: not genuine, sincere, or authentic
When it comes to analysis of time series, just because you can, doesn't mean you should, particularly with regards to regression. In short, if you have highly autoregressive time series and you build an OLS model, you will find estimates and t-statistics indicating a relationship when non exists. Without getting into the theory of the problem, let's just simply go over an example using R. If you want to look at the proper way of looking at the relationship between x or several x's versus y, I recommend the VARS package in R. If you want to dabble in causality, then explore Granger Causality, which I touch on in my very first post (the ultimate econometrics cynic, Nassim Taleb even recommends the technique in his book, Antifragile: Things That Gain From Disorder).
# produce two randomwalks
> rwalk1 = c(cumsum(rnorm(200))) > rwalk1.ts = ts(rwalk1) > rwalk2 = c(cumsum(rnorm(200))) > rwalk2.ts = ts(rwalk2)
#use the seqplot from tseries package
These two series are completely random walks (highly autoregressive) and we should have no relationship whatsoever between them.
#build a linear model and examine it
We have a highly significant p-value. This will happen whenever you regress a random walk on another. The implication is that you must have stationary data e.g. first differencing or do dynamic regression.
> acf(resid(spurious)) #autocorrelation plot of residuals showing we violate the OLS assumption of no serial correlation
To do a dynamic regression, we need to regress Y on X and lagged Y.
> lag.walk1 = lag(rwalk1.ts, -1) #creates lagged Ys