The naive kernel density estimation
nekd.RdThe `nekd()` function enables to implement the naive kernel density estimation without bias correction 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::nekd(data = data)
#> $mean
#>
#> $acov
#>
#> $acor
#>
#> $mean_func
#> function (x)
#> {
#> kdest(x = x, X = mean_est, h = mean_bw)
#> }
#> <bytecode: 0x56308f298f60>
#> <environment: 0x56308f299f20>
#>
#> $acov_func
#> function (x)
#> {
#> kdest(x = x, X = acov_est, h = acov_bw)
#> }
#> <bytecode: 0x56308f2992a8>
#> <environment: 0x56308f299f20>
#>
#> $acor_func
#> function (x)
#> {
#> kdest(x = x, X = acor_est, h = acor_bw)
#> }
#> <bytecode: 0x56308f2995f0>
#> <environment: 0x56308f299f20>
#>
#> $bandwidth
#> mean autocovariance autocorrelation
#> 0.35605017 0.05144543 0.06734172
#>
#> $quantity
#> mean autocovariance autocorrelation
#> [1,] 0.990865136 0.46650031 0.092054388
#> [2,] 0.376291248 0.39027353 0.149450786
#> [3,] -2.265495072 0.78156306 0.137845819
#> [4,] -1.214334932 0.19671643 0.095093454
#> [5,] -0.860734550 0.23498650 0.178790257
#> [6,] -0.098839354 0.41814844 0.106509560
#> [7,] 0.530735300 0.09367492 0.358387586
#> [8,] -0.799044965 0.26567879 0.375943912
#> [9,] 1.463751370 0.22128183 0.098993551
#> [10,] 1.714683395 0.28682199 0.217475213
#> [11,] 0.741508474 0.09424717 0.184717651
#> [12,] 0.234245589 0.43464557 0.371507732
#> [13,] -0.299229616 0.18114963 -0.054887905
#> [14,] 1.425237835 0.20843405 0.292385041
#> [15,] 0.095027885 0.97005224 0.205579562
#> [16,] 0.045084831 0.45225647 0.226636272
#> [17,] -0.331770999 0.34070393 0.073689730
#> [18,] -0.335128821 0.14796517 0.304410151
#> [19,] -3.623004928 0.14470745 0.367821706
#> [20,] -1.443884910 0.18565843 0.167416677
#> [21,] -0.186552374 0.23878736 0.333379952
#> [22,] -0.484841561 0.41603885 0.057382452
#> [23,] -0.799471884 0.94740658 -0.020483369
#> [24,] -1.500378980 0.36769003 0.376054331
#> [25,] -1.273593657 0.54774818 0.281810987
#> [26,] -0.508112616 0.52168123 0.485358073
#> [27,] 0.139240976 0.99615446 0.093395382
#> [28,] 0.304300352 0.79275026 0.294416856
#> [29,] 0.170490407 0.17881819 0.350711502
#> [30,] 0.728237699 0.24572132 0.039212957
#> [31,] -0.359128298 0.26670551 -0.234862095
#> [32,] 1.929109531 0.55745838 0.201567046
#> [33,] -0.691685802 0.23099758 0.018824187
#> [34,] 1.731708012 0.21998267 0.192598353
#> [35,] -1.270484237 0.28951376 -0.095068253
#> [36,] 2.542528226 0.36044730 0.526767163
#> [37,] 0.085400987 0.32085050 0.340553927
#> [38,] -0.739524877 0.21864596 0.212991203
#> [39,] -1.764619178 0.32123688 0.434336607
#> [40,] 0.347356796 0.67155305 0.072390217
#> [41,] -0.761036151 0.48782405 0.145268243
#> [42,] 0.747305558 0.34878800 0.200910033
#> [43,] -0.647273181 0.57744782 0.301980982
#> [44,] 0.703830937 0.26086682 -0.293220287
#> [45,] -0.022000852 0.10652863 0.591871146
#> [46,] -0.594828114 0.28309554 0.004288754
