In relation to the question below I have uploaded the detrended plot and the differenced plot to the following links (I tried to add the images to the post but I got a 'new user' error msg). If anybody knows a way to make a statistical connection between the two without doing regression analysis (because of the nonstationary red line) I'd be grateful to hear.
I'm trying to work out how to regress one set of time series data against another.
I have attached a graph of two lines:
The blue line (8 yrs of monthly data) has a blip just at the time when the red line (5 yrs of semi-annl data) rapidly increases. As the red line falls the blue line returns to its original trend.
Does anyone know of a standard method to show whether or not the red line 'caused' or 'is associated with' the blue line along the lines of 'Step1: A followed by Step 2: B...etc'?
I have a working knowledge of regression of cross-sectional data but, after 2 weeks of trying to work this out by googling and trial-and-error, I'm not all that much further.
I'm using excel.
In terms of what I have tried...
- I found out that both data was autocorrelated and that it had a unit root, using an online Dickey-Fuller test. I also tested the residuals of a regression of each against time using a D-W test and that showed autocorrelation too.
- I detrended the blue line by plotting a graph of the residuals from a regression over time. However, the detrended line (the residuals) still visually had a trend which seemed odd. Also it had unit root according to a D-F test.
- I detrended the blue line just using data to the start of the red line and it showed no trend
- I detrended the blue line just for the period the red line exists and it still showed a trend at the begining of the red line and then returned to the trend when the red line starting falling. Inbetween it leapt up along with the red line but lagged.
I would be grateful to hear any comments.