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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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What do you want to do with the time series? –  whuber Dec 15 '12 at 3:53
    
@whuber I'm just studying for an introductory econometrics final exam and I'm studying basic time series. I see very often a lagged time series in this form:$$y_t=\alpha_0+\delta_0z_t+\delta_1z_{t-1}+\delta_2z_{t-2}+...+\delta_qz_{t‌​-q}$$ and I'm just wondering if each variable observation has to be taken from consecutive years. –  Kyle Dec 15 '12 at 4:23
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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. –  Placidia Dec 15 '12 at 4:51
    
@Placidia yes annual or equal interval would be a better term(s). But yes you answered my question I think. So a interval of say 1996, 1998, 2004 wouldn't work then? –  Kyle Dec 15 '12 at 4:54
    
@Placidia I think you should make that comment an answer - there's not much more to say really. –  Peter Ellis Dec 15 '12 at 4:55
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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.

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Different analysis methods have different requirements. For example, wavelets do not assume equal intervals. Fourier transform does require equidistant sampling.

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