The TOJ bias-corrected kernel density estimation
tojkd.RdThe `tojkd()` function enables to implement the TOJ 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::tojkd(data = data)
#> $mean
#>
#> $acov
#>
#> $acor
#>
#> $mean_func
#> function (x)
#> {
#> tojkdest2(x = x, X = mean_est, X21 = mean_est21, X22 = mean_est22,
#> X31 = mean_est31, X32 = mean_est32, X33 = mean_est33,
#> X34 = mean_est34, X35 = mean_est35, X36 = mean_est36,
#> X37 = mean_est37, X38 = mean_est38, X39 = mean_est39,
#> h = mean_bw)
#> }
#> <bytecode: 0x5630973d06e8>
#> <environment: 0x5630983ad300>
#>
#> $acov_func
#> function (x)
#> {
#> tojkdest2(x = x, X = acov_est, X21 = acov_est21, X22 = acov_est22,
#> X31 = acov_est31, X32 = acov_est32, X33 = acov_est33,
#> X34 = acov_est34, X35 = acov_est35, X36 = acov_est36,
#> X37 = acov_est37, X38 = acov_est38, X39 = acov_est39,
#> h = acov_bw)
#> }
#> <bytecode: 0x5630973d1750>
#> <environment: 0x5630983ad300>
#>
#> $acor_func
#> function (x)
#> {
#> tojkdest2(x = x, X = acor_est, X21 = acor_est21, X22 = acor_est22,
#> X31 = acor_est31, X32 = acor_est32, X33 = acor_est33,
#> X34 = acor_est34, X35 = acor_est35, X36 = acor_est36,
#> X37 = acor_est37, X38 = acor_est38, X39 = acor_est39,
#> h = acor_bw)
#> }
#> <bytecode: 0x5630973ce678>
#> <environment: 0x5630983ad300>
#>
#> $bandwidth
#> mean autocovariance autocorrelation
#> 0.35466670 0.04619656 0.07022076
#>
#> $quantity
#> mean autocovariance autocorrelation
#> [1,] 0.77967245 0.39281602 0.304169077
#> [2,] 0.31505700 0.49352789 0.125429191
#> [3,] -0.27732824 0.22615213 0.263426844
#> [4,] 0.53940856 0.87941379 0.415071001
#> [5,] -0.65772344 0.55620304 -0.080413971
#> [6,] 0.67651984 0.61765960 0.367801410
#> [7,] -1.00039011 0.22114647 -0.008778793
#> [8,] 0.74444858 0.93979632 0.239165642
#> [9,] 0.11832446 0.22779751 0.047413292
#> [10,] -0.15944346 0.20213859 0.571993477
#> [11,] 0.12059125 0.45724089 0.308292169
#> [12,] 0.59143307 0.44110810 0.339254667
#> [13,] -1.45131937 0.53509907 0.174044381
#> [14,] -0.60664229 0.70067277 0.071584376
#> [15,] 0.18157139 0.43934298 -0.196019184
#> [16,] -1.15536104 0.27046576 0.230026000
#> [17,] 1.77458706 0.28180918 0.196451771
#> [18,] -0.25175488 0.70005954 0.057172453
#> [19,] -1.30439121 0.38674725 0.133006940
#> [20,] 0.49728507 0.41179805 0.295971129
#> [21,] 1.31736428 0.08879579 0.642774534
#> [22,] 0.28949646 0.37003698 0.360164002
#> [23,] 1.24297542 0.23964482 0.361069219
#> [24,] -0.71498015 0.23310581 0.522525165
#> [25,] -0.19491272 0.18490762 0.440613678
#> [26,] -1.24187574 0.24275813 0.413850520
#> [27,] -0.02867669 0.16210680 0.334868849
#> [28,] 1.15766856 0.17614707 0.224297105
#> [29,] 1.49086802 0.35598957 0.306587803
#> [30,] 0.25163613 0.17262657 0.227672181
#> [31,] 0.96071338 0.21864608 -0.153854442
#> [32,] -1.01640151 0.28791452 0.205250402
#> [33,] 0.31688011 0.31668241 0.132828100
#> [34,] -0.78575209 0.18187432 0.138837893
#> [35,] -0.74031309 0.16911505 0.134440028
