High frequency time series estimation
2016-06-12 — 2015-12-02
Wherein estimation from a single high-frequency time series is considered, and asymptotics in sampling density for processes with jumps such as Lévy models are employed to infer parameters including across series.
a.k.a. “Fancy ARIMA”.
Classically, you estimate statistics from many i.i.d. realisations from a presumed generating process.
What if your data are realisations of sequentially dependent time series? How do you estimate parameters from a single time series realisation?
By being a flashy quant!
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. I think that the original framework is due to Jacod. (i.e. when you don’t have an asymptotic limit in number of data points, but in how densely you sample a single time series.)
This feels contrived for me, but it is probably interesting if you are not working with a multivariate Brownian motion, but a rather general Lévy process or something with interesting jumps AND continuous movement, and can sample with arbitrary density but not arbitrarily long. AFAICT this is little outside finance.