How can I detect spurious regressions results? I run bivariate Granger-causality regressions. Let $y_{t}$ and $x_{t}$ be stationary time series. I test if $x_{t}$ can forecast $y_{t}$ with the following regression:
$$y_{t+1} = \alpha + \beta_{1}y_{t} + \beta_{2}x_{t} + \varepsilon_{t+1}$$
I find that $\beta_{2}$ is significantly larger than zero, so $x_{t}$ appears to forecast $y_{t}$.
However, I do not find any plausible explanation for this effect. So I am thinking that the result might be spurious. Is there any way to test if my result is spurious? How would one go about to argue that the result might be spurious?
 A: While I can't speak for your specific statistical method, I can give the following general advice.
Understand your p values.
When you say that $\beta_2$ is significantly larger than zero, I presume you mean that  you obtained a p value $< .05$ for that term. What this means is often poorly understood, but it is set in stone: the probability of observing $\beta_2$ this high if the true value is $0$ is less than 5%. Nothing can be done about this.
Replicate Replicate Replicate
If your result doesn't make sense given your theory, try to replicate it with a new data set. From a purely Poperian point of view, this might not seem to make sense, but this is how science works, and you're right to question your result if it doesn't fit in with what you know: the more surprising a result is, the more likely it is to be spurious. Take for example, the Daryl Bem affair in psychology, or, more famously, think back to that time CERN had data showing that neutrinos could move faster than the speed of light - the unexpectedness of the result forced the researchers to look extra hard for explanations that didn't violate special relativity, and found one ultimately. Do you think they would have done this if the data disproved a less well known theory?