#> [47,] 0.348629297 0.76815492 0.335823066
#> [48,] 0.509892718 0.22067103 0.269814418
#> [49,] 0.555469424 0.11852734 0.164322838
#> [50,] 0.074937060 1.21857989 0.027786421
#> [51,] 1.258158804 0.28063110 -0.010125267
#> [52,] 0.274083886 0.15148058 0.133082816
#> [53,] 1.295763235 0.61230450 0.307596437
#> [54,] 0.135142066 0.30558773 0.055581424
#> [55,] 0.799987805 0.52045696 0.001943795
#> [56,] -0.326002706 0.61833670 0.082930004
#> [57,] 0.606400955 0.21741277 0.800293291
#> [58,] 0.572244287 0.23036604 0.503077463
#> [59,] -0.144190477 0.15677092 0.135493933
#> [60,] 1.419649821 0.37253205 0.082223963
#> [61,] 1.687823638 0.61033396 0.031429385
#> [62,] 1.368887503 0.38267733 0.309822636
#> [63,] 1.365437728 0.48707949 0.505216389
#> [64,] -0.622977482 0.61899323 0.246025168
#> [65,] 0.201466435 0.44943659 0.339849335
#> [66,] 0.206722333 0.70961218 0.034830403
#> [67,] 0.952403445 0.55936710 -0.029696440
#> [68,] -1.113056921 1.14807526 -0.070703502
#> [69,] -0.731362939 0.35785347 0.239196174
#> [70,] 0.972358953 0.89092513 0.382557925
#> [71,] 0.451051014 0.10203143 0.503926764
#> [72,] 0.906563732 0.35121120 0.118335914
#> [73,] 0.426087010 0.33304882 0.174595121
#> [74,] 0.038918409 0.05476516 0.555773654
#> [75,] -0.168339162 0.35170092 0.292831814
#> [76,] 0.930079819 0.88459982 0.111263269
#> [77,] -1.714725330 0.32262992 0.347311749
#> [78,] 1.021365408 1.06748792 0.092866358
#> [79,] -0.633621989 0.53478226 0.077351518
#> [80,] 0.956424513 0.46326928 0.178394827
#> [81,] 1.303815716 0.18870079 0.732318126
#> [82,] -0.242338731 0.65175705 0.125064375
#> [83,] -0.361786233 0.43997200 -0.082223054
#> [84,] 0.785726006 0.09457220 0.650824543
#> [85,] -0.405949131 0.11874017 0.497962720
#> [86,] -0.143744394 0.14413974 0.505828510
#> [87,] 0.178952225 0.14762400 0.503544289
#> [88,] 1.266215694 0.38964259 0.114753581
#> [89,] -0.774852505 0.24982826 0.128135873
#> [90,] 1.686146448 0.35696799 0.349450979
#> [91,] 0.124082422 0.16694448 0.080480025
#> [92,] 0.091533781 0.37613874 0.312005158
#> [93,] -0.798153588 0.71678087 0.188734572
#> [94,] 2.411869744 0.34879265 0.254034924
#> [95,] 0.142582110 0.10449712 0.597747879
#> [96,] -1.760012601 0.26275342 0.097987135
#> [97,] -0.392098782 0.30129288 0.485724125
#> [98,] 0.189096936 0.57837913 0.291856153
#> [99,] -0.709299464 0.13128140 0.313842342
#> [100,] 0.549609570 0.13737823 0.490485941
#> [101,] 0.756475322 0.40374307 0.275372560
#> [102,] 1.044746330 0.41587796 0.432132900
#> [103,] 0.559197051 0.17770043 0.009444480
#> [104,] -1.245580816 0.58680224 0.269286163
#> [105,] -0.155759648 0.24901537 0.247756176
#> [106,] -1.416586395 0.61979892 0.268340847
#> [107,] -2.222005396 0.53395016 0.045544019
#> [108,] -0.461953887 0.52933128 0.143136000
#> [109,] 0.338283210 0.37144542 0.352608123
#> [110,] -1.098539662 0.52632782 0.408594664
#> [111,] -1.040656057 0.32570566 -0.020022409
