I have two time series on google Trends weekly data for the search of the terms 'machine learning' and 'data science'. The data can be found here http://www.filehosting.org/file/details/524910/dataScience.csv
The Augmented Dickey Fuller test (CADFtest command in R) shows that both time series are stationary when I difference them twice.
Augmented DF test ADF test t-test statistic: -1.283348e+01 p-value: 2.006856e-25 Max lag of the diff. dependent variable: 1.200000e+01
How to check if there's an annual seasonality (52 weeks) which would require differencing with a lag of 52? Should I just stop at differencing twice with lag 1 since the ADF test shows that the series become stationary in this case?