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更新日時:2019-11-21 17:41:06

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Environment Data Windy 気象庁観測所 海表面積の各種時系列分析 R関数のコードとヘルプそして関連キーワードの検索結果 Rパッケージのタイトルと説明の検索/Title and Description of R package Online Calculation

Environment Data

  • 水文水質観測所毎の時刻水位 - 江戸川水門上、田園調布(上)、西新井 -、世界の天候、黄砂観測日数、気象データ(日平均気温、相対湿度)、UVインデックス、紫外線量、台風発生数、気温偏差、緯度別気温偏差、太陽黒点数、海面水温値と南方振動指数、海氷面積、オゾン全量、二酸化炭素濃度、世界の年平均降水量偏差、降水のpHの年平均値の時系列推移
  • 発生地震リスト
  • 日の出、日の入り、可照時間、日の出方位、日の入り方位、高度一覧
  • 原則として毎週金曜日に更新
No. Title Update
1 水文水質観測所毎の時刻水位の時系列推移 - 江戸川水門上、田園調布(上)、西新井 - 2019-11-15 10:19:15
2 発生地震リスト/List of earthquakes 2019-11-15 10:13:38
3 世界の天候の時系列推移 2019-11-15 10:10:27
4 黄砂観測日数の時系列推移 2019-11-15 10:03:45
5 気象データ(日平均気温、相対湿度)の時系列推移 2019-11-15 10:03:26
6 UVインデックスの時系列推移 2019-11-15 10:02:15
7 紫外線量の時系列推移 2019-11-15 10:01:52
8 台風発生数の時系列推移 2019-11-15 10:00:34
9 気温偏差の時系列推移 2019-11-15 10:00:15
10 緯度別気温偏差の時系列推移 2019-11-15 09:59:31
11 太陽黒点数の時系列推移 2019-11-15 09:58:45
12 海面水温値と南方振動指数の時系列推移 2019-11-15 09:57:30
13 海氷面積の時系列推移 2019-11-15 09:56:48
14 オゾン全量の時系列推移 2019-11-15 09:56:05
15 二酸化炭素濃度の時系列推移 2019-11-15 09:55:13
16 世界の年平均降水量偏差の時系列推移 2019-11-15 09:54:41
17 降水のpHの年平均値の時系列推移 2019-11-15 09:54:24
18 札幌対東京 涼しいのはどちらだ?! - 2014年から2019年までの各年7月24日~8月9日(2020年オリンピック開催期間)における札幌と東京の1時間毎の気温の比較 - 2019-11-04 16:06:48
19 水害統計調査 2019-10-15 19:52:22
20 日の出、日の入り、可照時間、日の出方位、日の入り方位、高度 2019-09-20 08:49:50

Windy

  • https://www.windy.com

気象庁観測所

  • 左から綾里大気環境観測所、南鳥島気象観測所、与那国島特別地域気象観測所

海表面積の各種時系列分析

  • Original timeseries data souce:National Snow and Ice Data Center https://nsidc.org/
  • R version 3.6.1 (2019-07-05)
  • CADFtest:0.3-3, devtools:2.2.1, dlm:1.1-5, dplyr:0.8.3, forecast:8.9, ggplot2:3.2.1, glmnet:2.0-18, knitr:1.26, lmtest:0.9-37, markdown:1.1, plyr:1.8.4, rmarkdown:1.17, rstan:2.19.2, rvest:0.3.5, tibble:2.1.3, tidyr:1.0.0, tseries:0.10-47

Original daily data Monthly average Unit root test Correlation ACF Q-Q Plot Arima model Decomposition State space model Simulation of SARIMA

