Bayesian sampling of mixture autoregressive models
bayes_mixAR.RdSamples parameters of a mixture autoregressive model from respective posterior distributions.
Arguments
- y
a time series (currently a numeric vector).
- model
an object of class
MixAR. Currently only handlesMixARGaussianobjects.- fix_shift
should
shiftbe kept fixed? IfFALSE(default)shiftis sampled.- a, c
numeric hyperparameters, default values are from RichardsonGreen1997;textualmixAR.
- tau
numericvector of length g, the number of components in the mixture. Tuning parameter for M-H move in updating AR parameters. Iflength(tau)is 1, same tuning parameter is taken for all components.- nsim
numeric, the number of iterations.- burnin
numeric, the number of iterations taken as burn-in period.
Value
a list with following elements:
- mix_weights
a
gcolumns matrix with samples from the posterior distributions of the mixing weights.- scale
a
gcolumns matrix with samples from posterior distributions of scale parameters.- precision
a
gcolumns matrix with samples from posterior distributions of precision parameters, defined as1 / (scale ^ 2).- shift
a
gcolumns matrix with samples from posterior distributions of shift parameters, namely phi_k0.- mu
a
gcolumns matrix with samples from posterior distributions of component means, calculated asphi_k0 / (1 - phi_k1 - phi_k2 - ...).- ARcoeff
a list which elements are matrices, one for each AR component in the mixture.
- acc_rate
numericvector, the acceptance rate for M-H moves.- n_samp
the sample size, calculated as
nsim - burnin.- LatentZ
the latest Z variables drawn (for utility only).
- n_comp
the number of components in the mixture.
- fix_shift
same as input, whether the shift parameter was kept fixed or not.
Examples
prob <- c(0.5, 0.5)
sigma <- c(1, 2)
ar <- list(-0.5, 1)
model <- new("MixARGaussian", prob = prob, scale = sigma, arcoef = ar)
## MAR(1,1) model
y <- mixAR_sim(model, 300, rep(0, max(model@order)))
bayes_mixAR(y, model, fix_shift = FALSE, tau = c(.15,.25), nsim = 20, burnin = 10)
#> $mix_weights
#> [,1] [,2]
#> [1,] 0.5859404 0.4140596
#> [2,] 0.5675420 0.4324580
#> [3,] 0.6090409 0.3909591
#> [4,] 0.5816917 0.4183083
#> [5,] 0.5090090 0.4909910
#> [6,] 0.4638817 0.5361183
#> [7,] 0.4745710 0.5254290
#> [8,] 0.5371336 0.4628664
#> [9,] 0.5879339 0.4120661
#> [10,] 0.5532978 0.4467022
#>
#> $scale
#> [,1] [,2]
#> [1,] 1.1431564 2.074092
#> [2,] 1.0450437 2.314067
#> [3,] 1.0833460 1.938325
#> [4,] 1.0272325 1.843347
#> [5,] 1.0229076 2.113068
#> [6,] 1.0677279 1.984406
#> [7,] 0.9103989 2.082002
#> [8,] 0.9609276 2.259794
#> [9,] 1.1051917 2.143391
#> [10,] 1.1997655 2.147962
#>
#> $precision
#> [,1] [,2]
#> [1,] 0.7652242 0.2324578
#> [2,] 0.9156534 0.1867446
#> [3,] 0.8520510 0.2661625