#> [112,] -2.929185175 0.37031285 0.269799041
#> [113,] 0.277389019 0.26885213 0.551197217
#> [114,] 3.928060927 0.43184513 0.350330849
#> [115,] -0.606471064 0.25590407 0.128784698
#> [116,] -0.233926572 0.39656397 0.080775763
#> [117,] 0.501450338 0.90825829 0.325997004
#> [118,] -1.742224538 0.17995376 0.147100635
#> [119,] 0.308834869 0.91084767 0.025680702
#> [120,] -0.010685738 0.60522653 -0.103204098
#> [121,] 2.957064358 0.14575062 0.150993958
#> [122,] -0.734034258 0.42353339 0.284231891
#> [123,] -0.179751555 0.67200845 -0.093923580
#> [124,] -0.235828123 0.43487145 0.439161130
#> [125,] -0.779957141 0.24278788 0.338781520
#> [126,] -0.544039387 0.25431530 0.285139850
#> [127,] 0.227706855 0.53646981 0.337982283
#> [128,] -1.335663612 0.52493847 0.031829742
#> [129,] 1.503460010 1.31243880 0.063187996
#> [130,] -0.809494489 0.13233910 0.342584942
#> [131,] 2.231864105 0.11466245 0.209050731
#> [132,] -0.750028472 0.12689495 0.558870777
#> [133,] 1.619812216 0.44963946 0.468769341
#> [134,] -0.220386648 0.31838023 0.212234457
#> [135,] 0.134435766 0.87599322 0.173738969
#> [136,] -0.297443557 0.35533287 0.122908909
#> [137,] -0.059628964 0.11764026 0.315275036
#> [138,] 0.261840720 0.23707351 -0.006773256
#> [139,] -1.700510335 0.74085236 0.232502754
#> [140,] 0.200612926 0.23918609 0.077756884
#> [141,] -0.250106204 0.22350392 0.420942043
#> [142,] 1.941823898 0.17637769 0.272197959
#> [143,] -0.768950426 0.28211386 0.081240850
#> [144,] -1.562814292 0.43592216 0.003902645
#> [145,] 2.331259852 0.25231753 0.373089082
#> [146,] -0.367956806 0.15089961 0.482454547
#> [147,] -0.183806819 0.34336385 0.114274995
#> [148,] -1.105878840 0.12959146 0.564069052
#> [149,] -0.613342094 0.25446401 0.524992359
#> [150,] -1.103440439 0.34328580 0.429321372
#> [151,] 0.367633931 0.27989403 0.153086570
#> [152,] 1.816497218 0.07580479 0.263694218
#> [153,] -0.987450976 0.10840049 0.435030033
#> [154,] 0.260139555 0.16948619 0.405083735
#> [155,] -0.418240517 0.18681059 -0.006188901
#> [156,] 1.081324668 0.28202646 0.031808016
#> [157,] 1.592496068 0.84819382 0.055029842
#> [158,] 0.542824550 0.26229212 0.081506128
#> [159,] -0.384011208 0.34202333 -0.077143174
#> [160,] -0.971745508 0.12150283 -0.211959246
#> [161,] 1.176044458 0.23815269 0.161470412
#> [162,] 0.009391157 0.15070797 0.229571363
#> [163,] -0.630388972 0.16522660 0.277881788
#> [164,] -1.405241222 0.78536417 0.180432251
#> [165,] -0.221739365 0.54974553 -0.010487700
#> [166,] -0.828889951 0.21301117 0.121520362
#> [167,] 0.662028254 0.42221741 0.003200604
#> [168,] 0.939414368 0.53568114 0.012345987
#> [169,] -0.811063344 0.11084815 0.432076420
#> [170,] 0.909671340 0.15857954 0.192886993
#> [171,] -0.213806821 1.05222229 0.070145923
#> [172,] 0.721128878 0.27145075 0.005272572
#> [173,] -0.907965889 0.15577822 0.679978751
#> [174,] -2.125283971 0.27623573 0.263834678
#> [175,] 2.362076252 0.27693876 0.360219251
