Do you remove the seasonal component, the trend component, or both, when adjusting a time series to avoid finding spurious correlations?
I have two time series x and y with trends and yearly seasonality and I would like to test for correlation. I read this article about spurious correlation in time series https://svds.com/avoiding-common-mistakes-with-time-series/ which recommends taking the trendline out by first differencing or decomposition. However I have also seen sources suggesting instead to remove the seasonality component.
What is the correct way to adjust the time series to avoid detecting spurious correlations? If I removed both the trend and seasonality would I not be left with random noise? Should I only remove the trend or seasonality if they are the same in both series?