The HPJ bias-corrected kernel density estimation
hpjkd.RdThe `hpjkd()` function enables to implement the HPJ bias-corrected kernel density estimation for the heterogeneous mean, the autocovariance, and the autocorrelation. The method is developed by Okui and Yanagi (2020). For more details, see the package vignette with `vignette("panelhetero")`.
Arguments
- data
A matrix of panel data. Each row corresponds to individual time series.
- acov_order
A non-negative integer of the order of autocovariance. Default is 0.
- acor_order
A positive integer of the order of autocorrelation. Default is 1.
- mean_bw
A scalar of bandwidth used for the estimation of the denisty of mean. Default is NULL, and the plug-in bandwidth is used.
- acov_bw
A scalar of bandwidth used for the estimation of the denisty of autocovariance. Default is NULL, and the plug-in bandwidth is used.
- acor_bw
A scalar of bandwidth used for the estimation of the denisty of autocorrelation. Default is NULL, and the plug-in bandwidth is used.
Value
A list that contains the following elements:
- mean
A plot of the corresponding density
- acov
A plot of the corresponding density
- acor
A plot of the corresponding density
- mean_func
A function that returns the corresponding density
- acov_func
A function that returns the corresponding density
- acor_func
A function that returns the corresponding density
- bandwidth
A Vector of the bandwidths
- quantity
A matrix of the estimated heterogeneous quantities
- acov_order
The order of autocovariance
- acor_order
The order of autocorrelation
- N
The number of cross-sectional units
- S
The length of time series
References
Okui, R. and Yanagi, T., 2020. Kernel estimation for panel data with heterogeneous dynamics. The Econometrics Journal, 23(1), pp.156-175.
Examples
data <- panelhetero::simulation(N = 300, S = 50)
panelhetero::hpjkd(data = data)
#> $mean
#>
#> $acov
#>
#> $acor
#>
#> $mean_func
#> function (x)
#> {
#> hpjkdest1(x = x, X = mean_est, X1 = mean_est1, X2 = mean_est2,
#> h = mean_bw)
#> }
#> <bytecode: 0x56308f3737b0>
#> <environment: 0x56308f36ca80>
#>
#> $acov_func
#> function (x)
#> {
#> hpjkdest1(x = x, X = acov_est, X1 = acov_est1, X2 = acov_est2,
#> h = acov_bw)
#> }
#> <bytecode: 0x56308f373c48>
#> <environment: 0x56308f36ca80>
#>
#> $acor_func
#> function (x)
#> {
#> hpjkdest1(x = x, X = acor_est, X1 = acor_est1, X2 = acor_est2,
#> h = acor_bw)
#> }
#> <bytecode: 0x56308f3740e0>
#> <environment: 0x56308f36ca80>
#>
#> $bandwidth
#> mean autocovariance autocorrelation
#> 0.35188660 0.04743256 0.06049790
#>
#> $quantity
#> mean autocovariance autocorrelation
#> [1,] 0.3074430002 0.97750186 0.256812830
#> [2,] 0.0533456348 0.64948428 0.197807877
#> [3,] 0.8062331195 0.43211441 0.109427020
#> [4,] -0.2544504667 0.23903232 0.170289222
#> [5,] 0.5726174458 0.34382515 0.167531146
#> [6,] 0.1090859528 0.11164407 0.684638750
#> [7,] -0.1590057164 0.21049250 0.192979873
#> [8,] -0.1723369166 0.32103255 0.235990239
#> [9,] 1.0206140144 0.82995122 -0.032513916
#> [10,] 1.1287166572 0.55885619 0.058836432
#> [11,] -0.3565712928 0.20398919 0.183340677
#> [12,] -0.8496453169 0.21923184 0.369147414
#> [13,] 0.6313125247 0.27799606 0.278850546
#> [14,] 0.7318918262 0.49126598 0.346986093
#> [15,] 0.5247057164 0.51146202 0.186092194
#> [16,] 0.0766111862 0.79880417 0.198060088