Original daily data 
# original daily data
head(dataf0)
        Date Sea Ice Index:NORTH:Extent:10^6sqkm Sea Ice Index:SOUTH:Extent:10^6sqkm Sea Ice Index:Total(North+South):10^6sqkm
1 1978-10-26                              10.231                              17.624                                    27.855
2 1978-10-28                              10.420                              17.803                                    28.223
3 1978-10-30                              10.557                              17.670                                    28.227
4 1978-11-01                              10.670                              17.527                                    28.197
5 1978-11-03                              10.777                              17.486                                    28.263
6 1978-11-05                              10.968                              17.343                                    28.311
# original daily data
tail(dataf0)
            Date Sea Ice Index:NORTH:Extent:10^6sqkm Sea Ice Index:SOUTH:Extent:10^6sqkm Sea Ice Index:Total(North+South):10^6sqkm
13344 2019-11-14                               9.359                              15.064                                    24.423
13345 2019-11-15                               9.387                              14.965                                    24.352
13346 2019-11-16                               9.396                              14.856                                    24.252
13347 2019-11-17                               9.443                              14.796                                    24.239
13348 2019-11-18                               9.554                              14.689                                    24.243
13349 2019-11-19                               9.716                              14.499                                    24.215
Monthly average 
# monthly average
north
           Jan       Feb       Mar       Apr       May       Jun       Jul       Aug       Sep       Oct       Nov       Dec
1978                                                                                                     11.645133 13.667063
1979 15.414000 16.175286 16.341938 15.446800 13.856867 12.530000 10.311250  8.041067  7.051133  8.747937 10.943067 13.336267
1980 14.861875 15.955143 16.041313 15.429067 13.792600 12.204600 10.100062  7.984267  7.667067  9.182750 11.382867 13.592933
1981 14.909688 15.604071 15.631533 15.009933 13.801625 12.429733 10.271000  7.844313  7.138467  8.856267 10.929000 13.341125
1982 15.176733 15.973500 16.043875 15.466000 13.973200 12.476067 10.367062  8.139533  7.301733  9.421062 11.627467 13.641800
1983 14.942438 16.006143 16.085267 15.172067 13.491312 12.295667 10.570267  8.185875  7.394600  9.334067 11.461000 13.298438
1984 14.473267 15.298933 15.584200 15.014467 13.576688 12.151667  9.977533  7.771063  6.805200  8.560600 10.841533 12.989437
1985 14.724867 15.465714 15.885938 15.356533 14.073400 12.219067  9.744563  7.401867  6.697667  8.545938 11.024533 13.049933
1986 14.889625 15.784857 15.909467 15.058800 13.379563 11.975933 10.146467  7.979563  7.410667  9.483933 11.453267 13.222437
1987 14.969800 16.050143 15.815938 15.210867 13.742933 12.485667 10.332562  7.499905  7.278700  9.048774 11.224033 12.540500
1988 15.090474 15.583379 15.957226 15.123333 13.560871 11.943433  9.808677  7.891581  7.369000  9.135032 11.330833 13.625548
1989 14.954806 15.495536 15.423290 14.328400 13.044129 12.244533 10.129710  7.881774  7.008333  8.828903 11.115233 13.386806
1990 14.782613 15.578214 15.866742 14.650067 13.225839 11.640567  9.246613  6.797484  6.142800  8.484935 11.075200 13.105548
1991 14.363806 15.249393 15.416129 14.859733 13.473129 12.108033  9.514032  7.415355  6.472900  8.541419 10.884600 12.945097
1992 14.642677 15.462103 15.481129 14.676900 13.215548 12.146767 10.323129  7.925258  7.473700  9.319516 11.378667 13.407387
1993 14.896065 15.685643 15.813161 15.077200 13.368226 11.870900  9.476355  7.335000  6.396667  8.786129 11.318733 13.318968
1994 14.729774 15.561893 15.553613 14.888033 13.624387 12.016400  9.925161  7.639290  7.137600  8.915290 11.123200 13.271871
1995 14.586387 15.225679 15.260161 14.448600 12.972065 11.440433  8.987097  6.744355  6.080133  7.828935 10.760867 12.920839
1996 14.180871 15.154828 15.122806 14.215867 13.094548 12.083833 10.164258  8.180452  7.582533  9.160968 10.401700 12.861258
1997 14.417484 15.436714 15.467516 14.563033 13.177161 11.738367  9.410839  7.285032  6.686333  8.336548 10.684167 13.076194
1998 14.720516 15.745821 15.598097 14.891933 13.589839 11.705700  9.415161  7.508871  6.536033  8.451871 10.440600 12.758645
1999 14.359387 15.308929 15.397677 15.083900 13.750968 11.779167  9.488290  7.225581  6.116867  8.602806 10.796467 12.641194
2000 14.220355 15.141483 15.224839 14.558167 13.152677 11.665233  9.513000  7.168323  6.246067  8.379419 10.321100 12.637258
2001 14.202613 15.211143 15.516323 14.856833 13.509613 11.455933  9.070355  7.460806  6.732167  8.298290 10.657833 12.490742
2002 14.272613 15.342357 15.348903 14.299433 12.970613 11.583400  9.274161  6.599000  5.827133  8.161903 10.341867 12.608452
2003 14.390839 15.193143 15.484903 14.512067 13.016065 11.604033  9.214774  6.935871  6.116100  7.848290 10.125333 12.588355
2004 14.026419 14.914379 14.992581 13.987333 12.558419 11.447067  9.431355  6.854839  5.984500  7.925290 10.343267 12.553581
2005 13.661452 14.372857 14.686613 14.089833 12.911097 11.162033  8.648742  6.301129  5.503767  7.351968 10.216333 12.227613
2006 13.465581 14.324964 14.420968 13.905867 12.517355 10.919500  8.459839  6.495613  5.862433  7.541097  9.658733 11.954677
2007 13.703032 14.513250 14.542097 13.845200 12.779677 11.220067  7.942839  5.342323  4.267267  6.039710  9.760167 12.033968
2008 13.887258 14.953448 15.178903 14.351933 12.974000 11.208333  8.677935  5.913065  4.687433  7.349871 10.342867 12.358484
2009 13.913710 14.811536 14.983613 14.495633 13.186710 11.320267  8.465452  6.135742  5.261633  6.920323  9.771733 12.199871
2010 13.739065 14.581429 15.136710 14.658733 12.866097 10.585100  8.074677  5.874903  4.865067  6.983903  9.613967 11.830839
2011 13.463968 14.363036 14.546516 14.107800 12.680774 10.748667  7.724387  5.502452  4.561333  6.464548  9.771800 12.153581
