Is the above graph a white noise? I'm confused by the spikes at certain places. The above plot has been obtained after doing a first order differencing on a time series. How can I justify whether there is seasonality present/absent in the data after differencing?
How can I justify whether there is seasonality present/absent in the data after differencing?
Plot the amplitude of the Fourier transform of the signal.
If there is seasonality, you will see a peak at the appropriate frequency on the Fourier plot. This should be close to the plot's origin, because seasonality means slow changes and thus low frequencies.
There are several ways to identify seasonal cycles in time series data.
First, if the seasonal pattern is very clear, you may be able to detect it in a plot of the time series (time = t on the X axis; X at time t on the Y axis).
Second, you can obtained a lagged autocorrelation function. For example, if each data point represents a measure for one month, and there is a 12 month cycle, a graph of the lagged autocorrelation function should show a relatively large positive autocorrelation at lag 12, with smaller peaks at lags 24 and 36 (if larger number of time lags are examined).