#> [17,] 0.8367618777 0.27894740 0.305444564
#> [18,] -1.2729165422 0.25117192 0.479592621
#> [19,] 0.7235416340 0.25696211 -0.021087277
#> [20,] 1.5474340173 0.44782890 0.238335908
#> [21,] 0.6242044552 0.14531453 0.191674073
#> [22,] -0.8130640186 0.25848885 0.374118271
#> [23,] -0.0544813302 0.88713606 0.274205745
#> [24,] -0.5842921275 0.51433724 0.386834659
#> [25,] 2.2589804135 0.13377908 0.337327210
#> [26,] 0.1201514918 0.43242092 0.138134324
#> [27,] 1.4014437370 0.33003379 0.234633627
#> [28,] -0.3943390047 0.26499135 0.387877875
#> [29,] 0.9990498039 0.37160035 0.143137354
#> [30,] -0.8745499432 0.19759903 0.157904216
#> [31,] 1.1937654320 0.27232469 0.205532067
#> [32,] -0.1666321669 0.54389213 0.265946692
#> [33,] 1.7352777366 0.12367655 0.587098679
#> [34,] -0.7627231636 0.55931370 -0.024485190
#> [35,] 0.9554650018 0.55823287 0.302344094
#> [36,] 0.7607335285 0.25422784 -0.125360768
#> [37,] -0.4261756766 0.31238769 -0.060419772
#> [38,] -0.9113866406 0.20246498 0.063793672
#> [39,] -0.8533753611 0.55367292 -0.180109251
#> [40,] -0.5871820169 0.22515031 0.424763286
#> [41,] -1.4217002805 0.26762822 0.523403470
#> [42,] 0.4937276008 0.10606949 0.304905220
#> [43,] -2.2356116683 0.29602908 0.241607934
#> [44,] -1.5103604193 0.13644817 0.384555617
#> [45,] 1.4228928129 0.32327485 0.182015647
#> [46,] -0.0690924250 0.19296885 0.500164888
#> [47,] 0.4899857571 0.14207281 0.225713183
#> [48,] -1.3190968135 0.08307067 0.486067045
#> [49,] -0.5783468796 0.12471992 0.713105666
#> [50,] 0.1579815451 0.34666748 0.403297705
#> [51,] 0.0949679624 0.13077395 0.628496032
#> [52,] -0.6849158758 0.17589074 0.266295313
#> [53,] -1.4034105318 0.04851174 0.688531654
#> [54,] -1.0581470533 0.83159753 -0.099013269
#> [55,] -1.0143078195 0.34028589 0.293594734
#> [56,] -0.2385326079 0.96198859 0.005302933
#> [57,] 0.3809045310 0.36731436 0.363421418
#> [58,] -0.6261248748 0.26468570 0.295774940
#> [59,] -0.3956367251 0.25300413 -0.015733914
#> [60,] -1.0190775017 0.17786404 0.356947961
#> [61,] -0.8423295418 0.21899738 0.342450852
#> [62,] -0.3832679832 0.75863490 0.037839256
#> [63,] 0.1616352851 0.10102832 0.614274281
#> [64,] 0.2457788108 0.04786332 0.503365932
#> [65,] 0.6099898300 0.68269813 0.553543068
#> [66,] -0.2707039348 0.18161552 0.356903022
#> [67,] 1.5199220599 0.35554010 -0.030497117
#> [68,] 2.1182417714 0.72425879 -0.077461590
#> [69,] 1.4209234354 0.33365112 -0.027915224
#> [70,] 0.4699223550 0.51805365 0.001515935
#> [71,] -0.3847144149 0.46182735 0.116003098
#> [72,] -1.5779338372 0.18464730 0.149526493
#> [73,] -0.0608929739 0.31352556 0.288447007
#> [74,] 2.3425146068 0.36950962 0.268643994
#> [75,] -0.1683907866 0.30460644 0.413881080
#> [76,] 0.6546313793 0.31077314 0.630557309
#> [77,] -0.3356454401 0.91529476 0.412793828
#> [78,] -1.3515438505 0.43695961 0.226573695
#> [79,] -0.5686966271 0.24439968 0.468145416
#> [80,] -0.8143773533 0.52906697 0.515473977
#> [81,] -1.0721629958 0.33101014 -0.102026726
#> [82,] 0.7617833801 0.44697090 0.412568060
#> [83,] 1.2854277237 0.82616008 0.125949977
#> [84,] -0.5833040909 0.37462439 0.303648365
#> [85,] 0.9519333452 0.61976712 -0.013614180
#> [86,] 1.0230910413 0.30775463 0.383101827
#> [87,] -0.2314836138 0.62851073 0.159782275
#> [88,] 0.1091454068 0.16532997 0.091322647