2012 13.729419 14.553345 15.196258 14.625767 13.011806 10.674533  7.671774  4.723290  3.565600  5.885871  9.387967 12.006387
2013 13.702645 14.723536 15.032032 14.298733 12.997258 11.360133  8.131677  6.013516  5.208267  7.454839  9.939033 12.184258
2014 13.647484 14.417571 14.757516 14.087867 12.700710 11.032600  8.108452  6.077871  5.219933  7.232452 10.114600 12.352581
2015 13.602323 14.400643 14.370516 13.893167 12.468097 10.878900  8.377871  5.598742  4.615767  6.966226  9.846167 12.044774
2016 13.456774 14.202724 14.399935 13.681267 11.924419 10.412900  7.937548  5.370548  4.528500  6.081645  8.657833 11.459419
2017 13.190129 14.119429 14.290065 13.753467 12.630452 10.756400  7.939355  5.480645  4.821900  6.767129  9.492833 11.742677
2018 13.077355 13.967250 14.297581 13.696067 12.232032 10.777500  8.268097  5.614806  4.785233  6.134097  9.823133 11.861484
2019 13.555677 14.398357 14.551968 13.454600 12.163161 10.527467  7.591710  5.029355  4.315533  5.664677  8.887105          
# monthly average
south
           Jan       Feb       Mar       Apr       May       Jun       Jul       Aug       Sep       Oct       Nov       Dec
1978                                                                                                     15.896400 10.395250
1979  5.402200  3.141071  3.999312  7.485533 10.826667 14.187000 16.516875 17.698267 18.195533 17.820500 15.337067  9.235800
1980  4.562000  2.818357  3.294875  5.405000  8.856667 12.490267 15.564438 17.805600 18.817267 18.567875 16.133133 10.155867
1981  4.411875  2.873500  3.391533  5.838467  9.354625 13.108533 16.038733 17.736500 18.596467 18.293733 16.111333 10.894813
1982  5.260067  3.128500  4.287813  7.722933 10.758333 13.416733 15.872187 17.789200 18.353467 17.788375 15.536600  9.215667
1983  4.770500  3.070286  4.015667  6.470400  9.526000 12.642600 15.466667 17.250813 18.585200 17.915333 16.014200 10.393875
1984  4.778667  2.677267  3.612333  6.422000  9.748437 13.230467 16.394867 17.927688 18.171467 17.572600 16.134000 10.473000
1985  4.455400  2.836429  3.717188  6.493200 10.152800 13.428533 15.720937 17.632200 18.703200 18.204438 16.140200 11.352200
1986  5.422250  3.193143  3.698400  6.385533  9.295625 12.687000 15.316800 16.998812 17.683133 17.183733 15.006600  9.653937
1987  5.126000  3.253714  4.112750  6.796933  9.694067 12.684333 15.751563 17.661429 18.246067 17.674097 15.584100 13.379000
1988  3.817158  2.885690  3.966194  6.287400  9.602290 13.092800 15.748677 17.561000 18.307200 18.361032 16.147667 11.060613
1989  4.736806  2.977607  3.927290  6.306267 10.297161 13.580433 15.710581 17.465645 18.121067 17.856097 15.733433  9.837516
1990  4.867387  3.036179  3.965968  6.999867  9.715452 13.082900 15.570935 17.567452 18.193000 17.945323 15.468300  9.953516
1991  5.338258  3.161107  3.806839  7.053467 10.279452 13.065667 15.550419 17.718968 18.312600 17.917290 15.583533 10.192323
1992  4.748871  2.837379  3.573290  6.794100  9.924774 12.808500 15.894419 17.727032 18.147200 17.933968 15.895500 10.205742
1993  4.409387  2.482179  3.668194  6.651600 10.103774 13.147167 15.854871 17.491774 18.543200 18.127548 16.042067  9.933355
1994  4.965710  3.197536  4.549355  7.221567 10.408000 13.560133 16.295968 17.839581 18.612633 18.090065 15.880433 10.100516
1995  5.636000  3.560786  4.626419  7.267633 10.415484 13.289867 15.743871 17.780194 18.372733 18.029645 15.633933 10.621903
1996  5.871129  2.984586  4.183484  7.279933 10.916742 13.870367 16.119677 17.741387 18.631600 17.964548 15.717900  9.653161
1997  4.197258  2.489536  3.457387  6.492333 10.123968 13.116033 15.920677 17.684355 18.596433 17.993387 15.732767 10.285387
1998  4.464903  2.989571  4.107484  6.853833 10.328452 13.313233 15.962677 17.881355 18.903500 18.660452 16.300400 10.519484
1999  4.815871  2.966000  3.977774  6.891800 10.265323 13.648833 16.281613 17.957903 18.696367 18.352161 15.964600 10.722032
2000  4.748871  2.906517  4.085871  7.132300 10.920581 13.892700 16.097742 18.206129 18.887833 18.130516 15.757633  9.909710
2001  5.233097  3.650357  4.731452  7.044267 10.329903 13.418067 15.851871 17.422742 18.174967 17.726000 15.610300 10.345903
2002  4.739613  2.960393  3.748258  6.327833  9.511548 12.375767 15.414710 17.066677 17.887367 17.865774 15.405833 10.785419
2003  5.772710  3.788571  4.444355  7.208267 10.735806 13.985367 16.401968 17.582484 18.298300 18.198000 16.109533 10.563581
2004  5.590516  3.583552  4.526194  7.279767 10.470032 13.780000 16.332516 18.010065 18.919233 18.456935 16.084833 10.228903
2005  4.751839  2.969607  4.081613  7.031967 10.288806 13.291500 16.157839 17.922484 18.804800 18.476806 16.316167  9.680258
2006  4.163548  2.651393  3.214613  6.010400  9.456258 13.344767 16.114129 18.097645 19.094100 18.732613 16.229833  9.854129
2007  4.672581  2.904607  3.834806  6.418267  9.647806 13.287300 15.955774 17.681903 18.860633 18.507742 15.892133 11.980516
2008  6.413710  3.894517  5.284452  8.242300 11.049355 14.061667 16.094839 17.644516 18.145033 17.993903 16.248133 11.511742
2009  5.707355  2.990571  4.441065  7.798500 10.925742 13.907467 16.261323 18.097806 18.960467 18.298226 15.847833 10.738548
2010  4.958097  3.105500  3.846742  6.715433 10.639258 14.410200 16.921323 18.607065 18.798600 18.648323 16.754900 11.271161
2011  4.511710  2.519071  3.367839  6.096600 10.092742 13.333300 15.752548 17.805452 18.739233 18.218484 15.757367 11.198968
2012  5.653871  3.553241  4.550258  7.309233 10.457000 13.546667 16.298000 18.096968 19.207833 18.593871 16.109933 10.394226
2013  5.543290  3.836429  5.017387  7.622633 10.919742 14.154833 16.808548 18.663774 19.388667 19.017774 16.872167 11.853581
2014  6.326806  3.843000  4.901516  8.343000 11.519355 14.686667 17.105742 18.907968 19.756400 19.002806 16.387767 11.928290
2015  6.851871  3.798929  4.964258  8.373200 11.716129 14.474900 16.775226 17.749355 18.444000 18.409258 16.175100 10.655226
2016  4.689129  2.789517  4.069032  7.221600 10.102387 13.241933 16.023839 17.892032 18.150067 17.460000 14.222667  8.279387
2017  3.783903  2.287929  2.699065  5.435933  9.013839 12.408767 15.296677 17.218903 17.905900 17.776097 15.113033  9.482065
2018  4.210968  2.325786  3.540000  6.033167  9.321355 12.885233 15.700323 17.417387 17.961300 17.732194 15.101833  9.188129
2019  3.831323  2.656214  3.164161  5.708633  8.835516 12.220800 15.269129 17.395742 18.243867 17.845355 15.611895