#> [176,] 0.660102255 0.79536009 0.103917675
#> [177,] -0.716417944 0.31295943 0.137085481
#> [178,] 0.235748873 0.13255176 0.793931379
#> [179,] -0.822421563 0.33816654 0.130882886
#> [180,] -1.594959412 0.56715693 0.094318876
#> [181,] 0.016454127 0.17266498 0.530212305
#> [182,] -1.378061676 0.16451993 0.147842984
#> [183,] 0.503541299 0.06722209 0.452628464
#> [184,] 0.725293469 0.26327351 0.114047501
#> [185,] -0.095185541 0.17520178 0.324901168
#> [186,] 0.812860997 0.41870179 0.342952441
#> [187,] -1.466208002 1.08866045 0.209704609
#> [188,] 0.278453402 0.46834889 0.470348695
#> [189,] -0.017587277 0.13807310 0.486003655
#> [190,] 0.842337891 0.40746090 0.270893968
#> [191,] 1.299392287 0.34913523 0.255804876
#> [192,] 0.662813491 0.09561483 0.422409321
#> [193,] -1.142309284 0.39316735 0.019999288
#> [194,] -0.814339430 0.08728260 0.320037825
#> [195,] -0.370915683 0.39378115 0.465565318
#> [196,] -1.095367780 0.31491839 -0.004269562
#> [197,] 0.562547827 0.47417178 0.143652336
#> [198,] -0.384597701 0.13000005 0.597758219
#> [199,] 0.080266773 0.07963358 0.354233142
#> [200,] 0.643318325 0.14234205 0.604508162
#> [201,] 0.196620648 0.05324766 0.637240728
#> [202,] -0.091031126 0.33022296 0.199498448
#> [203,] -1.158445834 0.24097884 0.366053144
#> [204,] -0.258121236 0.74565835 0.449014515
#> [205,] 0.242601898 0.53500186 -0.124713691
#> [206,] -0.024949338 0.19201390 0.488185980
#> [207,] 0.125025726 0.49545292 0.174850007
#> [208,] -0.521730822 0.16256488 0.585659539
#> [209,] 0.692029506 0.41724339 0.303514511
#> [210,] 0.055970761 0.19668131 0.048069878
#> [211,] -0.785607383 0.19517844 0.024398516
#> [212,] 0.562033932 0.15025956 0.084579824
#> [213,] 1.345893692 0.25072339 0.546812652
#> [214,] 0.622400678 0.12261176 0.472157349
#> [215,] 0.011188306 0.65148546 0.277438039
#> [216,] 1.198294444 0.23587042 0.075916362
#> [217,] -1.454814487 0.27815483 0.185268699
#> [218,] -0.246361682 0.21809665 0.218616326
#> [219,] 0.216111821 0.11780306 0.078739791
#> [220,] -0.808316382 0.44454128 0.209348764
#> [221,] -0.131580440 0.41056996 -0.113233692
#> [222,] 0.717702631 0.31547046 -0.175393635
#> [223,] -1.985577634 0.10478331 0.557777159
#> [224,] -0.789773572 0.13234027 0.158575349
#> [225,] 0.404426654 1.11494666 -0.004137798
#> [226,] -1.789787969 0.21881040 0.127007230
#> [227,] -0.231952694 0.76738067 -0.085181791
#> [228,] -0.283397419 0.25849039 0.172271598
#> [229,] 0.936303494 0.53930735 0.245546373
#> [230,] -0.004089354 0.44724154 0.291769553
#> [231,] 0.371538433 0.59649584 0.241454249
#> [232,] -0.650992845 0.24498229 -0.159157941
#> [233,] -0.604831940 0.16680626 0.545788385
#> [234,] 1.474606024 0.14618490 0.538767820
#> [235,] 0.138793871 0.26655847 0.225976696
#> [236,] 0.549908940 0.18517846 0.250973365
#> [237,] -0.814776780 0.32962147 0.525208870
#> [238,] -0.666246081 0.54786216 0.017728020