#> [89,] 0.7708907810 0.72494876 0.296841574
#> [90,] -3.2397869757 0.17896226 0.483195884
#> [91,] -1.0777860285 0.31357195 0.173441707
#> [92,] 0.0032962878 0.25196709 0.338475793
#> [93,] -1.2352561452 1.34743319 0.246509769
#> [94,] 1.0230518403 0.23208515 0.141193833
#> [95,] 0.0228901911 0.23938822 0.453751889
#> [96,] 2.2746140598 0.02218516 0.319877457
#> [97,] 0.0007465796 0.86253459 0.134164914
#> [98,] -2.4765824942 0.56126008 0.228844798
#> [99,] -0.3496930256 0.44241083 0.272661417
#> [100,] -0.2086390842 0.34465269 0.126177958
#> [101,] -1.8968082355 0.19456150 0.255718630
#> [102,] -0.9689367428 0.17235529 0.329006638
#> [103,] 1.3600019963 0.56653348 -0.005882379
#> [104,] -0.2335016462 0.18999215 0.215456138
#> [105,] -1.5933167684 0.13010242 0.382686535
#> [106,] 0.6514731807 0.75709772 0.104800586
#> [107,] 1.1883574392 0.20886816 0.444465045
#> [108,] -0.7236442884 0.12176633 0.057846640
#> [109,] 1.3580330228 0.31178516 0.147221211
#> [110,] -0.7340553889 0.57011302 -0.029563632
#> [111,] -1.5340491092 0.18529721 0.404481474
#> [112,] 0.0414520879 0.42031549 0.554360089
#> [113,] 0.6721410485 0.10777906 0.405834248
#> [114,] -0.4924442510 0.58080604 0.205342273
#> [115,] 0.8253774331 0.32731241 -0.116528047
#> [116,] 0.3038208534 0.24044449 0.345339645
#> [117,] -2.5841277856 0.44765956 -0.024181327
#> [118,] 1.2541806678 0.14319031 0.481659593
#> [119,] -0.6696377475 0.18234321 0.366472428
#> [120,] 0.0910105339 0.31719738 0.066098724
#> [121,] -1.6115097379 0.82985497 0.252225753
#> [122,] -0.0626028180 0.06304446 0.623891112
#> [123,] 0.0675283541 0.27821123 0.484391117
#> [124,] 1.0942086072 0.40434205 -0.101680188
#> [125,] 1.0670132430 0.86913550 0.045274085
#> [126,] -1.1340497503 0.41307306 -0.082224055
#> [127,] -1.4892791611 0.08134587 0.526841204
#> [128,] -0.9116419086 0.23511736 0.325749228
#> [129,] -1.1159224502 0.18767489 0.596084411
#> [130,] 0.8173862656 0.13164140 0.618889908
#> [131,] -0.6760369612 0.27673266 0.610239554
#> [132,] -0.7907120352 0.18409086 0.438514881
#> [133,] 0.2600868794 0.27297684 0.488269520
#> [134,] -0.3918177335 0.28634598 -0.028700559
#> [135,] 1.7621996309 0.29551151 0.314839965
#> [136,] -0.0464052570 0.28518395 0.108297790
#> [137,] 0.8553671262 0.51942701 0.333244661
#> [138,] -0.2088993077 0.74123576 0.279392077
#> [139,] -1.2677771070 0.72957389 0.249609170
#> [140,] 0.5699595004 0.04815978 0.910716624
#> [141,] -0.5857138672 0.08232698 0.739426337
#> [142,] -0.3146485840 0.54732052 0.207168354
#> [143,] 0.7546034734 0.24867814 0.210642775
#> [144,] 0.9454199026 0.54838272 0.335397079
#> [145,] 0.3725431177 0.24258071 0.122150571
#> [146,] -0.8994443872 0.23962023 0.334705689
#> [147,] 0.3558364713 0.84964575 0.213343341
#> [148,] 0.8363468166 0.35329062 0.208132658
#> [149,] -0.4424057789 0.62073884 0.348501924
#> [150,] -0.2843623850 0.36244642 0.348453494
#> [151,] 1.2092459634 1.17097892 0.194361852
#> [152,] 0.8163174205 1.02424835 0.232595515
#> [153,] 0.3456844324 0.31359497 0.192249405
#> [154,] 0.3194779686 0.14808596 0.590613677
#> [155,] -0.5920358504 0.56765724 0.336853334
#> [156,] 0.0170691743 0.31302983 0.160617295
#> [157,] -0.4804170348 0.61343753 0.331092083
#> [158,] 0.2247752948 0.44226199 -0.139639548
#> [159,] 1.6723405544 0.38788904 0.225591450
#> [160,] 0.3600933726 0.33624462 0.011288588