#> [36,] -0.06591595 0.36471906 0.275446923
#> [37,] -1.43676491 0.18648415 0.667856193
#> [38,] 0.10479563 0.45920700 -0.184056464
#> [39,] 1.00462512 0.34100639 0.325169854
#> [40,] -1.05840075 0.38236895 0.439602030
#> [41,] 0.46987633 0.21250336 0.242585296
#> [42,] 0.96751224 0.34470290 0.550645135
#> [43,] 0.14749837 0.10763299 0.717466527
#> [44,] -0.86869603 0.51415513 0.043809766
#> [45,] -1.52783933 0.22624839 -0.064210507
#> [46,] -0.11379511 0.34260649 0.302661174
#> [47,] -0.97399636 0.41241022 0.042737337
#> [48,] 0.47481231 0.28647384 0.366870470
#> [49,] -1.14230420 0.16800304 0.758128492
#> [50,] -0.99687897 0.20557489 0.301567500
#> [51,] 0.34132598 0.27785481 0.374029335
#> [52,] 0.08091590 0.74612911 0.141821557
#> [53,] 2.25246158 0.42710263 -0.016377051
#> [54,] -0.22373802 0.27696865 0.210313176
#> [55,] 0.06698620 0.49579983 0.452224146
#> [56,] 1.42181148 0.54517760 0.332460922
#> [57,] -0.30690876 0.26390541 0.307381157
#> [58,] 1.05487990 0.07787342 -0.021879786
#> [59,] 0.28745261 0.50535192 0.177694816
#> [60,] -1.01311351 0.14628079 0.416661466
#> [61,] -0.32760683 0.24781664 0.275911347
#> [62,] -0.27601498 0.05791999 0.390153307
#> [63,] 0.15184675 0.38693668 0.007822189
#> [64,] 0.24508391 0.34342433 0.424451097
#> [65,] -1.32707974 0.25955400 0.140445859
#> [66,] -0.81937256 0.40169026 0.088759514
#> [67,] -1.12262618 0.16224668 0.296372140
#> [68,] 1.55118006 0.12964186 0.443448681
#> [69,] 1.44668793 0.35334846 0.255145595
#> [70,] 0.03280341 0.27289684 0.513433060
#> [71,] -1.17097160 0.59434252 0.134897314
#> [72,] -1.58380152 0.09663832 0.388758973
#> [73,] -0.32105726 0.29313201 0.126236684
#> [74,] -1.07824709 0.43064490 -0.245108662
#> [75,] 1.33758245 0.35964137 0.307612320
#> [76,] 1.52729523 0.26367705 0.408815705
#> [77,] 1.60799094 0.74206132 0.144631614
#> [78,] 1.51343491 0.21790512 0.185774680
#> [79,] -0.44768618 0.37653850 0.142054402
#> [80,] -2.33417447 0.29039620 0.134421386
#> [81,] -0.30940666 0.20468021 0.516662305
#> [82,] 0.69851221 0.47121763 0.101907324
#> [83,] -0.72722735 0.39491159 -0.085598413
#> [84,] 1.00435914 0.22548645 -0.035852726
#> [85,] -0.52304252 0.28959159 0.118448311
#> [86,] 2.21674237 0.64915682 0.014155355
#> [87,] 0.89766877 0.23364429 0.108175166
#> [88,] 0.13283372 0.46631624 0.129253284
#> [89,] 0.66779130 0.28120328 0.553435338
#> [90,] 0.97452032 0.41234797 0.172688294
#> [91,] -2.15683435 0.58863529 0.056035600
#> [92,] 0.69381298 0.24115889 0.264257406
#> [93,] -0.87687271 0.27820595 0.073229411
#> [94,] -0.42931844 0.29079429 0.249513322
#> [95,] -0.53508279 0.35469916 0.224989352
#> [96,] 0.29860785 0.14358559 0.111543778
#> [97,] 0.54243712 0.36441012 0.191005455
#> [98,] -2.72887841 0.26858157 0.216732854
#> [99,] 1.08011783 0.38965040 0.391703027
#> [100,] -0.57746968 0.34767637 0.286586166
#> [101,] 0.08294231 0.09094625 -0.123757070
#> [102,] -1.05236318 0.76907238 0.025225893
#> [103,] 0.68256737 0.67323711 0.178175403
