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,]  0.8664918009
#>  [2,] -1.0305169634
#>  [3,] -0.8394335021
#>  [4,]  0.1036149628
#>  [5,]  0.9691371597
#>  [6,]  0.4004593953
#>  [7,] -0.4659213697
#>  [8,]  0.2194382697
#>  [9,]  0.2623765448
#> [10,] -0.8838569961
#> [11,]  0.2203912973
#> [12,]  0.0193348934
#> [13,] -0.5273540750
#> [14,] -0.4930196153
#> [15,]  0.1504712121
#> [16,]  1.7373033148
#> [17,]  1.2767313513
#> [18,] -0.2948880282
#> [19,]  0.0784973208
#> [20,] -0.8198797236
#> [21,] -1.0696898103
#> [22,] -0.3666841788
#> [23,]  0.5440717820
#> [24,]  0.4275929077
#> [25,]  0.0775698892
#> [26,] -1.8662880969
#> [27,] -0.4598015970
#> [28,] -0.3005042222
#> [29,] -0.2517220862
#> [30,] -0.3564220702
#> [31,]  0.0926245523
#> [32,] -0.2287827958
#> [33,] -0.8909104475
#> [34,] -1.0095862255
#> [35,] -0.6531892411
#> [36,] -0.1911872084
#> [37,]  0.0009281557
#> [38,]  0.3537662998
#> [39,] -0.4019830292
#> [40,] -0.3984190215
#> [41,]  0.1824080422
#> [42,] -0.7299864093
#> [43,] -0.7527605618
#> [44,] -0.2612097130
#> [45,]  0.4836294709
#> [46,]  0.8317855535
#> [47,]  0.2936458598
#> [48,] -0.1728446440
#> [49,] -0.0171635906
#> [50,]  0.2585772846
#> 
#> $state_cov
#> , , 1
#> 
#>            [,1]
#>  [1,] 0.9036017
#>  [2,] 0.6024016
#>  [3,] 0.5647516
#>  [4,] 0.5593730
#>  [5,] 0.5585906
#>  [6,] 0.5584766
#>  [7,] 0.5584599
#>  [8,] 0.5584575
#>  [9,] 0.5584571
#> [10,] 0.5584571
#> [11,] 0.5584571
#> [12,] 0.5584571
#> [13,] 0.5584571
#> [14,] 0.5584571
#> [15,] 0.5584571
#> [16,] 0.5584571
#> [17,] 0.5584571
#> [18,] 0.5584571
#> [19,] 0.5584571
#> [20,] 0.5584571
#> [21,] 0.5584571
#> [22,] 0.5584571
#> [23,] 0.5584571
#> [24,] 0.5584571
#> [25,] 0.5584571
#> [26,] 0.5584571
#> [27,] 0.5584571
#> [28,] 0.5584571
#> [29,] 0.5584571
#> [30,] 0.5584571
#> [31,] 0.5584571
#> [32,] 0.5584571
#> [33,] 0.5584571
#> [34,] 0.5584571
#> [35,] 0.5584571
#> [36,] 0.5584571
#> [37,] 0.5584571
#> [38,] 0.5584571
#> [39,] 0.5584571
#> [40,] 0.5584571
#> [41,] 0.5584571
#> [42,] 0.5584571
#> [43,] 0.5584571
#> [44,] 0.5584571
#> [45,] 0.5584571
#> [46,] 0.5584571
#> [47,] 0.5584571
#> [48,] 0.5584571
#> [49,] 0.5584571
#> [50,] 0.5584571
#> 
#> 
#> $innovations
#>               [,1]
#>  [1,]  0.000000000
#>  [2,] -2.845513575
#>  [3,]  0.305733545
#>  [4,]  1.523385987
#>  [5,]  1.400109437
#>  [6,] -0.920107844
#>  [7,] -1.401826388
#>  [8,]  1.108934367
#>  [9,]  0.069475581
#> [10,] -1.854644799
#> [11,]  1.786711267
#> [12,] -0.325316095
#> [13,] -0.884561332
#> [14,]  0.055554323
#> [15,]  1.041190030
#> [16,]  2.567548277
#> [17,] -0.745221091
#> [18,] -2.542933573
#> [19,]  0.604150186
#> [20,] -1.453604592
#> [21,] -0.404201211
#> [22,]  1.137487006
#> [23,]  1.473634100
#> [24,] -0.188466778
#> [25,] -0.566349141
#> [26,] -3.145228291
#> [27,]  2.275742962
#> [28,]  0.257748567
#> [29,]  0.078931154
#> [30,] -0.169408133
#> [31,]  0.726572698
#> [32,] -0.520048013
#> [33,] -1.071345045
#> [34,] -0.192021442
#> [35,]  0.576662434
#> [36,]  0.747534992
#> [37,]  0.310849189
#> [38,]  0.570904110
#> [39,] -1.222828101
#> [40,]  0.005766686
#> [41,]  0.939797931
#> [42,] -1.476285234
#> [43,] -0.036849353
#> [44,]  0.795345981
#> [45,]  1.205175116
#> [46,]  0.563328375
#> [47,] -0.870728315
#> [48,] -0.754797491
#> [49,]  0.251897236
#> [50,]  0.446158108
#> 
#> $innovation_variance
#> , , 1
#> 
#>               [,1]
#>  [1,] 1.000002e+06
#>  [2,] 2.710807e+00
#>  [3,] 2.409607e+00
#>  [4,] 2.371957e+00
#>  [5,] 2.366578e+00
#>  [6,] 2.365796e+00
#>  [7,] 2.365682e+00
#>  [8,] 2.365665e+00
#>  [9,] 2.365662e+00
#> [10,] 2.365662e+00
#> [11,] 2.365662e+00
#> [12,] 2.365662e+00
#> [13,] 2.365662e+00
#> [14,] 2.365662e+00
#> [15,] 2.365662e+00
#> [16,] 2.365662e+00
#> [17,] 2.365662e+00
#> [18,] 2.365662e+00
#> [19,] 2.365662e+00
#> [20,] 2.365662e+00
#> [21,] 2.365662e+00
#> [22,] 2.365662e+00
#> [23,] 2.365662e+00
#> [24,] 2.365662e+00
#> [25,] 2.365662e+00
#> [26,] 2.365662e+00
#> [27,] 2.365662e+00
#> [28,] 2.365662e+00
#> [29,] 2.365662e+00
#> [30,] 2.365662e+00
#> [31,] 2.365662e+00
#> [32,] 2.365662e+00
#> [33,] 2.365662e+00
#> [34,] 2.365662e+00
#> [35,] 2.365662e+00
#> [36,] 2.365662e+00
#> [37,] 2.365662e+00
#> [38,] 2.365662e+00
#> [39,] 2.365662e+00
#> [40,] 2.365662e+00
#> [41,] 2.365662e+00
#> [42,] 2.365662e+00
#> [43,] 2.365662e+00
#> [44,] 2.365662e+00
#> [45,] 2.365662e+00
#> [46,] 2.365662e+00
#> [47,] 2.365662e+00
#> [48,] 2.365662e+00
#> [49,] 2.365662e+00
#> [50,] 2.365662e+00
#> 
#> 
#> $loglik
#> [1] -89.07486
#> 
#> $n
#> [1] 50
#> 
#> $method
#> [1] "Linear Gaussian Kalman filter (base R)"
#>