Does high standard error and high r-square imply spurious regression?

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Does a regression passed on time series data with one independent variable and one dependent variable which yields parameters with very high standard errors (t-values) and also a high r-squared imply that the regression results are spurious and that there is no real correlation between the variables?

The model is: $ln(y_t)=a+bln(x_t)$, $R^2>0.95$

edit: just to clarify, these standard errors arent just high but are also high in comparison to their equivalent parameter estimates.

Thank you for any help.