Kalman filter predict-update for a linear-Gaussian state-space model

Defaults to a univariate local-level model when matrices are omitted.

Usage

morie_kalman_filter(
  x,
  transition = NULL,
  H = NULL,
  Q = NULL,
  R = NULL,
  x0 = NULL,
  P0 = NULL
)

Arguments

x

Numeric vector or matrix of observations.

transition

Transition matrix (default identity).

H

Observation matrix (default identity).

Q

State-innovation covariance (default sigma^2 I).

R

Observation covariance (default sigma^2 I).

x0

Initial state mean.

P0

Initial state covariance.

Value

Named list with state, state_cov, innovations, innovation_variance, loglik, n, method.

Examples

morie_kalman_filter(x = rnorm(50))
#> $state
#>              [,1]
#>  [1,]  0.86730052
#>  [2,]  0.75748748
#>  [3,]  1.29876544
#>  [4,] -0.48961617
#>  [5,] -0.56402983
#>  [6,] -0.40905321
#>  [7,] -0.72615357
#>  [8,] -0.43587950
#>  [9,] -1.45376622
#> [10,] -1.43113861
#> [11,] -0.16916288
#> [12,]  0.08465359
#> [13,]  0.83822938
#> [14,]  0.11342510
#> [15,] -0.19433419
#> [16,] -0.33452533
#> [17,] -0.72007341
#> [18,] -0.12108122
#> [19,] -0.77483643
#> [20,]  0.01033231
#> [21,] -0.10588071
#> [22,]  0.43836907
#> [23,]  0.93871536
#> [24,]  0.10132126
#> [25,] -0.22687901
#> [26,] -0.11541424
#> [27,] -0.45111627
#> [28,]  0.81814035
#> [29,]  0.27315031
#> [30,]  0.64129914
#> [31,]  0.47880338
#> [32,]  1.05783002
#> [33,]  0.27486947
#> [34,] -1.55013178
#> [35,] -0.21560342
#> [36,] -0.72117794
#> [37,]  0.03193939
#> [38,] -0.58969880
#> [39,] -0.28363175
#> [40,] -0.45071411
#> [41,] -0.32404524
#> [42,] -0.52845403
#> [43,] -0.80987656
#> [44,] -0.18795883
#> [45,] -0.82364849
#> [46,] -0.49077191
#> [47,] -0.37308226
#> [48,] -0.53719392
#> [49,]  0.87194942
#> [50,] -0.82229807
#> 
#> $state_cov
#> , , 1
#> 
#>            [,1]
#>  [1,] 1.0155602
#>  [2,] 0.6770407
#>  [3,] 0.6347258
#>  [4,] 0.6286808
#>  [5,] 0.6278015
#>  [6,] 0.6276733
#>  [7,] 0.6276546
#>  [8,] 0.6276518
#>  [9,] 0.6276514
#> [10,] 0.6276514
#> [11,] 0.6276514
#> [12,] 0.6276514
#> [13,] 0.6276514
#> [14,] 0.6276514
#> [15,] 0.6276514
#> [16,] 0.6276514
#> [17,] 0.6276514
#> [18,] 0.6276514
#> [19,] 0.6276514
#> [20,] 0.6276514
#> [21,] 0.6276514
#> [22,] 0.6276514
#> [23,] 0.6276514
#> [24,] 0.6276514
#> [25,] 0.6276514
#> [26,] 0.6276514
#> [27,] 0.6276514
#> [28,] 0.6276514
#> [29,] 0.6276514
#> [30,] 0.6276514
#> [31,] 0.6276514
#> [32,] 0.6276514
#> [33,] 0.6276514
#> [34,] 0.6276514
#> [35,] 0.6276514
#> [36,] 0.6276514
#> [37,] 0.6276514
#> [38,] 0.6276514
#> [39,] 0.6276514
