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How can a single observation possess variance (by definition it is 0)? For example, we read notation such as sigma(t) as the conditional variance at time t? Yet GARCH's generate conditional variances for each observation? Please expand.

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  • $\begingroup$ I don’t understand how linear would imply deterministic. $\endgroup$ – Bob Jansen Mar 13 at 14:25
  • $\begingroup$ @Jansen. Deterministic forms are linear in shape, following a predefined path from beginning to end, holding constant variance? Or am I mistaken here also? $\endgroup$ – Geoffrey Turner Mar 13 at 21:10
  • $\begingroup$ I don't know, I'm confused by your terminology. Could you provide definitions? $\endgroup$ – Bob Jansen Mar 13 at 21:13
  • $\begingroup$ @Jansen. What I am trying to ascertain is: how can a single observation possess variance (it's not possible by definition)? Yet GARCH's generate conditional variances for each observation? $\endgroup$ – Geoffrey Turner Mar 14 at 8:55
  • $\begingroup$ Please clarify your question more then. I think I'm starting to understand what an answer could be but am not sure. $\endgroup$ – Bob Jansen Mar 14 at 9:05

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