#> [239,] -0.792465807 0.31558557 0.439148331
#> [240,] -0.719959053 0.33827403 0.104368437
#> [241,] -0.079858576 0.63283279 0.021883965
#> [242,] 1.618115737 0.30466888 0.279080914
#> [243,] -0.430342920 0.62924464 -0.102269176
#> [244,] -0.166424044 0.31042902 0.227398607
#> [245,] 1.268891239 0.25420897 0.143693549
#> [246,] -1.908168129 0.34843099 -0.034915255
#> [247,] 1.294960466 0.11455671 0.521662223
#> [248,] 0.894470405 0.20983056 0.320551915
#> [249,] 0.109289010 0.45920705 0.350899185
#> [250,] 0.674227954 0.51627551 0.224516735
#> [251,] -0.241313486 0.04970841 0.174955468
#> [252,] -0.619759342 0.39605349 0.217859436
#> [253,] 0.935351555 0.52053980 0.206165374
#> [254,] 0.265232881 0.13577118 0.486900904
#> [255,] 0.416089472 0.40944156 0.372140911
#> [256,] -0.952017617 0.75024834 0.212252901
#> [257,] 0.710205724 0.18619194 0.315016368
#> [258,] 1.234438870 0.11523531 0.668603323
#> [259,] -1.899861149 0.50375959 0.453196031
#> [260,] 0.222450841 0.64991661 0.362508974
#> [261,] -0.146099804 0.86122770 0.014230848
#> [262,] 0.257305765 0.40487436 -0.263399112
#> [263,] -0.293327952 0.47218487 0.632699585
#> [264,] 0.605883088 0.11605091 0.381873406
#> [265,] 0.293912862 0.45037670 0.362217040
#> [266,] -1.054949209 0.43634372 0.063604203
#> [267,] -0.976557720 0.24997897 0.391191617
#> [268,] -0.665200922 0.24268497 0.173262071
#> [269,] 1.059268774 0.40245220 0.346011757
#> [270,] 0.941457819 0.49691703 -0.075338205
#> [271,] 0.609777093 0.14227834 0.252883019
#> [272,] -2.284771516 0.69859644 0.092359641
#> [273,] -0.476049047 0.24050606 0.207255641
#> [274,] -1.081990951 0.34290912 -0.006158764
#> [275,] -1.308844291 0.52849947 0.712538362
#> [276,] -0.831740821 0.12343899 0.125638358
#> [277,] 3.031215977 0.43345266 0.482136038
#> [278,] 0.637611821 0.32664977 -0.077384736
#> [279,] 1.383266235 0.76367059 0.090369394
#> [280,] 0.191222202 0.19337347 0.230288886
#> [281,] -1.549881726 0.21442985 0.366328005
#> [282,] -1.260622168 0.19613661 0.341290221
#> [283,] 0.011609159 0.32296179 0.081013654
#> [284,] 1.462568429 0.27748132 0.479751083
#> [285,] 0.037835603 0.36155924 0.244384170
#> [286,] -1.128769934 0.41014938 0.241132690
#> [287,] -0.481452174 0.31553408 0.296133207
#> [288,] 0.650854281 0.53034404 0.150577807
#> [289,] -1.529604532 0.28480893 0.324019785
#> [290,] -0.761174237 0.76025029 0.217950504
#> [291,] -0.297728748 0.19822494 0.190738643
#> [292,] 1.494097702 0.56663843 0.006672565
#> [293,] 1.723505292 0.13431272 0.396356659
#> [294,] -0.623864900 0.16554578 0.458883338
#> [295,] 0.976408464 0.23554535 0.111856661
#> [296,] 0.465911156 0.34958736 0.249603375
#> [297,] 1.832798959 1.04956596 0.233558785
#> [298,] 1.495787224 0.99885893 -0.174694089
#> [299,] 1.902270247 0.23442297 0.130743449
#> [300,] -0.660334790 0.21823472 0.107900870
#>
#> $acov_order
#> [1] 0
#>
#> $acor_order
#> [1] 1
#>
#> $N
#> [1] 300
#>
#> $S
#> [1] 50
#>