#> [4,] 0.9476817 0.2942969
#> [5,] 0.9557124 0.2239614
#> [6,] 0.8771600 0.2539446
#> [7,] 1.2065256 0.2306948
#> [8,] 1.0829756 0.1958223
#> [9,] 0.8186999 0.2176694
#> [10,] 0.6947160 0.2167438
#>
#> $shift
#> [,1] [,2]
#> [1,] -0.17388804 -0.33229027
#> [2,] 0.07111309 -0.19669854
#> [3,] 0.04899561 -0.20119328
#> [4,] -0.02118783 -0.36544546
#> [5,] -0.08636606 -0.33550322
#> [6,] -0.07308396 -0.16964398
#> [7,] -0.05537787 -0.35371554
#> [8,] -0.13936048 -0.04630361
#> [9,] -0.05377540 -0.23745943
#> [10,] -0.05190417 -0.07954147
#>
#> $mu
#> [,1] [,2]
#> [1,] -0.11596246 3.1612893
#> [2,] 0.04742389 1.2848873
#> [3,] 0.03267419 1.3142482
#> [4,] -0.01412974 2.3871872
#> [5,] -0.05759580 2.1915965
#> [6,] -0.04873823 1.1081598
#> [7,] -0.03693039 2.3105643
#> [8,] -0.09293672 0.3024675
#> [9,] -0.03586174 1.5511483
#> [10,] -0.03461385 0.5195861
#>
#> $ARcoeff
#> $ARcoeff$Component_1
#> [,1]
#> [1,] -0.4995202
#> [2,] -0.4995202
#> [3,] -0.4995202
#> [4,] -0.4995202
#> [5,] -0.4995202
#> [6,] -0.4995202
#> [7,] -0.4995202
#> [8,] -0.4995202
#> [9,] -0.4995202
#> [10,] -0.4158659
#>
#> $ARcoeff$Component_2
#> [,1]
#> [1,] 1.153086
#> [2,] 1.153086
#> [3,] 1.153086
#> [4,] 1.153086
#> [5,] 1.153086
#> [6,] 1.153086
#> [7,] 1.153086
#> [8,] 1.153086
#> [9,] 1.153086
#> [10,] 1.153086
#>
#>
#> $acc_rate
#> [1] 0.1 0.1
#>
#> $n_samp
#> [1] 10
#>
#> $LatentZ
#> latent Z 1 latent Z 2
#> [1,] 0 1
#> [2,] 0 1
#> [3,] 0 1
#> [4,] 0 1
#> [5,] 1 0
#> [6,] 1 0
#> [7,] 0 1
#> [8,] 0 1
#> [9,] 1 0
#> [10,] 1 0
#> [11,] 0 1
#> [12,] 1 0
#> [13,] 1 0
#> [14,] 1 0
#> [15,] 0 1
#> [16,] 1 0
#> [17,] 0 1
#> [18,] 1 0
#> [19,] 0 1
#> [20,] 0 1
#> [21,] 1 0
#> [22,] 1 0
#> [23,] 0 1
#> [24,] 1 0
#> [25,] 1 0
#> [26,] 0 1
#> [27,] 1 0
#> [28,] 0 1
#> [29,] 0 1
#> [30,] 1 0
#> [31,] 1 0
#> [32,] 1 0
#> [33,] 0 1
#> [34,] 1 0
#> [35,] 1 0
#> [36,] 1 0
#> [37,] 0 1
#> [38,] 1 0
#> [39,] 1 0
#> [40,] 1 0
#> [41,] 1 0
#> [42,] 1 0
#> [43,] 1 0
#> [44,] 0 1
#> [45,] 0 1
#> [46,] 1 0
#> [47,] 1 0
#> [48,] 0 1
#> [49,] 1 0
#> [50,] 0 1
#> [51,] 1 0
#> [52,] 0 1
#> [53,] 1 0
#> [54,] 1 0
#> [55,] 1 0
#> [56,] 1 0
#> [57,] 0 1
#> [58,] 0 1
#> [59,] 0 1
#> [60,] 1 0
#> [61,] 0 1
#> [62,] 1 0
#> [63,] 0 1
#> [64,] 1 0
#> [65,] 0 1
#> [66,] 0 1
#> [67,] 1 0
#> [68,] 0 1
#> [69,] 1 0
#> [70,] 0 1
#> [71,] 1 0
#> [72,] 1 0
#> [73,] 0 1
#> [74,] 0 1
#> [75,] 0 1
#> [76,] 1 0
#> [77,] 1 0
#> [78,] 0 1
#> [79,] 0 1
#> [80,] 1 0
#> [81,] 0 1
#> [82,] 0 1
#> [83,] 0 1
#> [84,] 1 0
#> [85,] 0 1
#> [86,] 1 0
#> [87,] 0 1
#> [88,] 0 1
#> [89,] 1 0
#> [90,] 1 0
#> [91,] 1 0
#> [92,] 1 0
#> [93,] 0 1
#> [94,] 1 0
#> [95,] 0 1
#> [96,] 0 1
#> [97,] 1 0
#> [98,] 1 0
#> [99,] 1 0
#> [100,] 0 1
#> [101,] 0 1
#> [102,] 0 1
#> [103,] 0 1
#> [104,] 0 1
#> [105,] 1 0