Unit root test 
CADFtest(model = north, type = "trend", criterion = "AIC", max.lag.y = 1)

    ADF test

data:  north
ADF(1) = -31.765, p-value < 0.00000000000000022
alternative hypothesis: true delta is less than 0
sample estimates:
     delta 
-0.2876731 
CADFtest(model = south, type = "trend", criterion = "AIC", max.lag.y = 1)

    ADF test

data:  south
ADF(1) = -32.77, p-value < 0.00000000000000022
alternative hypothesis: true delta is less than 0
sample estimates:
    delta 
-0.287052 
CADFtest(model = north + south, type = "trend", criterion = "AIC", max.lag.y = 1)

    ADF test

data:  north + south
ADF(1) = -20.853, p-value < 0.00000000000000022
alternative hypothesis: true delta is less than 0
sample estimates:
     delta 
-0.4096057
Correlation 
cor.test(x = north, y = south, alternative = "two", method = "pearson")

    Pearson's product-moment correlation

data:  north and south
t = -54.047, df = 491, p-value < 0.00000000000000022
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 -0.9370053 -0.9114186
sample estimates:
       cor 
-0.9252573

ACF

Q-Q Plot

ARIMA model
  • North
train <- head(tail(north, 12 * 5), -12)
test <- tail(north, 12)
arimamodel <- auto.arima(y = train, seasonal = T)
forecastdata <- forecast(arimamodel, h = 12)
arimamodel
Series: train 
ARIMA(0,1,0)(1,1,0)[12] 

Coefficients:
         sar1
      -0.6135
s.e.   0.1467

sigma^2 estimated as 0.08931:  log likelihood=-9.71
AIC=23.41   AICc=23.79   BIC=26.52
forecast::accuracy(f = forecastdata, test)
                      ME      RMSE       MAE         MPE      MAPE      MASE        ACF1 Theil's U
Training set  0.02813187 0.2515215 0.1584777   0.1787124  1.802693 0.5040282 -0.03011541        NA
Test set     -1.05841912 1.1381114 1.0584191 -13.8516784 13.851678 3.3662347  0.74962008 0.7376245
# 『rwf() returns forecasts and prediction intervals for a random walk with drift model applied to y.』
forecast::accuracy(f = rwf(y = train), test)
                      ME     RMSE      MAE       MPE     MAPE      MASE      ACF1 Theil's U
Training set -0.05381803 1.820561 1.590302 -3.038105 18.73080  5.057855 0.7394960        NA
Test set      0.92179786 3.726042 3.428358 -9.042024 41.42429 10.903675 0.7413269  2.766013
# 『Returns forecasts and prediction intervals for an iid model applied to y.』
forecast::accuracy(f = meanf(y = train), test)
                                     ME     RMSE      MAE       MPE     MAPE      MASE      ACF1 Theil's U
Training set -0.00000000000000005551115 3.343904 2.953603 -14.86653 36.75563  9.393746 0.8510169        NA
Test set      0.34520374795849007032444 3.626685 3.197721 -15.44253 41.50789 10.170147 0.7413269  2.946652
  • South
train <- head(tail(south, 12 * 5), -12)
test <- tail(south, 12)
arimamodel <- auto.arima(y = train, seasonal = T)
forecastdata <- forecast(arimamodel, h = 12)
arimamodel
Series: train 
ARIMA(0,1,0)(0,1,1)[12] 

Coefficients:
         sma1
      -0.7238
s.e.   0.4890

sigma^2 estimated as 0.2193:  log likelihood=-26.54
AIC=57.08   AICc=57.46   BIC=60.19
forecast::accuracy(f = forecastdata, test)
                     ME      RMSE       MAE        MPE     MAPE      MASE      ACF1 Theil's U
Training set 0.05167834 0.3941297 0.2738208 1.26579638 4.869694 0.3314382 0.1158752        NA
Test set     0.07193823 0.4881389 0.4255473 0.05798647 5.265553 0.5150908 0.5178527 0.1702123
# 『rwf() returns forecasts and prediction intervals for a random walk with drift model applied to y.』
forecast::accuracy(f = rwf(y = train), test)
                      ME     RMSE      MAE         MPE     MAPE     MASE      ACF1 Theil's U
Training set  0.06752219 2.996411 2.539248   -7.952581  34.6412 3.073556 0.7622971        NA
Test set     -5.45048190 7.812550 6.571129 -143.189078 149.4900 7.953825 0.7659837  5.074296
# 『Returns forecasts and prediction intervals for an iid model applied to y.』
forecast::accuracy(f = meanf(y = train), test)
                                    ME     RMSE      MAE       MPE      MAPE     MASE      ACF1 Theil's U
Training set  0.0000000000000006106227 5.553280 4.996378 -50.35933  80.12543 6.047715 0.8526133        NA
Test set     -1.7050858001836253219352 5.851112 5.245844 -82.87591 103.90929 6.349673 0.7659837  3.408436
Decomposition

State space model 
# 状態空間モデル:ローカルレベルモデル + 季節成分

\[y_t=\mu_t + \gamma_t + \epsilon_t,\ μ_{t+1} = μ_t + ξ_t,\ t = 11,\dots,n に対して γ_{t+1} = −(γ_t + γ_{t−1} + \cdots + γ_{t−10}) + ω_t,\ \epsilon_t \sim NID(0,σ^2_\epsilon),\ \xi _t \sim NID(0,σ^2_\xi),\ \omega_t \sim NID(0,σ^2_\omega)\]

\[観測値:y_t,\ 不規則要素:\epsilon_t,\ レベル:\mu_t,\ レベル撹乱要素:\xi_t,\ 季節要素:\gamma_t,\ 季節撹乱要素:\omega_t\]

LaTeX Source: http://elsur.jpn.org/ck 
library(dlm)
f_build <- function(param) {
    m1 <- dlmModPoly(order = 1, dV = exp(param[1]), dW = exp(param[2]))  # m0は0とする。m0 = rep(0, order)
    m2 <- dlmModSeas(frequency = 12, dV = 0, dW = c(exp(param[3]), rep(0, 10)))
    return(m1 + m2)
}
  • North
parameter <- dlmMLE(y = north, parm = log(c(var(north), 10^-3, 10^-3)), build = f_build)
parameter
# optim {stats}による最尤推定
# $`par` パラメータ最尤推定値
# $value 上記推定パラメータの下でのモデルの結果
# $counts 繰り返し計算回数
# $convergence 収束した場合はゼロ
$par
[1] -16.155232  -2.707688  -7.465117

$value
[1] -258.2288

$counts
function gradient 
      42       42 

$convergence
[1] 0

$message
[1] "CONVERGENCE: REL_REDUCTION_OF_F <= FACTR*EPSMCH"
fit <- dlmMLE(y = north, parm = parameter$par, build = f_build, method = "BFGS")
fit
exp(fit$par)
sqrt(exp(fit$par))
$par
[1] -16.155232  -2.707699  -7.465122

$value
[1] -258.2288

$counts
function gradient 
       6        1 

$convergence
[1] 0

$message
NULL

[1] 0.00000009635444 0.06669005367988 0.00057271501046
[1] 0.0003104101 0.2582441745 0.0239314649
model <- f_build(param = fit$par)
model
$FF
     [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12]
[1,]    1    1    0    0    0    0    0    0    0     0     0     0

