はじめに

歓談タイムにお越しいただいた皆様、ありがとうございました。歓談タイムでは「decomp」「auto.arima」などの関数を紹介し、成分モデルに分解する実演をしました。ここに、その際に用いたパッケージやコードを載せておきます。

季節調整用関数「decomp」in timsac by統数研

#パッケージのインストール
#install.packages("timsac")
#パッケージの読み込み
library(timsac)
## Warning: package 'timsac' was built under R version 3.4.4

1)イギリスの気管支系疾患による死者数(1974-1979)

ts.plot(ldeaths)#デフォルトで入っているデータセットです

decomp(ldeaths)

## $trend
##  [1] 2201.629 2200.278 2198.942 2197.599 2196.224 2194.793 2193.283
##  [8] 2191.666 2189.921 2188.027 2185.967 2183.733 2181.324 2178.732
## [15] 2175.951 2172.965 2169.763 2166.337 2162.677 2158.778 2154.629
## [22] 2150.222 2145.545 2140.585 2135.331 2129.797 2123.982 2117.931
## [29] 2111.700 2105.337 2098.888 2092.392 2085.877 2079.362 2072.865
## [36] 2066.406 2060.008 2053.696 2047.506 2041.448 2035.523 2029.734
## [43] 2024.079 2018.556 2013.163 2007.899 2002.756 1997.721 1992.777
## [50] 1987.896 1983.048 1978.214 1973.373 1968.503 1963.591 1958.625
## [57] 1953.600 1948.512 1943.357 1938.138 1932.845 1927.469 1922.015
## [64] 1916.477 1910.854 1905.145 1899.352 1893.480 1887.539 1881.542
## [71] 1875.511 1869.458
## 
## $seasonal
##  [1]  866.5813  831.5513  678.2404  191.6857 -273.7814 -455.5184 -495.0989
##  [8] -634.8983 -664.0415 -379.3732 -158.2512  492.8976  866.5715  831.5792
## [15]  678.2361  191.6764 -273.7831 -455.5053 -495.1131 -634.8915 -664.0389
## [22] -379.3801 -158.2555  492.9045  866.5485  831.6217  678.2272  191.6573
## [29] -273.7737 -455.5046 -495.1127 -634.8986 -664.0248 -379.3890 -158.2411
## [36]  492.8536  866.6195  831.5728  678.2336  191.6627 -273.7759 -455.5023
## [43] -495.1063 -634.8987 -664.0186 -379.3972 -158.2286  492.8089  866.6524
## [50]  831.5665  678.2472  191.6357 -273.7528 -455.5111 -495.1033 -634.8968
## [57] -664.0123 -379.4061 -158.2111  492.7603  866.7046  831.5326  678.2629
## [64]  191.6334 -273.7553 -455.5100 -495.1033 -634.8946 -664.0024 -379.4302
## [71] -158.1701  492.7115
## 
## $ar
##  [1]  -20.3103921 -312.6545893 -119.2636697  147.1443423   91.6390659
##  [6]  -49.8123799  -36.1358390  -40.7146707   37.5212189  168.8881556
## [11]  102.9912458  -97.4193625 -115.4711611  -56.3112244   69.0632520
## [16]   82.9590785  -11.2070626  -16.6479594  -15.4716568   -2.9117933
## [21]  -48.6398079   17.7540536   65.4097290  -31.7786590  -85.1591335
## [26]  483.2983733  267.9461908 -221.7494342 -185.2915446    2.1175785
## [31]   -2.9647198  -66.1817405  -65.2081919  -57.5662452   69.0581854
## [36]  234.8506558   84.9293940 -362.4025575 -217.8794373  154.5846932
## [41]   75.1625710  -38.3533534  -45.4049497   -0.1521272   36.2129408
## [46]  -10.2598227 -127.6299822 -146.8200532   20.4214071  203.6207567
## [51]    0.6570994 -141.6869097   58.5945700   92.9817214   19.3501628
## [56]   17.7620106   56.3990721  -32.5609027 -153.6872628   49.7160919
## [61]  168.1415750  -62.8084338  -67.4950049   20.2952251   43.8699471
## [66]   19.6698534   10.2203518   37.0011291   61.3719135   51.5089566
## [71]   -6.5660861 -238.4033159
## 
## $trad
##  [1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [36] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [71] 0 0
## 
## $noise
##  [1]  -12.90031684 -167.17517696  -53.91838607   17.57137567   -0.08139466
##  [6]  -34.46241579   58.95160059    7.94676689   32.59925950   96.45797326
## [11]   68.29320868  -67.21083282    0.57606583  -65.00006571   14.75006831
## [16]   49.39941917  -14.77280315   31.81672409  -45.09199553   24.02561904
## [21]  -45.95019293   -1.59623622   23.30047157  235.28906948 -129.72060916
## [26]  446.28306324  108.84466058  -76.83902794  -16.63509644  -71.95020689
## [31] -111.81062768  -91.31168338   -0.64401694   10.59360275   29.31816702
## [36]   28.88979380   90.44311377 -228.86677215 -122.86009115   56.30442424
## [41]  -88.90933832   18.12135633   14.43187939  -22.50508264  -39.35765280
## [46]  -54.24182290  -76.89702131  -50.71031985  -64.85038316  113.91670395
## [51]   17.04732497  -59.16235167  111.78484938   27.02591982   41.16230758
## [56]   24.50981898   11.01336652   33.45542811  -96.45900826   10.38557256
## [61]  116.30921113  -91.19312468   40.21726043   14.59457577   12.03183307
## [66]   34.69520651   46.53056532   58.41306651   48.09191117  -61.62060986
## [71]   70.22561165 -208.76643818
## 
## $aic
## [1] 1023.644
## 
## $lkhd
## [1] -490.8222
## 
## $sigma2
## [1] 17714.17
## 
## $tau1
## [1] 0.0001000002
## 
## $tau2
## [1] 1.0001
## 
## $tau3
## [1] 0.0001000138
## 
## $arcoef
## [1]  0.2777541 -0.5395628
## 
## $tdf
## [1] 0 0 0 0 0 0 0

