Nonlinearity Testing of Stream Flow Processes by BDS Test (Case study: Shaharchi River in Urmia)

Document Type : Research Paper

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Abstract

Streamflow processes are commonly accepted as a nonlinear over space and times. In many researches linear time series models have been used for streamflow processes with assumption of linearity. It is better to test nonlinearity of these series before modeling. However, it is not clear what kind of nonlinearity is acting underlying the streamflow processes and how strong the nonlinearity is for the streamflow processes at different time scales. Streamflow data of Shaharchai River in Urmia on four timescales (i.e. yearly, monthly, 10-days and daily) were investigated with BDS test in order to study the character and type of nonlinearity that are present in streamflow dynamics. First stationarity was tested with ADF and KPSS tests then after pre-whitening series with AR models, BDS test was applied to the residuals. All daily and 10 days and monthly streamflow series appeared to be nonlinear but yearly series were linear.  It is found that as the timescale increases from a day to a year, the nonlinearity weakens and there are stronger and more complicated nonlinear mechanisms acting at small timescales than at large ones. Standardization with seasonal variance indicated nonlinearity in series. BDS test is not enough powerful for detecting weak nonlinearity like monthly series in the current study and need further investigations. Thus nonlinear time series modeling should be used for daily, 10 days and monthly series. Linear time series models may be applied for yearly series as utilized in this study.

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References

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