Spurious regression /correlation In a time series regression I am finding a certain predictor variable significant which should not be,  according to the client. Could this be due to the higher variance that this predictor exhibits compared to the other variables in the model? 
In general, is there a relationship between variance and correlation and hence p-values in regression? 
In anothe time series regression model I am finding the log differences of a predictor  (currency rates) to be significant. Our response is also log difference which fluctuates a lot.The thing is the actual currency rate moves only by a few cents a year. However we are using log differences of the currency rates and there seems to be a certain amount of variance here though not much. My question is :Can a relatively flat or constant variable be a significant predictor of something that fluctuates a lot? Doesn't taking the log difference of an almost constant variable introduce an artificial variance here,  since very minor fluctuations seem to get amplified when we convert currency rates to the log scale?
Note : by Log difference I mean take the log and then difference the variable.
 A: In response to your first question .... when dealing with time series it is often possible to misuse regression. Consider y and x unrelated for a period of time and an exogenous (unknown to the analyst) variable causes an increase in x and simultaneously an increase in y. Overall there is now a correlation between y and x (GLOBALLY) but not locally. This phenomenon is sometimes referred to as Simpson's Paradox , spurious correlation , lurking variable phenomenon , etc.. Good analysis of this time series regression problem might unveil a level shift variable (step) which would then possibly eliminate the spurious correlation between y and x. You probably need to learn about time series methods and about Intervention Detection http://www.unc.edu/~jbhill/tsay.pdf . One simple place to start is here http://www.autobox.com/cms/index.php/afs-university/intro-to-forecasting and more specifically here http://www.autobox.com/cms/index.php/afs-university/intro-to-forecasting/doc_download/24-regression-vs-box-jenkins
See the comments regarding the Slutsky-Yule effect . In 1927 Slutsky showed that subjecting a sequence of independent random variables to a sequence of moving averages generated an almost periodic sequence