#> [104,] -0.62389562 0.21747720 0.265163886
#> [105,] 0.70127047 0.21851001 0.128230989
#> [106,] -1.37142210 0.22176475 0.440236175
#> [107,] 0.71054647 0.15667375 0.362164251
#> [108,] 1.16942663 0.07788642 0.253527458
#> [109,] -0.10207761 0.20885346 0.229567118
#> [110,] -0.04390427 0.53814083 0.094501111
#> [111,] -0.69267811 0.06948468 0.554963258
#> [112,] 0.98360019 0.19748323 0.394748350
#> [113,] -0.22303418 0.55090029 0.589047317
#> [114,] -1.57043242 0.38500196 -0.238045587
#> [115,] 1.35098816 0.32752078 0.068463271
#> [116,] -0.02539275 0.12115774 0.530584747
#> [117,] 0.21278518 0.10305960 0.567696644
#> [118,] -0.31938025 0.36038404 0.360215292
#> [119,] -1.21927279 0.24868372 -0.005239527
#> [120,] -0.37759096 0.14206383 0.332808821
#> [121,] 1.10402424 0.38337800 0.160917953
#> [122,] 0.19605560 0.11123304 0.570725218
#> [123,] 0.62333755 0.19146314 -0.149548538
#> [124,] 0.50732952 0.18095186 0.157206910
#> [125,] -1.71131494 0.33209516 0.126876363
#> [126,] 0.92197211 0.28200948 0.166423170
#> [127,] 0.77963723 0.68882606 0.035745626
#> [128,] 0.57058495 0.67281613 0.413693436
#> [129,] 1.21090936 0.24594250 0.168834821
#> [130,] 0.04613922 0.09109463 0.695474911
#> [131,] 1.23365956 0.30205255 0.439552665
#> [132,] 0.11897745 0.58760328 -0.177390634
#> [133,] -0.43548429 0.44943960 -0.006073062
#> [134,] 0.60469375 0.31156938 -0.079150561
#> [135,] -1.58919786 0.36777309 0.436894413
#> [136,] -0.30122244 0.30234602 -0.093896289
#> [137,] 0.88387163 0.33016716 0.169376992
#> [138,] -1.22611795 0.95655284 -0.133605353
#> [139,] -0.02912155 0.13676102 0.440147139
#> [140,] 0.76286627 0.19004921 0.397371495
#> [141,] 0.25023016 0.22128326 0.074826072
#> [142,] -1.40262781 0.12142257 0.449915736
#> [143,] -2.62723656 0.27475961 0.292642818
#> [144,] 0.50886253 0.34123051 0.524775422
#> [145,] -2.07058199 0.28782849 0.650883851
#> [146,] -0.75646104 0.17678334 0.894589404
#> [147,] 0.39472855 0.27123932 -0.092011538
#> [148,] 0.29730561 0.16082612 0.203021484
#> [149,] -2.12717753 0.30340655 0.235298439
#> [150,] -0.50307434 0.30115584 0.418692906
#> [151,] -1.35770820 0.82527480 -0.468715190
#> [152,] -1.87822249 0.32160006 0.042565496
#> [153,] -1.38676451 0.21771502 0.524124604
#> [154,] 0.01649640 0.41352389 0.487734671
#> [155,] 0.39872161 0.14166851 0.560506703
#> [156,] -0.88171485 0.23398800 0.359259644
#> [157,] -1.20466649 0.12276906 0.201846191
#> [158,] 0.25589328 0.33173210 0.363345760
#> [159,] -1.68092360 0.31581427 0.060632294
#> [160,] -0.63121693 0.16375381 0.465567623
#> [161,] -0.18428320 0.44438814 0.111545254
#> [162,] -0.32979996 0.36817926 0.133183750
#> [163,] 0.24769434 0.09086193 0.251639559
#> [164,] -1.30386118 0.15139863 0.083583607
#> [165,] 0.46139146 0.27364349 0.721080173
#> [166,] 2.33528841 0.24820841 -0.262788213
#> [167,] 0.28740174 0.22711781 0.290816937
#> [168,] -0.75531577 0.15543242 0.274226070
#> [169,] -1.25496255 0.24507650 0.312140637