2)イギリスのガス消費量(1960-1986)

ts.plot(UKgas)#デフォルトで入っているデータセットです

decomp(UKgas)

## $trend
##   [1] 118.8711 119.8730 120.8734 121.8711 122.8664 123.8608 124.8554
##   [8] 125.8500 126.8450 127.8421 128.8423 129.8479 130.8632 131.8944
##  [15] 132.9495 134.0373 135.1682 136.3517 137.5961 138.9097 140.3008
##  [22] 141.7770 143.3447 145.0107 146.7842 148.6744 150.6891 152.8361
##  [29] 155.1255 157.5657 160.1644 162.9312 165.8768 169.0118 172.3456
##  [36] 175.8933 179.6735 183.6968 187.9720 192.5140 197.3398 202.4544
##  [43] 207.8536 213.5380 219.5204 225.7989 232.3633 239.1976 246.2884
##  [50] 253.6221 261.1771 268.9284 276.8567 284.9518 293.1944 301.5592
##  [57] 310.0208 318.5611 327.1618 335.8050 344.4784 353.1750 361.8877
##  [64] 370.6105 379.3385 388.0660 396.7866 405.4904 414.1660 422.8060
##  [71] 431.3941 439.9174 448.3596 456.6977 464.9086 472.9766 480.8894
##  [78] 488.6315 496.2020 503.6146 510.8842 518.0198 525.0386 531.9505
##  [85] 538.7646 545.5034 552.1965 558.8712 565.5517 572.2754 579.0804
##  [92] 585.9958 593.0426 600.2431 607.6110 615.1565 622.8782 630.7710
##  [99] 638.8339 647.0560 655.4121 663.8714 672.4098 681.0007 689.6135
## [106] 698.2243 706.8298 715.4325
## 
## $seasonal
##   [1]   44.709498    9.637261  -39.916593   -5.775493   39.190307
##   [6]    4.211805  -42.112978  -11.461097   43.530632   10.880678
##  [11]  -45.081549  -11.264569   51.854228    9.606927  -43.427375
##  [16]  -11.913686   43.924311   10.656393  -46.882104  -15.084007
##  [21]   49.594087   11.812837  -50.050638  -13.677259   57.149554
##  [26]   12.339599  -53.119072  -13.619074   52.911727   12.510732
##  [31]  -49.857656  -22.863971   65.231720   11.136127  -65.355851
##  [36]  -13.850523   70.765313   14.796727  -75.102917   -7.296514
##  [41]   71.079851    0.974229  -49.564304  -34.323823  104.472468
##  [46]  -15.345044 -101.672157   27.833678   91.926087  -14.673094
##  [51] -123.856615   44.169256  117.449688  -28.822865 -134.532488
##  [56]   35.259563  139.437319  -32.307307 -162.090098   53.172672
##  [61]  147.336846  -33.676581 -187.520818   41.305036  216.703420
##  [66]  -49.624059 -216.630185   67.963428  192.442593  -35.286548
##  [71] -236.200601   63.582939  220.099928  -54.262255 -257.668713
##  [76]   43.866626  309.479155  -59.334339 -289.216188   54.213391
##  [81]  307.989080  -84.226560 -305.047888  103.644728  291.545812
##  [86] -102.379609 -334.712777  108.106536  358.054160 -105.412102
##  [91] -344.148350   95.057577  345.961518  -75.444681 -353.298780
##  [96]   89.193050  355.690679 -127.837348 -368.093719   97.814508
## [101]  413.992966 -123.291909 -379.139813   88.676679  420.585042
## [106]  -99.978595 -359.975146   74.461169
## 
## $ar
##   [1]  6.876825e-04  1.489588e-03  1.228352e-03  1.715161e-03  1.277632e-03
##   [6]  1.532845e-03  1.699323e-03  1.955235e-03  1.959953e-03  2.184896e-03
##  [11]  2.480945e-03  2.278407e-03  2.357452e-03  1.860216e-03  1.782411e-03
##  [16]  1.201963e-03  8.814177e-04  9.364031e-04  4.841820e-04  7.282893e-04
##  [21]  2.514107e-04  6.888876e-04  6.247355e-04  4.757006e-04  1.674158e-04
##  [26]  3.147144e-04  2.734854e-04  8.683723e-05 -3.199679e-04  3.358445e-04
##  [31] -5.187661e-04 -2.176333e-04 -1.072564e-03 -8.678299e-04 -1.197277e-03
##  [36] -3.811954e-03 -2.564515e-03 -4.346792e-03 -3.215848e-03 -7.736652e-03
##  [41] -4.756253e-03 -7.427751e-03 -3.009294e-03 -9.909788e-03 -5.604962e-03
##  [46] -8.256995e-03 -5.013388e-03 -5.543157e-03 -5.506508e-03 -3.369367e-03
##  [51] -3.420590e-03 -1.517464e-04 -3.944299e-03 -8.658902e-05 -1.720879e-03
##  [56]  2.555173e-03  1.471397e-04  2.931612e-03  1.759702e-03  3.664319e-03
##  [61]  1.300528e-03  2.747838e-03  8.512791e-04  1.858784e-03 -1.307025e-04
##  [66]  1.559895e-03 -9.510739e-04  2.837241e-03 -1.499902e-03  3.191634e-03
##  [71]  7.670600e-04  2.934357e-03  4.087716e-03  5.689937e-03  7.634023e-03
##  [76]  6.178641e-03  1.066192e-02  8.113070e-03  9.365608e-03  4.951400e-03
##  [81]  8.697370e-03  4.134485e-03  5.906949e-03  6.264094e-03  4.020029e-03
##  [86]  3.831405e-03 -2.893432e-04  2.788117e-03 -3.754195e-03 -2.697927e-03
##  [91] -8.090182e-03 -4.696252e-03 -1.044685e-02 -7.118975e-03 -1.085087e-02
##  [96] -8.505488e-03 -7.962120e-03 -9.143657e-03 -7.294024e-03 -6.870068e-03
## [101] -1.723855e-03 -3.175317e-03  1.354279e-03  8.810360e-04  6.440268e-03
## [106]  2.128264e-03  4.528797e-03  1.100978e-03
## 
## $trad
##   [1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
##  [36] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
##  [71] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [106] 0 0 0
## 
## $noise
##   [1]  -3.48131696   0.18828275   3.84196327   4.00264136  -1.95794453
##   [6]  -3.17413546   2.05585432   2.50915293  -0.67762675   2.17506732
##  [11]   5.93672484   4.71434894   4.58017508   2.59678217   3.37611897
##  [16]  -2.02484188  -2.99344184   0.29094548  -1.01445813  -0.52646798
##  [21]  -4.19511706   1.70945533   6.00531947  -0.03390688  -3.83393045
##  [26]   0.68564773   4.92970961  -3.11714680  -3.13685702   6.02322288
##  [31]   1.79379932   0.83295326  -3.80741308  15.15297604   8.31148411
##  [36] -19.53900074  -5.53620420  16.01085229   5.63415110 -31.50972809
##  [41] -23.51490936  12.67880340  30.61375055 -36.70431475 -22.98724327
##  [46] -13.54564182   5.41391516   0.27424678 -21.20899566  -8.44567625
##  [51]  14.78293011  23.10252205 -22.90244578 -16.02880437  -0.16016204
##  [56]  18.57867962   0.44168741   0.34331568  14.22656867  14.41862815
##  [61]  -0.31654728   2.29886564   3.33225032  -2.11740819  -2.14179837
##  [66]  -8.64353841  -4.05547265  10.04333619 -22.30711413   7.87739602
##  [71]  -7.89427005 -18.40324647   0.73633585  18.55885156   8.85244004
##  [76]  -7.74945155  37.32081049  38.19476029   2.70486204 -15.13295921
##  [81]  21.61798609 -19.19736248  -2.29659085  35.19851711  18.18560778
##  [86]  -6.12758786  -7.78343443  34.21947606   1.69789943 -23.46061126
##  [91] -20.42398540   2.55134567 -21.69368739  -9.29129814 -30.20137121
##  [96]  -9.54107343  10.83904833 -25.82450860 -37.03287105 -14.86362788
## [101]  17.59661428  -5.87635842 -11.47131071  17.92170237  53.69497591
## [106]  14.85218454   0.54085476  -7.09477698
## 
## $aic
## [1] 1244.653
## 
## $lkhd
## [1] -601.3266
## 
## $sigma2
## [1] 1033.829
## 
## $tau1
## [1] 0.0003854931
## 
## $tau2
## [1] 0.0001000485
## 
## $tau3
## [1] 1.0001
## 
## $arcoef
## [1] 0.0817936 0.6767834
## 
## $tdf
## [1] 0 0 0 0 0 0 0