$V
                 [,1]
[1,] 0.00000009635444

$GG
      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12]
 [1,]    1    0    0    0    0    0    0    0    0     0     0     0
 [2,]    0   -1   -1   -1   -1   -1   -1   -1   -1    -1    -1    -1
 [3,]    0    1    0    0    0    0    0    0    0     0     0     0
 [4,]    0    0    1    0    0    0    0    0    0     0     0     0
 [5,]    0    0    0    1    0    0    0    0    0     0     0     0
 [6,]    0    0    0    0    1    0    0    0    0     0     0     0
 [7,]    0    0    0    0    0    1    0    0    0     0     0     0
 [8,]    0    0    0    0    0    0    1    0    0     0     0     0
 [9,]    0    0    0    0    0    0    0    1    0     0     0     0
[10,]    0    0    0    0    0    0    0    0    1     0     0     0
[11,]    0    0    0    0    0    0    0    0    0     1     0     0
[12,]    0    0    0    0    0    0    0    0    0     0     1     0

$W
            [,1]        [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12]
 [1,] 0.06669005 0.000000000    0    0    0    0    0    0    0     0     0     0
 [2,] 0.00000000 0.000572715    0    0    0    0    0    0    0     0     0     0
 [3,] 0.00000000 0.000000000    0    0    0    0    0    0    0     0     0     0
 [4,] 0.00000000 0.000000000    0    0    0    0    0    0    0     0     0     0
 [5,] 0.00000000 0.000000000    0    0    0    0    0    0    0     0     0     0
 [6,] 0.00000000 0.000000000    0    0    0    0    0    0    0     0     0     0
 [7,] 0.00000000 0.000000000    0    0    0    0    0    0    0     0     0     0
 [8,] 0.00000000 0.000000000    0    0    0    0    0    0    0     0     0     0
 [9,] 0.00000000 0.000000000    0    0    0    0    0    0    0     0     0     0
[10,] 0.00000000 0.000000000    0    0    0    0    0    0    0     0     0     0
[11,] 0.00000000 0.000000000    0    0    0    0    0    0    0     0     0     0
[12,] 0.00000000 0.000000000    0    0    0    0    0    0    0     0     0     0

$m0
 [1] 0 0 0 0 0 0 0 0 0 0 0 0

$C0
          [,1]     [,2]     [,3]     [,4]     [,5]     [,6]     [,7]     [,8]     [,9]    [,10]    [,11]    [,12]
 [1,] 10000000        0        0        0        0        0        0        0        0        0        0        0
 [2,]        0 10000000        0        0        0        0        0        0        0        0        0        0
 [3,]        0        0 10000000        0        0        0        0        0        0        0        0        0
 [4,]        0        0        0 10000000        0        0        0        0        0        0        0        0
 [5,]        0        0        0        0 10000000        0        0        0        0        0        0        0
 [6,]        0        0        0        0        0 10000000        0        0        0        0        0        0
 [7,]        0        0        0        0        0        0 10000000        0        0        0        0        0
 [8,]        0        0        0        0        0        0        0 10000000        0        0        0        0
 [9,]        0        0        0        0        0        0        0        0 10000000        0        0        0
[10,]        0        0        0        0        0        0        0        0        0 10000000        0        0
[11,]        0        0        0        0        0        0        0        0        0        0 10000000        0
[12,]        0        0        0        0        0        0        0        0        0        0        0 10000000
# カルマンフィルター
filtered <- dlmFilter(y = north, mod = model)
residata <- residuals(filtered, sd = F)
Box.test(x = residata, type = "Ljung-Box", lag = 10)
adf.test(x = residata, k = 10)
tail(filtered$m)

    Box-Ljung test

data:  residata
X-squared = 62.476, df = 10, p-value = 0.000000001228


    Augmented Dickey-Fuller Test

data:  residata
Dickey-Fuller = -11.256, Lag order = 10, p-value = 0.01
alternative hypothesis: stationary

              [,1]       [,2]       [,3]       [,4]       [,5]       [,6]      [,7]     [,8]       [,9]      [,10]      [,11]      [,12]
Jun 2019 10.313154  0.2143123  1.7972963  3.1250809  3.8221601  3.5960821 2.7904849 1.340175 -0.7578577 -3.6308528 -5.3737669 -4.6376872
Jul 2019  9.915850 -2.3241394  0.2495926  1.7996073  3.1260475  3.8231011 3.5967898 2.790774  1.3399687 -0.7585084 -3.6317812 -5.3747627
Aug 2019  9.688221 -4.6588661 -2.3039245  0.2509172  1.8001603  3.1265846 3.8235035 3.596952  2.7906534  1.3395950 -0.7590391 -3.6323489
Sep 2019  9.689588 -5.3740545 -4.6589874 -2.3039325  0.2509139  1.8001571 3.1265822 3.823503  3.5969528  2.7906556  1.3395982 -0.7590357
Oct 2019  9.331879 -3.6672015 -5.3422881 -4.6569066 -2.3030644  0.2517569 1.8007885 3.126836  3.8233127  3.5963661  2.7898230  1.3387076
Nov 2019  9.617415 -0.7303104 -3.6925540 -5.3439433 -4.6575944 -2.3037340 0.2512539 1.800584  3.1269843  3.8237756  3.5970249  2.7905292