#> [161,] 0.4665956136 0.33866252 0.263920948
#> [162,] -3.2753340580 0.25435424 0.338794998
#> [163,] -1.2398015585 0.12237455 0.461309362
#> [164,] -1.4761326669 0.18848718 0.357601915
#> [165,] 1.3111756350 0.48117411 0.093786573
#> [166,] -0.5558518942 0.29000167 -0.070058923
#> [167,] 1.4864924647 0.12720438 0.767042304
#> [168,] -1.4344456849 0.56960809 -0.075607071
#> [169,] -0.2501331846 0.25977317 0.126827234
#> [170,] -0.1645885484 0.11908856 0.060638232
#> [171,] -0.5172998970 0.51917008 0.187929319
#> [172,] 0.5892643425 0.04611229 0.356507523
#> [173,] 2.1455280330 0.13092608 0.310709877
#> [174,] 1.8884518503 0.53155930 0.191089043
#> [175,] 1.1182814986 0.21314889 0.365838452
#> [176,] 0.2787110870 0.07096616 0.541197387
#> [177,] -1.0994094125 0.19758996 0.293010200
#> [178,] -1.6313025034 0.08207880 0.536321581
#> [179,] -0.8211320706 0.12006529 0.360944531
#> [180,] 0.3479986954 0.49269177 0.041198550
#> [181,] 1.2523727591 0.16625460 0.584692171
#> [182,] -0.0766080730 0.48084560 0.307598205
#> [183,] -0.6409676389 0.30001661 -0.081752457
#> [184,] 0.8133809699 0.13886050 0.252955287
#> [185,] -0.3075225394 0.36247371 0.248151145
#> [186,] -1.7217618264 0.40656999 0.029773820
#> [187,] -0.1789421848 0.07731931 0.286458332
#> [188,] 0.2841819644 0.18642158 0.234928397
#> [189,] -1.1695022218 0.31215621 0.424490535
#> [190,] -0.0011826699 0.07255745 0.418520301
#> [191,] -0.6302887201 0.31304594 0.169546976
#> [192,] -0.0870174920 0.35080835 0.035830213
#> [193,] -0.4048445711 0.50512641 0.215103359
#> [194,] -0.1610451573 0.24471463 0.147630260
#> [195,] -0.6452196089 0.22972255 0.290358390
#> [196,] 0.5169971349 0.33814087 0.140534804
#> [197,] -0.3306613880 0.19145458 0.254305261
#> [198,] -0.0622626963 0.69155112 -0.023119092
#> [199,] -0.6379391675 0.43544766 0.368319239
#> [200,] -1.0826486103 0.26287194 -0.023258321
#> [201,] -0.2487217066 0.65755045 0.231184488
#> [202,] 0.5473222592 0.26831797 0.009596384
#> [203,] 0.7453116967 0.26703108 0.195692836
#> [204,] -0.6253387909 0.32950045 0.101371303
#> [205,] -1.0362005303 0.46868943 0.138681967
#> [206,] 0.6586150970 0.43958655 0.007655410
#> [207,] 0.7959228303 0.31717276 0.395350525
#> [208,] 1.6434007427 0.34568117 0.234346213
#> [209,] 0.6255751170 0.22353730 0.615253319
#> [210,] 0.6114187019 0.20742222 0.682818866
#> [211,] -0.1024883447 0.15051580 0.507568294
#> [212,] 1.4394331161 0.42526427 0.284570423
#> [213,] 1.1983758816 0.19020393 0.249146389
#> [214,] -0.1907465985 0.37084544 -0.038231563
#> [215,] -0.5032262955 0.62278066 0.342649491
#> [216,] -2.6969293770 0.26819563 0.146549016
#> [217,] 1.8104527144 0.25326080 0.287366879
#> [218,] 1.6703918451 1.03763451 -0.046424653
#> [219,] -0.5702798377 0.19638354 0.228140361
#> [220,] 0.7779889997 0.24451157 0.166219988
#> [221,] 1.3872003987 0.37973270 0.191751886
#> [222,] 0.8163835201 0.07603432 0.478449234
#> [223,] -0.9409657612 0.28266323 0.221742959
#> [224,] -0.0647316373 0.35754916 0.207768268
#> [225,] -0.3505672863 0.18107349 0.286350934
#> [226,] -0.9354311963 0.41741584 0.366676999
#> [227,] 1.2663397065 0.18454552 0.103445869
#> [228,] -1.4728959950 0.45136835 0.034659565
#> [229,] -0.1801408012 0.23160709 0.441447571
#> [230,] 0.1561403120 0.10001402 0.492544837
#> [231,] 1.3561554940 0.64854054 0.088979188