#> [40,] 0.6276514
#> [41,] 0.6276514
#> [42,] 0.6276514
#> [43,] 0.6276514
#> [44,] 0.6276514
#> [45,] 0.6276514
#> [46,] 0.6276514
#> [47,] 0.6276514
#> [48,] 0.6276514
#> [49,] 0.6276514
#> [50,] 0.6276514
#> 
#> 
#> $innovations
#>              [,1]
#>  [1,]  0.00000000
#>  [2,] -0.16471958
#>  [3,]  0.86604476
#>  [4,] -2.88892415
#>  [5,] -0.12037505
#>  [6,]  0.25074870
#>  [7,] -0.51307656
#>  [8,]  0.46967297
#>  [9,] -1.64697514
#> [10,]  0.03661225
#> [11,]  2.04191962
#> [12,]  0.41068368
#> [13,]  1.21931123
#> [14,] -1.17275795
#> [15,] -0.49796500
#> [16,] -0.22683402
#> [17,] -0.62382991
#> [18,]  0.96918972
#> [19,] -1.05779815
#> [20,]  1.27042971
#> [21,] -0.18803662
#> [22,]  0.88061464
#> [23,]  0.80957730
#> [24,] -1.35493212
#> [25,] -0.53103920
#> [26,]  0.18035379
#> [27,] -0.54317730
#> [28,]  2.05370035
#> [29,] -0.88181239
#> [30,]  0.59567732
#> [31,] -0.26292366
#> [32,]  0.93688479
#> [33,] -1.26685678
#> [34,] -2.95291407
#> [35,]  2.15931226
#> [36,] -0.81803676
#> [37,]  1.21856944
#> [38,] -1.00583173
#> [39,]  0.49522690
#> [40,] -0.27034494
#> [41,]  0.20495454
#> [42,] -0.33074037
#> [43,] -0.45535121
#> [44,]  1.00628402
#> [45,] -1.02856748
#> [46,]  0.53860563
#> [47,]  0.19042584
#> [48,] -0.26553824
#> [49,]  2.28004182
#> [50,] -2.74135001
#> 
#> $innovation_variance
#> , , 1
#> 
#>               [,1]
#>  [1,] 1.000002e+06
#>  [2,] 3.046683e+00
#>  [3,] 2.708163e+00
#>  [4,] 2.665848e+00
#>  [5,] 2.659803e+00
#>  [6,] 2.658924e+00
#>  [7,] 2.658796e+00
#>  [8,] 2.658777e+00
#>  [9,] 2.658774e+00
#> [10,] 2.658774e+00
#> [11,] 2.658774e+00
#> [12,] 2.658774e+00
#> [13,] 2.658774e+00
#> [14,] 2.658774e+00
#> [15,] 2.658774e+00
#> [16,] 2.658774e+00
#> [17,] 2.658774e+00
#> [18,] 2.658774e+00
#> [19,] 2.658774e+00
#> [20,] 2.658774e+00
#> [21,] 2.658774e+00
#> [22,] 2.658774e+00
#> [23,] 2.658774e+00
#> [24,] 2.658774e+00
#> [25,] 2.658774e+00
#> [26,] 2.658774e+00
#> [27,] 2.658774e+00
#> [28,] 2.658774e+00
#> [29,] 2.658774e+00
#> [30,] 2.658774e+00
#> [31,] 2.658774e+00
#> [32,] 2.658774e+00
#> [33,] 2.658774e+00
#> [34,] 2.658774e+00
#> [35,] 2.658774e+00
#> [36,] 2.658774e+00
#> [37,] 2.658774e+00
#> [38,] 2.658774e+00
#> [39,] 2.658774e+00
#> [40,] 2.658774e+00
#> [41,] 2.658774e+00
#> [42,] 2.658774e+00
#> [43,] 2.658774e+00
#> [44,] 2.658774e+00
#> [45,] 2.658774e+00
#> [46,] 2.658774e+00
#> [47,] 2.658774e+00
#> [48,] 2.658774e+00
#> [49,] 2.658774e+00
#> [50,] 2.658774e+00
#> 
#> 
#> $loglik
#> [1] -89.70534
#> 
#> $n
#> [1] 50
#> 
#> $method
#> [1] "Linear Gaussian Kalman filter (base R)"
#>