I removed trends and seasons from given time series and plotted the residual time series. I would like to know if there is any way that this plot could suggest that residual series is stationary? What are the key things I should look in time series plot to infer stationarity?
From everywhere: A time series can be said to be stationary when the mean , standard deviation and auto-correlation is the same for all sub-intervals of time. If you have Pulses,Seasonal Pulses, Level Shifts or Local Time Trends this would be a violation of the stationarity of the mean. If the standard deviation changes over time for example dependent on the mean then this would be a violation of the assumption of a constant standard deviation. If the auto-correlation function changes over time then this might be an indication of time varying parameters BUT it could have other causes. If your visually descriptive plot confirms all of these issues then you are good to go otherwise you need to get involved with time series analysis and do some inferential analysis..
If you removed the trend and seasonality then the remaining of the series must be stationary at least in mean. This means that the main thing to look at is heteroscedasticity, which can be tested with Engle's ARCH test and such