Statistical inference was a concept that was not too difficult to understand when using cross-sectional data

Question

For example, it is obvious that a population mean is not the same as a sample mean (take weight of students at your college/university as an example). With a bit of thought, it also became clear that the sample mean had a distribution. This meant that there was uncertainty regarding the population mean given the sample information, and that you had to consider confidence intervals when making statements about the population mean. The same concept carried over into the two-dimensional analysis of a simple regression: knowing the height-weight relationship for a sample of students, for example, allowed you to make statements about the population height-weight relationship. In other words, it was easy to understand the relationship between a sample and a population in cross-sections. But what about time-series? Why should you be allowed to make statistical inference about some population, given a sample at hand (using quarterly data from 1962-2010, for example)? Write an essay explaining the relationship between a sample and a population when using time series.
What will be an ideal response?

Answer 1

Answer: Essays will differ by students. What is crucial here is the emphasis on stationarity or the concept that the distribution remains constant over time. If the dependent variable and regressors are non-stationary, then conventional hypothesis tests, confidence intervals, and forecasts can be unreliable. However, if they are stationary, then it is plausible to argue that a sample will repeat itself again and again and again, when getting additional data. It is in that sense that inference to a larger population can be made. There are two concepts crucial to stationarity which are discussed in the textbook: (i) trends, and (ii) breaks. Students should bring up methods for testing for stationarity and breaks, such as the DF and ADF statistics, and the QLR test.