smoothed <- dlmSmooth(y = filtered)
tail(smoothed$s, 6)
smoothdata <- smoothed$s
tail(smoothdata)
              [,1]       [,2]       [,3]       [,4]       [,5]       [,6]      [,7]     [,8]       [,9]      [,10]      [,11]      [,12]
Jun 2019 10.276212  0.2512539  1.8005841  3.1269843  3.8237756  3.5970249 2.7905292 1.340218 -0.7396091 -3.6783000 -5.3550471 -4.6536051
Jul 2019  9.895444 -2.3037340  0.2512539  1.8005841  3.1269843  3.8237756 3.5970249 2.790529  1.3402182 -0.7396091 -3.6783000 -5.3550471
Aug 2019  9.686949 -4.6575944 -2.3037340  0.2512539  1.8005841  3.1269843 3.8237756 3.597025  2.7905292  1.3402182 -0.7396091 -3.6783000
Sep 2019  9.659476 -5.3439433 -4.6575944 -2.3037340  0.2512539  1.8005841 3.1269843 3.823776  3.5970249  2.7905292  1.3402182 -0.7396091
Oct 2019  9.357232 -3.6925540 -5.3439433 -4.6575944 -2.3037340  0.2512539 1.8005841 3.126984  3.8237756  3.5970249  2.7905292  1.3402182
Nov 2019  9.617415 -0.7303104 -3.6925540 -5.3439433 -4.6575944 -2.3037340 0.2512539 1.800584  3.1269843  3.8237756  3.5970249  2.7905292
              [,1]       [,2]       [,3]       [,4]       [,5]       [,6]      [,7]     [,8]       [,9]      [,10]      [,11]      [,12]
Jun 2019 10.276212  0.2512539  1.8005841  3.1269843  3.8237756  3.5970249 2.7905292 1.340218 -0.7396091 -3.6783000 -5.3550471 -4.6536051
Jul 2019  9.895444 -2.3037340  0.2512539  1.8005841  3.1269843  3.8237756 3.5970249 2.790529  1.3402182 -0.7396091 -3.6783000 -5.3550471
Aug 2019  9.686949 -4.6575944 -2.3037340  0.2512539  1.8005841  3.1269843 3.8237756 3.597025  2.7905292  1.3402182 -0.7396091 -3.6783000
Sep 2019  9.659476 -5.3439433 -4.6575944 -2.3037340  0.2512539  1.8005841 3.1269843 3.823776  3.5970249  2.7905292  1.3402182 -0.7396091
Oct 2019  9.357232 -3.6925540 -5.3439433 -4.6575944 -2.3037340  0.2512539 1.8005841 3.126984  3.8237756  3.5970249  2.7905292  1.3402182
Nov 2019  9.617415 -0.7303104 -3.6925540 -5.3439433 -4.6575944 -2.3037340 0.2512539 1.800584  3.1269843  3.8237756  3.5970249  2.7905292
tmpts <- dropFirst(smoothdata)[, 1]
Date <- as.Date(time(tmpts))
Value <- as.matrix(tmpts)
smoothdf <- data.frame(Date, Value, stringsAsFactors = F, check.names = F)
head(smoothdf)
        Date    Value
1 1978-11-01 12.68084
2 1978-12-01 12.48822
3 1979-01-01 12.60002
4 1979-02-01 12.46763
5 1979-03-01 12.49160
6 1979-04-01 12.31726
tmpts <- dropFirst(smoothdata)[, 3]
Date <- as.Date(time(tmpts))
Value <- as.matrix(tmpts)
smoothseasondf <- data.frame(Date, Value, stringsAsFactors = F, check.names = F)
head(smoothseasondf)
        Date     Value
1 1978-11-01 -3.355561
2 1978-12-01 -1.035709
3 1979-01-01  1.178838
4 1979-02-01  2.813977
5 1979-03-01  3.707657
6 1979-04-01  3.850333

  • South
parameter <- dlmMLE(y = south, parm = log(c(var(south), 10^-3, 10^-3)), build = f_build)
parameter
# optim {stats}による最尤推定
# $`par` パラメータ最尤推定値
# $value 上記推定パラメータの下でのモデルの結果
# $counts 繰り返し計算回数
# $convergence 収束した場合はゼロ
$par
[1]  -2.752496  -2.779012 -25.782568

$value
[1] -72.39518

$counts
function gradient 
      51       51 

$convergence
[1] 0

$message
[1] "CONVERGENCE: REL_REDUCTION_OF_F <= FACTR*EPSMCH"
fit <- dlmMLE(y = south, parm = parameter$par, build = f_build, method = "BFGS")
fit
exp(fit$par)
sqrt(exp(fit$par))
$par
[1]  -2.752474  -2.779038 -25.782568

$value
[1] -72.39518

$counts
function gradient 
       4        1 

$convergence
[1] 0

$message
NULL

[1] 0.063769915150624273 0.062098211895611224 0.000000000006349989
[1] 0.252527058254 0.249195128154 0.000002519918
model <- f_build(param = fit$par)
model
$FF
     [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12]
[1,]    1    1    0    0    0    0    0    0    0     0     0     0

$V
           [,1]
[1,] 0.06376992

$GG
      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12]
 [1,]    1    0    0    0    0    0    0    0    0     0     0     0
 [2,]    0   -1   -1   -1   -1   -1   -1   -1   -1    -1    -1    -1
 [3,]    0    1    0    0    0    0    0    0    0     0     0     0
 [4,]    0    0    1    0    0    0    0    0    0     0     0     0
 [5,]    0    0    0    1    0    0    0    0    0     0     0     0
 [6,]    0    0    0    0    1    0    0    0    0     0     0     0
 [7,]    0    0    0    0    0    1    0    0    0     0     0     0
 [8,]    0    0    0    0    0    0    1    0    0     0     0     0
 [9,]    0    0    0    0    0    0    0    1    0     0     0     0
[10,]    0    0    0    0    0    0    0    0    1     0     0     0
[11,]    0    0    0    0    0    0    0    0    0     1     0     0
[12,]    0    0    0    0    0    0    0    0    0     0     1     0

$W
            [,1]                 [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12]
 [1,] 0.06209821 0.000000000000000000    0    0    0    0    0    0    0     0     0     0
 [2,] 0.00000000 0.000000000006349989    0    0    0    0    0    0    0     0     0     0
 [3,] 0.00000000 0.000000000000000000    0    0    0    0    0    0    0     0     0     0
 [4,] 0.00000000 0.000000000000000000    0    0    0    0    0    0    0     0     0     0
 [5,] 0.00000000 0.000000000000000000    0    0    0    0    0    0    0     0     0     0
 [6,] 0.00000000 0.000000000000000000    0    0    0    0    0    0    0     0     0     0
 [7,] 0.00000000 0.000000000000000000    0    0    0    0    0    0    0     0     0     0
 [8,] 0.00000000 0.000000000000000000    0    0    0    0    0    0    0     0     0     0
 [9,] 0.00000000 0.000000000000000000    0    0    0    0    0    0    0     0     0     0
[10,] 0.00000000 0.000000000000000000    0    0    0    0    0    0    0     0     0     0
[11,] 0.00000000 0.000000000000000000    0    0    0    0    0    0    0     0     0     0
[12,] 0.00000000 0.000000000000000000    0    0    0    0    0    0    0     0     0     0