#> [106,] 0 1
#> [107,] 0 1
#> [108,] 0 1
#> [109,] 0 1
#> [110,] 1 0
#> [111,] 1 0
#> [112,] 1 0
#> [113,] 1 0
#> [114,] 1 0
#> [115,] 0 1
#> [116,] 0 1
#> [117,] 1 0
#> [118,] 1 0
#> [119,] 1 0
#> [120,] 1 0
#> [121,] 1 0
#> [122,] 0 1
#> [123,] 1 0
#> [124,] 0 1
#> [125,] 0 1
#> [126,] 1 0
#> [127,] 1 0
#> [128,] 0 1
#> [129,] 0 1
#> [130,] 1 0
#> [131,] 0 1
#> [132,] 0 1
#> [133,] 0 1
#> [134,] 1 0
#> [135,] 0 1
#> [136,] 1 0
#> [137,] 1 0
#> [138,] 0 1
#> [139,] 1 0
#> [140,] 1 0
#> [141,] 1 0
#> [142,] 0 1
#> [143,] 0 1
#> [144,] 1 0
#> [145,] 0 1
#> [146,] 1 0
#> [147,] 0 1
#> [148,] 1 0
#> [149,] 1 0
#> [150,] 1 0
#> [151,] 0 1
#> [152,] 0 1
#> [153,] 1 0
#> [154,] 1 0
#> [155,] 0 1
#> [156,] 0 1
#> [157,] 0 1
#> [158,] 1 0
#> [159,] 1 0
#> [160,] 0 1
#> [161,] 1 0
#> [162,] 1 0
#> [163,] 1 0
#> [164,] 1 0
#> [165,] 0 1
#> [166,] 1 0
#> [167,] 1 0
#> [168,] 1 0
#> [169,] 1 0
#> [170,] 0 1
#> [171,] 1 0
#> [172,] 1 0
#> [173,] 1 0
#> [174,] 1 0
#> [175,] 0 1
#> [176,] 1 0
#> [177,] 0 1
#> [178,] 1 0
#> [179,] 1 0
#> [180,] 1 0
#> [181,] 0 1
#> [182,] 0 1
#> [183,] 1 0
#> [184,] 1 0
#> [185,] 0 1
#> [186,] 1 0
#> [187,] 0 1
#> [188,] 1 0
#> [189,] 0 1
#> [190,] 0 1
#> [191,] 0 1
#> [192,] 1 0
#> [193,] 1 0
#> [194,] 1 0
#> [195,] 1 0
#> [196,] 0 1
#> [197,] 0 1
#> [198,] 1 0
#> [199,] 1 0
#> [200,] 1 0
#> [201,] 0 1
#> [202,] 1 0
#> [203,] 1 0
#> [204,] 1 0
#> [205,] 0 1
#> [206,] 1 0
#> [207,] 1 0
#> [208,] 1 0
#> [209,] 1 0
#> [210,] 1 0
#> [211,] 0 1
#> [212,] 0 1
#> [213,] 1 0
#> [214,] 1 0
#> [215,] 0 1
#> [216,] 0 1
#> [217,] 1 0
#> [218,] 1 0
#> [219,] 1 0
#> [220,] 1 0
#> [221,] 0 1
#> [222,] 1 0
#> [223,] 1 0
#> [224,] 0 1
#> [225,] 1 0
#> [226,] 0 1
#> [227,] 1 0
#> [228,] 0 1
#> [229,] 1 0
#> [230,] 0 1
#> [231,] 0 1
#> [232,] 1 0
#> [233,] 0 1
#> [234,] 1 0
#> [235,] 0 1
#> [236,] 0 1
#> [237,] 0 1
#> [238,] 1 0
#> [239,] 1 0
#> [240,] 0 1
#> [241,] 0 1
#> [242,] 1 0
#> [243,] 1 0
#> [244,] 0 1
#> [245,] 1 0
#> [246,] 0 1
#> [247,] 0 1
#> [248,] 0 1
#> [249,] 0 1
#> [250,] 1 0
#> [251,] 0 1
#> [252,] 1 0
#> [253,] 1 0
#> [254,] 0 1
#> [255,] 0 1
#> [256,] 1 0
#> [257,] 1 0
#> [258,] 1 0
#> [259,] 0 1
#> [260,] 1 0
#> [261,] 1 0
#> [262,] 0 1
#> [263,] 1 0
#> [264,] 1 0
#> [265,] 1 0
#> [266,] 0 1
#> [267,] 0 1
#> [268,] 0 1
#> [269,] 0 1
#> [270,] 1 0
#> [271,] 1 0
#> [272,] 0 1
#> [273,] 0 1
#> [274,] 0 1
#> [275,] 1 0
#> [276,] 0 1
#> [277,] 1 0
#> [278,] 1 0
#> [279,] 0 1
#> [280,] 0 1
#> [281,] 1 0
#> [282,] 1 0
#> [283,] 0 1
#> [284,] 1 0
#> [285,] 1 0
#> [286,] 0 1
#> [287,] 1 0
#> [288,] 1 0
#> [289,] 0 1
#> [290,] 0 1
#> [291,] 0 1
#> [292,] 1 0
#> [293,] 0 1
#> [294,] 1 0
#> [295,] 1 0
#> [296,] 1 0
#> [297,] 1 0
#> [298,] 0 1
#> [299,] 1 0
#>
#> $ncomp
#> [1] 2
#>
#> $fix_shift
#> [1] FALSE
#>