Time series estimation

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High frequency asymptotics

Classically, you estimate statistics from many i.i.d. realisations from a
presumed generating process.

What if your data are realisations of dependent time series?
Or more general nonscalar data, as in spatial satatistics?
How do you estimate parameters from a single time-series realisation?

Bonus points:
How do you do this with many time series,
whose parameters themselves have a distribution you wish to estimate?

See Mark Podolskij
who explains “high frequency asymptotics” well, although I think that the original framework is due to Jacod.
(That’s when you don’t have an asymptotic limit in number of data points,
but in how densely you sample a single time series.)

Read!

Nonstationary case

Where the number of parameters grows with the time series, and asymptotic theory gets nastier. See
high-dimensional statistics

See original: The Living Thing / Notebooks Time series estimation