#> [232,] -0.1764641222 0.39092961 0.285989330
#> [233,] -1.3605403690 0.17682347 0.021211462
#> [234,] 1.4200502799 0.23271904 0.047900876
#> [235,] 0.8529917375 0.06672689 0.172468141
#> [236,] -0.3737216094 0.51910587 0.058935371
#> [237,] 0.0322176021 0.32036291 0.600102579
#> [238,] -0.0759001932 0.37143125 0.454102923
#> [239,] -0.4693656011 0.21684451 0.568063088
#> [240,] -1.7176553681 0.49078902 0.051194871
#> [241,] -0.5210840328 0.27985630 0.287454046
#> [242,] -1.4540286990 0.65181122 0.041204715
#> [243,] -0.9518901570 0.35332707 -0.252113779
#> [244,] 0.3569849994 0.20744435 0.380248194
#> [245,] 1.1134897186 0.32405837 0.144827222
#> [246,] 0.0799940396 0.25693325 -0.148352593
#> [247,] 0.7423700333 0.24404960 0.444629195
#> [248,] -1.1829665778 1.34049084 0.225709632
#> [249,] 1.4683414572 0.23164106 0.247968788
#> [250,] 0.2943667451 0.26895035 0.252040813
#> [251,] 1.6066436774 0.40404506 0.074752698
#> [252,] 0.4640094952 0.21848066 0.338679376
#> [253,] -0.9436282976 0.11050544 0.432172883
#> [254,] 0.3768179691 0.25122746 0.105231476
#> [255,] -0.5346680753 0.31603772 0.388428847
#> [256,] 0.5527331093 0.29329480 0.181857242
#> [257,] 0.2793564390 0.28720013 0.097920445
#> [258,] 0.4120738935 0.52794713 0.113084864
#> [259,] 0.7478514896 0.67179003 0.220681833
#> [260,] -1.5520459357 0.44378777 0.050302754
#> [261,] 1.4427099670 0.24356039 0.587817160
#> [262,] 0.4025201636 0.21519814 0.227411173
#> [263,] 0.6401497607 0.24727673 -0.021334418
#> [264,] -0.5308023865 0.19428075 0.217303063
#> [265,] -0.1661862686 0.58337837 0.032218116
#> [266,] 0.0220617441 0.21248678 0.192051393
#> [267,] 1.0256908664 0.14892459 0.016270408
#> [268,] 0.2875451671 0.48897923 0.316612604
#> [269,] 1.1153589073 0.57102157 0.320260635
#> [270,] -0.3622868688 0.12106230 0.204965269
#> [271,] 0.1118680379 0.46380837 0.425392068
#> [272,] -0.7545479162 0.12726370 0.424971085
#> [273,] -1.3103518276 0.10494566 0.435273886
#> [274,] -1.3044668247 0.36962298 0.242979893
#> [275,] 0.6313667840 0.17060501 0.429813231
#> [276,] 1.0401643422 0.26234818 -0.003654278
#> [277,] -1.4897359332 0.14989346 0.517534735
#> [278,] -1.0305133185 0.25957672 0.362381942
#> [279,] 1.4534044724 0.25626305 0.234494461
#> [280,] 1.1580736568 0.11442053 0.532737535
#> [281,] 2.1061476590 0.28743647 0.005890792
#> [282,] 1.4441677793 0.22550449 -0.044609475
#> [283,] 0.2011323695 1.01410315 0.482675015
#> [284,] -0.0953409751 0.38786520 0.272705532
#> [285,] -0.4845106827 0.28325990 0.542507347
#> [286,] -1.8464074295 0.33581636 0.152589330
#> [287,] 0.3804989713 0.36887163 -0.084099771
#> [288,] 0.7965794476 0.18084318 0.466311682
#> [289,] -0.3198128999 0.35439947 0.264553639
#> [290,] -0.2728269390 0.14486137 0.272987109
#> [291,] 0.4606518702 0.18340787 0.474522983
#> [292,] 0.1114497671 0.17660220 0.456113001
#> [293,] 0.1038869676 0.16616631 0.251193194
#> [294,] 0.9383405931 0.42851143 0.351798243
#> [295,] -0.9087168995 0.18303602 0.365228080
#> [296,] -0.4071856786 0.62730445 -0.013712092
#> [297,] 0.0605160440 0.23391917 0.409237029
#> [298,] 1.2322791531 0.25568885 0.111185892
#> [299,] 0.3106853729 0.79729670 0.302857039
#> [300,] 0.3141422211 0.41195950 0.206144215
#>
#> $acov_order
#> [1] 0
#>
#> $acor_order
#> [1] 1
#>
#> $N
#> [1] 300
#>
#> $S
#> [1] 50
#>