So like the title states, do the time periods in time series data have to be of equal intervals? For example, if we wanted to have data on the level of education recorded by year, would we need observations for 1996, 1997, 1998,...,2002 or could we have data for 1996, 2000, and 2004? It seems to me that it would need to be of equal spacing intervals, but I just want to make sure that a time interval of say 1997, 1998, 2000, 2003 wouldn't be acceptable.
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Do you really mean consecutive .... or do you mean annual? Time series data have to be ordered in time ... and most methods assume equal spacing. But the interval can be anything you want. 1996-2000-2004 would be fine, so long as everything else is spaced 4 years apart.
The classic methods -- building an ARIMA model, or exponential smoothing -- all assume that the data are equally spaced.
Different analysis methods have different requirements. For example, wavelets do not assume equal intervals. Fourier transform does require equidistant sampling.