#> [170,] -1.54781818 0.24562091 0.415022368
#> [171,] -0.65906233 0.12167925 0.295567199
#> [172,] 0.25230801 0.20246336 0.674416737
#> [173,] 0.12664478 0.27359925 0.419821047
#> [174,] 0.01707104 0.31200314 0.175395320
#> [175,] -2.07134174 0.34990519 -0.040459190
#> [176,] -1.27654308 0.52414904 0.087200131
#> [177,] 0.00945767 0.23118181 0.257631452
#> [178,] -0.45530368 0.08227432 0.774793489
#> [179,] 0.03079507 0.12452300 0.394952888
#> [180,] 0.59047212 0.17073490 0.094422460
#> [181,] -0.56649187 0.21462285 0.314697419
#> [182,] 0.65501424 0.77641534 0.006670576
#> [183,] 1.22071059 0.79294758 0.190583452
#> [184,] 0.26107090 0.29414531 0.237803564
#> [185,] 0.85464379 0.13477271 0.188866637
#> [186,] -0.28688324 0.66928660 -0.049674175
#> [187,] -1.21504293 0.46690342 0.244072081
#> [188,] 0.01291758 0.25820238 0.451295281
#> [189,] 0.43519887 0.23690951 0.471268921
#> [190,] 1.16713930 0.18263649 0.490783723
#> [191,] -0.06417340 0.80968775 0.059980690
#> [192,] 0.24804341 0.60033059 0.299356934
#> [193,] 0.45909426 0.18763022 0.409367246
#> [194,] -0.95612919 0.36923198 0.348217624
#> [195,] -1.52471436 0.14007852 0.082835042
#> [196,] 1.17606183 0.16062507 0.248818035
#> [197,] -0.25978085 0.13377409 0.266974474
#> [198,] -0.29659043 0.65438630 0.341426170
#> [199,] -0.33415865 0.09274085 0.338104496
#> [200,] 0.58829055 0.26878378 0.048395875
#> [201,] 0.67941279 0.39736045 0.144802066
#> [202,] -0.01297179 0.37532905 0.247389270
#> [203,] -0.66804546 0.25998336 0.381936087
#> [204,] 1.14018013 0.19585373 0.258768722
#> [205,] -0.86439445 0.25260827 0.247379176
#> [206,] -0.43784842 0.06253396 0.633469903
#> [207,] 0.15966657 0.39170731 0.184183709
#> [208,] -0.95374086 0.38647945 0.474495866
#> [209,] -0.40726550 0.39226853 -0.040760856
#> [210,] 0.88373138 0.16006684 0.260657280
#> [211,] 0.43008003 0.83866148 0.165657872
#> [212,] 1.49568548 1.10985650 0.352002528
#> [213,] 0.52500849 0.32656953 0.277227428
#> [214,] 0.66538981 1.02318781 0.276363629
#> [215,] -0.22996479 0.43835950 0.309526272
#> [216,] 0.52601463 0.15011111 0.317027471
#> [217,] 1.49587470 0.26613786 0.277571678
#> [218,] -2.24339918 0.81998347 -0.099662859
#> [219,] -1.25176269 0.29673739 0.605531973
#> [220,] 1.27551853 0.17794100 0.373352773
#> [221,] -1.34673182 0.13055983 0.242147795
#> [222,] 0.16300918 0.36248728 0.175541822
#> [223,] 1.38034729 0.46155912 0.184560629
#> [224,] 0.29134132 0.31819805 0.435579100
#> [225,] 1.25897818 0.43555276 0.269076385
#> [226,] 0.75564474 0.24609597 -0.133693260
#> [227,] 0.26307942 0.14672264 0.436541746
#> [228,] -0.07499641 0.51251736 -0.102620690
#> [229,] 1.22438189 0.20933935 0.048041004
#> [230,] 0.70398334 0.31055177 0.046129764
#> [231,] 1.38264932 0.23936916 0.095225048
#> [232,] 0.75108599 0.54185011 0.361410687
#> [233,] 1.34655062 0.32392269 0.203919480
#> [234,] 0.96244395 0.42519588 0.516456775
#> [235,] 2.12693076 0.30232925 0.335663505
#> [236,] 0.37586014 0.08146036 0.356307047
