viking {viking}

Viking: Variational bayesIan variance tracKING

Description

viking is the state-space estimation realized by Viking, generalizing the Kalman Filter to variance uncertainty.

Usage

viking(
  X,
  y,
  theta0,
  P0,
  hata0,
  s0,
  hatb0,
  Sigma0,
  n_iter = 2,
  mc = 10,
  rho_a = 0,
  rho_b = 0,
  learn_sigma = TRUE,
  learn_Q = TRUE,
  K = NULL,
  mode = "diagonal",
  thresh = TRUE,
  phi = logt,
  phi1 = logt1,
  phi2 = logt2
)

Arguments

X

the explanatory variables

y

the time series

theta0

initial theta

P0

initial P

hata0

initial hata

s0

initial s

hatb0

initial hatb

Sigma0

initial Sigma

n_iter

(optional, default 2) number of alternate steps

mc

(optional, default 10) number of Monte-Carlo samples

rho_a

(optional, default 0) learning rate of a

rho_b

(optional, default 0) learning rate of b

learn_sigma

(optional, default TRUE) asserts the estimation of a

learn_Q

(optional, default TRUE) asserts the estimation of b

K

(optional, default NULL) if not NULL then it is a multiplicative factor of the state in the state update

mode

(optional, default 'diagonal')

thresh

(optional, default TRUE)

phi

(optional, default logt)

phi1

(optional, default logt1)

phi2

(optional, default logt2)

Value

a list composed of the evolving value of all the parameters: theta_arr, P_arr, q_arr, hata_arr, s_arr, hatb_arr, Sigma_arr

References

J. de Vilmarest, O. Wintenberger (2021), Viking: Variational Bayesian Variance Tracking. <arXiv:2104.10777>