LSS and Kalman Filter functionality in lectures

[jlperla]

• [ ] https://julia.quantecon.org/tools_and_techniques/linear_models.html

  • Canonical time-invariant LSS with/without observation equation and observation noise.
  • Simulation from a given initial value in https://julia.quantecon.org/tools_and_techniques/linear_models.html#id3
    • Ensemble simulations and plotting
    • Ensemble simulation from a distributional initial condition
  • Evolution of distributions in https://julia.quantecon.org/tools_and_techniques/linear_models.html#id5 for an ensemble in https://github.com/QuantEcon/QuantEcon.jl/blob/master/src/lss.jl#L173 though will need to look more carefully.
  • Stationary distributions replacing https://github.com/QuantEcon/QuantEcon.jl/blob/master/src/lss.jl#L195 and/or ricatti.
  • Check for stability

• [ ] https://julia.quantecon.org/tools_and_techniques/kalman.html

  • Basic kalman filter updates and simulations
  • See sequence of posteriors for random signals
  • stationary calculations
  • Could add in loglikelihood easily

• [ ] https://julia.quantecon.org/dynamic_programming/smoothing.html

• [ ] https://julia.quantecon.org/dynamic_programming/perm_income_cons.html

• [ ] https://julia.quantecon.org/dynamic_programming/lqcontrol.html

• [ ] https://julia.quantecon.org/dynamic_programming/perm_income.html

And in time-series:

• [ ] https://julia.quantecon.org/time_series_models/additive_functionals.html
• [ ] https://julia.quantecon.org/time_series_models/multiplicative_functionals.html
• [ ] https://julia.quantecon.org/time_series_models/classical_filtering.html maybe?
• [ ] https://julia.quantecon.org/time_series_models/lu_tricks.html maybe?

[jlperla]

Seems like differenceequations has most of the LSS and filtering requirements at this point. May try port of a few lectures to see how it does