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?


Sometimes neither. You might need to take differences or trends or seasonal differencing or multiple trends. For causal problems, you would want to use the cross-correlation to determine if you have a relationship. The transfer function process has you build a model for x and then use the residuals to correlate the X with the Y. Don't forget outliers and changes in trend....and seasonality and parameters and variance.

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