$m0
 [1] 0 0 0 0 0 0 0 0 0 0 0 0

$C0
          [,1]     [,2]     [,3]     [,4]     [,5]     [,6]     [,7]     [,8]     [,9]    [,10]    [,11]    [,12]
 [1,] 10000000        0        0        0        0        0        0        0        0        0        0        0
 [2,]        0 10000000        0        0        0        0        0        0        0        0        0        0
 [3,]        0        0 10000000        0        0        0        0        0        0        0        0        0
 [4,]        0        0        0 10000000        0        0        0        0        0        0        0        0
 [5,]        0        0        0        0 10000000        0        0        0        0        0        0        0
 [6,]        0        0        0        0        0 10000000        0        0        0        0        0        0
 [7,]        0        0        0        0        0        0 10000000        0        0        0        0        0
 [8,]        0        0        0        0        0        0        0 10000000        0        0        0        0
 [9,]        0        0        0        0        0        0        0        0 10000000        0        0        0
[10,]        0        0        0        0        0        0        0        0        0 10000000        0        0
[11,]        0        0        0        0        0        0        0        0        0        0 10000000        0
[12,]        0        0        0        0        0        0        0        0        0        0        0 10000000
# カルマンフィルター
filtered <- dlmFilter(y = south, mod = model)
residata <- residuals(filtered, sd = F)
Box.test(x = residata, type = "Ljung-Box", lag = 10)
adf.test(x = residata, k = 10)
tail(filtered$m)

    Box-Ljung test

data:  residata
X-squared = 37.062, df = 10, p-value = 0.00005522


    Augmented Dickey-Fuller Test

data:  residata
Dickey-Fuller = -9.7654, Lag order = 10, p-value = 0.01
alternative hypothesis: stationary

             [,1]     [,2]      [,3]      [,4]      [,5]      [,6]      [,7]      [,8]      [,9]     [,10]     [,11]     [,12]
Jun 2019 10.41866 1.785031 -1.427548 -4.748959 -7.581259 -8.531993 -6.616562 -1.158793  4.251030  6.533949  6.923270  6.166539
Jul 2019 10.68870 4.412218  1.781647 -1.430384 -4.751246 -7.582997 -8.533181 -6.617201 -1.158884  4.251489  6.534980  6.924864
Aug 2019 11.01526 6.177066  4.408123  1.778218 -1.433147 -4.753344 -7.584430 -8.533948 -6.617303 -1.158320  4.252718  6.536901
Sep 2019 11.19793 6.932147  6.174774  4.406204  1.776672 -1.434320 -4.754144 -7.584857 -8.534002 -6.616984 -1.157628  4.253783
Oct 2019 11.26409 6.540048  6.931316  6.174078  4.405644  1.776247 -1.434609 -4.754298 -7.584875 -8.533886 -6.616732 -1.157241
Nov 2019 11.32082 4.255741  6.539331  6.930716  6.173596  4.405279  1.775999 -1.434740 -4.754311 -7.584771 -8.533664 -6.616393

smoothed <- dlmSmooth(y = filtered)
tail(smoothed$s, 6)
smoothdata <- smoothed$s
tail(smoothdata)
             [,1]     [,2]      [,3]      [,4]      [,5]      [,6]      [,7]      [,8]      [,9]     [,10]     [,11]     [,12]
Jun 2019 10.59095 1.775999 -1.434740 -4.754311 -7.584771 -8.533664 -6.616393 -1.156784  4.255741  6.539331  6.930716  6.173596
Jul 2019 10.85192 4.405279  1.775999 -1.434740 -4.754311 -7.584771 -8.533664 -6.616393 -1.156784  4.255741  6.539331  6.930716
Aug 2019 11.10127 6.173596  4.405279  1.775999 -1.434740 -4.754311 -7.584771 -8.533664 -6.616393 -1.156784  4.255741  6.539331
Sep 2019 11.23291 6.930716  6.173596  4.405279  1.775999 -1.434740 -4.754311 -7.584771 -8.533664 -6.616393 -1.156784  4.255741
Oct 2019 11.28641 6.539331  6.930716  6.173596  4.405279  1.775999 -1.434740 -4.754311 -7.584771 -8.533664 -6.616393 -1.156784
Nov 2019 11.32082 4.255741  6.539331  6.930716  6.173596  4.405279  1.775999 -1.434740 -4.754311 -7.584771 -8.533664 -6.616393
             [,1]     [,2]      [,3]      [,4]      [,5]      [,6]      [,7]      [,8]      [,9]     [,10]     [,11]     [,12]
Jun 2019 10.59095 1.775999 -1.434740 -4.754311 -7.584771 -8.533664 -6.616393 -1.156784  4.255741  6.539331  6.930716  6.173596
Jul 2019 10.85192 4.405279  1.775999 -1.434740 -4.754311 -7.584771 -8.533664 -6.616393 -1.156784  4.255741  6.539331  6.930716
Aug 2019 11.10127 6.173596  4.405279  1.775999 -1.434740 -4.754311 -7.584771 -8.533664 -6.616393 -1.156784  4.255741  6.539331
Sep 2019 11.23291 6.930716  6.173596  4.405279  1.775999 -1.434740 -4.754311 -7.584771 -8.533664 -6.616393 -1.156784  4.255741
Oct 2019 11.28641 6.539331  6.930716  6.173596  4.405279  1.775999 -1.434740 -4.754311 -7.584771 -8.533664 -6.616393 -1.156784
Nov 2019 11.32082 4.255741  6.539331  6.930716  6.173596  4.405279  1.775999 -1.434740 -4.754311 -7.584771 -8.533664 -6.616393
tmpts <- dropFirst(smoothdata)[, 1]
Date <- as.Date(time(tmpts))
Value <- as.matrix(tmpts)
smoothdf <- data.frame(Date, Value, stringsAsFactors = F, check.names = F)
head(smoothdf)
        Date    Value
1 1978-11-01 11.65986
2 1978-12-01 11.67856
3 1979-01-01 11.82047
4 1979-02-01 11.76945
5 1979-03-01 11.81067
6 1979-04-01 12.07252
tmpts <- dropFirst(smoothdata)[, 3]
Date <- as.Date(time(tmpts))
Value <- as.matrix(tmpts)
smoothseasondf <- data.frame(Date, Value, stringsAsFactors = F, check.names = F)
head(smoothseasondf)
        Date     Value
1 1978-11-01  6.539331
2 1978-12-01  4.255741
3 1979-01-01 -1.156784
4 1979-02-01 -6.616393
5 1979-03-01 -8.533664
6 1979-04-01 -7.584771