#> [237,] -1.56423838 0.13836547 0.330474257
#> [238,] -0.07609463 0.10229750 0.178222480
#> [239,] 0.06232657 0.89113834 -0.135592038
#> [240,] 0.47230349 0.18122699 0.777611201
#> [241,] -1.67809417 0.45831799 0.139526772
#> [242,] 0.72787766 0.13182932 0.455323906
#> [243,] -1.28440233 0.31916359 0.233913665
#> [244,] -0.04973289 0.34071389 0.298632471
#> [245,] 1.76723682 0.53339458 0.164401597
#> [246,] 2.25082400 0.37319739 0.398980801
#> [247,] 0.87882170 0.52661764 0.320553863
#> [248,] 0.77883048 0.57322313 0.062857761
#> [249,] -0.65321235 0.13068901 0.656904120
#> [250,] -0.33180980 0.61843515 0.357545236
#> [251,] -0.48990989 0.26184615 0.148044458
#> [252,] -1.42209856 0.62696619 -0.017805177
#> [253,] -0.14182456 0.15337389 0.429488380
#> [254,] 1.21696274 0.30366440 0.081050452
#> [255,] -0.60130636 0.16295975 0.448878314
#> [256,] -0.40478163 0.37531565 0.219195320
#> [257,] 0.91325321 0.62883121 0.137741156
#> [258,] 0.56733512 0.60748996 0.119706834
#> [259,] 0.10429441 0.33948978 0.203975737
#> [260,] 0.62023056 0.33170154 0.511812173
#> [261,] 0.53887478 0.24281395 0.291728120
#> [262,] -1.14069446 0.41036929 -0.052302458
#> [263,] 2.05123020 0.18345656 0.123086879
#> [264,] 0.39240460 0.33511909 0.297704610
#> [265,] 0.45869503 0.57139217 0.078250809
#> [266,] 0.74553466 0.17747201 0.445038139
#> [267,] 1.28842853 0.61219226 -0.097788559
#> [268,] -0.85046594 0.25220384 0.345783424
#> [269,] -0.20907466 0.19837674 -0.134380858
#> [270,] -1.87300302 0.98460874 0.270765907
#> [271,] 1.63385189 0.37779883 -0.018263405
#> [272,] 1.61594307 0.22623019 0.307828221
#> [273,] -0.47516312 0.08416657 0.575159143
#> [274,] 1.51894451 0.28813163 0.299394730
#> [275,] -0.60651066 0.39428725 0.511104235
#> [276,] -1.14502390 0.19731393 0.357987365
#> [277,] -0.25807112 0.09466320 0.189493861
#> [278,] -2.73673159 0.79238983 0.455198013
#> [279,] 0.39451831 0.27490163 0.199841302
#> [280,] -0.79756192 0.43248777 0.411490638
#> [281,] 0.37808870 0.29793886 0.433846406
#> [282,] 1.72944908 0.61061613 0.431349149
#> [283,] -0.79396458 0.43432488 0.147714932
#> [284,] 1.49780045 0.12477441 0.520269536
#> [285,] 1.30040224 0.21321929 0.155314893
#> [286,] -0.59941016 0.28245364 0.309497153
#> [287,] 0.31218706 0.53517615 0.178747018
#> [288,] 2.35604343 0.28560436 0.243456405
#> [289,] -1.12169759 0.15090241 0.360703068
#> [290,] -0.24456074 0.33919715 0.148579782
#> [291,] -0.49556018 0.05988239 0.623218309
#> [292,] -1.37655088 0.59433842 0.478220203
#> [293,] 1.35503563 0.17209277 0.229243187
#> [294,] -0.46454427 0.18703372 0.547658606
#> [295,] 1.54653701 0.11380325 0.381301581
#> [296,] 0.77652434 0.58193163 0.149175393
#> [297,] -0.93358387 0.62052288 0.216529925
#> [298,] 0.19787158 0.92092823 0.093712609
#> [299,] -2.03904916 0.18789009 0.273281436
#> [300,] 0.87525786 0.57788956 0.018524472
#>
#> $acov_order
#> [1] 0
#>
#> $acor_order
#> [1] 1
#>
#> $N
#> [1] 300
#>
#> $S
#> [1] 50
#>