To verify that a signal or time series is indeed completely stationary is quite difficult if not impossible in practice, however you can check that a sequence is weakly stationary or wide-sense stationary. For most modeling strategies this is sufficient.

A weakly stationary time series has an autocovariance function which is only function of the time elapsed and not the specific time instants itself. Depending on how the measurement of the time series was performed, it is possible that there is a non-stationary effect disturbing your measured sequence which is called a transient due to the finite time horizon. Basically you can partition your time record into overlapping segments for which you compute the periodogram or correlogram of each segment. In the paper ( DOI:10.1109/TIM.2012.2198269 ) I derived a statistical test to partition the periodogram of the overlapping segments into a stationary group and a non-stationary group. If the non-stationary group is empty, you showed your claim. Of course in practice the first and final segment are very likely to be non-stationary due to transients and leakage. It mainly depends on the time constant of the measured system. If the time constant is very short, your measurements reach steady state soon such that all segments are expected to be stationary, however the longer the time constant the more initial segments that can be detected by the test as non-stationary. The advise is to correct these (see the same paper) or to throw these out of the analysis.

Hope this helps, cheers,

Kurt.

Singular spectrum analysis (SSA)

@kurt: thanks for such an explicit response.I will try out the above methodology and revert back

Box–Cox transformation and Autoregressive Integrated Moving Average (ARIMA) time series model could be used to transform correlated and nonstationar model residuals to white noise disturbances, which can be minimized with a least squared based program such as PEST program in order to obtain an optimized model parameters set.