Simulation of SARIMA 
# 余談
# https://rdrr.io/cran/sarima/man/sim_sarima.html
# https://newonlinecourses.science.psu.edu/stat510/lesson/4/4.1
x <- sim_sarima(n = 12 * 12, model = list(ar = c(1.2, -0.8), ma = 0.4, sar = 0.3, sma = 0.7, iorder = 1, siorder = 1, nseasons = 12, sigma2 = 1))
adf.test(x)

    Augmented Dickey-Fuller Test

data:  x
Dickey-Fuller = -3.7975, Lag order = 5, p-value = 0.02114
alternative hypothesis: stationary
adf.test(diff(x))

    Augmented Dickey-Fuller Test

data:  diff(x)
Dickey-Fuller = -11.209, Lag order = 5, p-value = 0.01
alternative hypothesis: stationary

  • 参照引用Webページ
  1. https://logics-of-blue.com/how-to-use-kfas/
  2. https://logics-of-blue.com/kalman-filter-mle/
  3. https://logics-of-blue.com/kalman-filter-concept/
  4. https://logics-of-blue.com/%e7%8a%b6%e6%85%8b%e7%a9%ba%e9%96%93%e3%83%a2%e3%83%87%e3%83%ab%e3%81%ae%e6%8e%a8%e5%ae%9a%e6%96%b9%e6%b3%95%e3%81%ae%e5%88%86%e9%a1%9e/
  5. https://logics-of-blue.com/dlm%e3%81%ab%e3%82%88%e3%82%8b%e6%99%82%e5%a4%89%e4%bf%82%e6%95%b0%e3%83%a2%e3%83%87%e3%83%ab/
  6. https://logics-of-blue.com/%e6%85%a3%e3%82%8c%e3%81%ae%e7%b5%b1%e8%a8%88%e3%83%a2%e3%83%87%e3%83%aa%e3%83%b3%e3%82%b0%ef%bc%9astan%e3%81%a7%e6%8e%a8%e5%ae%9a%e3%81%99%e3%82%8b%e6%99%82%e5%a4%89%e4%bf%82/
  7. https://logics-of-blue.com/stan%e3%81%a7%e6%8e%a8%e5%ae%9a%e3%81%99%e3%82%8b%e3%83%ad%e3%83%bc%e3%82%ab%e3%83%ab%e3%83%ac%e3%83%99%e3%83%ab%e3%83%a2%e3%83%87%e3%83%ab/
  8. https://logics-of-blue.com/%e3%83%99%e3%82%a4%e3%82%ba%e3%81%a8mcmc%e3%81%a8%e7%b5%b1%e8%a8%88%e3%83%a2%e3%83%87%e3%83%ab%e3%81%ae%e9%96%a2%e4%bf%82/
  9. https://logics-of-blue.com/%e3%81%aa%e3%81%9c%e7%8a%b6%e6%85%8b%e7%a9%ba%e9%96%93%e3%83%a2%e3%83%87%e3%83%ab%e3%82%92%e4%bd%bf%e3%81%86%e3%81%ae%e3%81%8b/
  10. https://logics-of-blue.com/%e5%ad%a3%e7%af%80%e3%81%a8%e3%83%88%e3%83%ac%e3%83%b3%e3%83%89/
  11. https://logics-of-blue.com/%e3%83%ad%e3%83%bc%e3%82%ab%e3%83%ab%e3%83%ac%e3%83%99%e3%83%ab%e3%83%a2%e3%83%87%e3%83%ab/
  12. https://logics-of-blue.com/dlm%e3%81%ae%e4%bd%bf%e3%81%84%e6%96%b9/
  13. https://logics-of-blue.com/%e7%8a%b6%e6%85%8b%e7%a9%ba%e9%96%93%e3%83%a2%e3%83%87%e3%83%ab%e3%81%a8%e3%81%af/
  14. https://logics-of-blue.com/python-state-space-models/
  15. https://logics-of-blue.com/tsa-ssm-book-support/
  16. https://www.jstatsoft.org/index.php/jss/article/view/v036i12/v36i12.pdf
  17. http://elsur.jpn.org/ck
  18. http://sinhrks.hatenablog.com/archive/category/%E6%99%82%E7%B3%BB%E5%88%97%E5%88%86%E6%9E%90
  19. http://rtokei.tech/stan/1912/
  20. http://rtokei.tech/stan/bayesian-inference-with-stan-041/
  21. http://rtokei.tech/stan/bayesian-inference-with-stan-042/
  22. http://rtokei.tech/stan/2076/
  23. https://fisproject.jp/2017/09/state-space-model-with-r/
  24. https://radhakrishna.typepad.com/book-summary-and-r-code-1.pdf
  25. https://qiita.com/kenmatsu4/items/adb79f5c91d1099a3d5d
  26. https://stats.biopapyrus.jp/stats/optim.html
  27. http://www.ms.uky.edu/~mai/sta321/MLEexample.pdf
  28. http://www.okadajp.org/RWiki/?%E9%96%A2%E6%95%B0%E3%81%AE%E6%9C%80%E5%A4%A7%E3%83%BB%E6%9C%80%E5%B0%8F%E5%8C%96
  29. https://www.medi-08-data-06.work/entry/optim-optimize-of-R
  30. https://logics-of-blue.com/evaluation-method-of-forecast/

R関数のコードとヘルプそして関連キーワードの検索結果

No. Title Update
1 R関数のコードとヘルプそして関連キーワードの検索結果 - adf.test,CADFtest,unitrootTest,pp.test - 2019-11-21 17:36:55
2 R関数のコードとヘルプそして関連キーワードの検索結果 - gls,glsStruct,glsControl,glsApVar,fdHess - 2019-11-21 17:36:39
3 R関数のコードとヘルプそして関連キーワードの検索結果 - dwtest,lm.fit - 2019-11-21 17:36:23

Rパッケージのタイトルと説明の検索/Title and Description of R package

  • Rパッケージのタイトルと説明の検索/Title and Description of R package
    更新日時:2019-10-08 08:16:32

Online Calculation

  • Move to “Online Calculation”