This is a brief question because my lecturer mentioned it today in class but I don't quite understand. Why is omitted variable bias not a major problem in time series analysis?
My guess would be that, in econometrics at least, cross-sectional studies are often trying to get at causal relationships; the causal effect of an additional year of education on earnings, for example.
In time series, we are usually only after a prediction for future values of our outcome. Given some set of factors, what do we expect the GDP growth rate to be next quarter? We don't care if the measure of consumer confidence that we include directly causes growth, but are instead content to use its predictive power (as opposed to true explanatory power) to help with our forecast.
So perhaps positive news stories cause consumer confidence, which leads to economic growth. Leaving out a measure of the positivity of news stories would lead to omitted variables bias in that the coefficient on confidence isn't really a measure of the effect of confidence itself. But we are still able to get useful forecasts despite the omitted variable.
This is to correct another answer that any observational studies, whether cross-sectional or time-series or panel, do not give you causal relationships! If you run a cross-sectional regression of a group of people you may 'found' that there is a positive association between salary and whether a person wears trousers (as opposed to skirts). Of course what to wear does not cause higher/lower salary. The true omitted factor here is gender!