporary building techniques and underlying theories of periodic autoregressive (PAR) models are revisited, reviewed, modified and recast. New techniques for generating synthetic data from any PAR model with provision to constrain some parameter values to zero have been proposed. The developed method is applied to the Ganges river for its monthly flow forecasting and generation. The results demonstrate that the PAR model can capture the seasonal variability of the Ganges river flow reasonably well preserving both its short- and the long-term important historical statistics.