3)新宿の最高気温の年毎の平均(1960-2017)

(x<-read.csv(file="maxtemp.csv",header=T))
##    shinjuku okinawa
## 1      34.7    25.2
## 2      37.5    25.2
## 3      37.6    24.8
## 4      37.2    25.0
## 5      35.2    25.7
## 6      35.0    24.7
## 7      34.9    25.2
## 8      37.2    25.0
## 9      33.5    24.5
## 10     36.6    25.3
## 11     35.5    25.0
## 12     34.4    25.1
## 13     35.2    25.4
## 14     34.7    24.9
## 15     34.2    24.8
## 16     35.6    24.7
## 17     35.4    24.7
## 18     34.9    25.3
## 19     36.3    24.6
## 20     34.3    24.9
## 21     33.0    25.1
## 22     34.3    25.0
## 23     33.0    25.2
## 24     37.1    25.5
## 25     38.1    24.9
## 26     35.0    25.1
## 27     34.6    24.8
## 28     37.3    25.8
## 29     32.9    25.6
## 30     33.5    25.5
## 31     35.9    25.7
## 32     35.6    26.1
## 33     35.2    25.5
## 34     32.9    25.8
## 35     39.1    25.7
## 36     36.4    25.2
## 37     38.7    25.4
## 38     37.7    25.6
## 39     36.1    26.9
## 40     34.8    26.0
## 41     37.8    25.6
## 42     38.1    26.1
## 43     35.8    25.9
## 44     34.3    26.2
## 45     39.5    26.1
## 46     36.2    25.8
## 47     36.1    26.2
## 48     37.5    26.2
## 49     35.3    26.2
## 50     34.2    26.3
## 51     37.2    25.8
## 52     36.1    25.5
## 53     35.7    25.6
## 54     38.3    26.0
## 55     36.1    25.8
## 56     37.7    26.2
## 57     37.7    26.8
## 58     37.1    26.3
maxtemp_s<-ts(x[,1], start=c(1960,1), frequency=1)
ts.plot(maxtemp_s)

decomp(maxtemp_s)

## $trend
##  [1] 35.68123 35.64881 35.61624 35.58356 35.55098 35.51885 35.48753
##  [8] 35.45734 35.42854 35.40156 35.37670 35.35444 35.33522 35.31938
## [15] 35.30718 35.29878 35.29427 35.29371 35.29723 35.30492 35.31695
## [22] 35.33346 35.35436 35.37949 35.40849 35.44114 35.47734 35.51700
## [29] 35.55997 35.60619 35.65536 35.70706 35.76087 35.81630 35.87291
## [36] 35.93007 35.98735 36.04436 36.10099 36.15719 36.21292 36.26805
## [43] 36.32260 36.37672 36.43061 36.48427 36.53796 36.59201 36.64675
## [50] 36.70247 36.75929 36.81712 36.87587 36.93532 36.99525 37.05554
## [57] 37.11596 37.17641
## 
## $seasonal
##  [1]  0.66950548 -0.01176314  0.01084029  0.38171858 -0.44720331
##  [6] -0.04960354 -0.14076736 -0.06352098 -0.29397964 -0.66944770
## [11]  0.11995597  0.49414002  0.66993966 -0.01207441  0.01080026
## [16]  0.38165047 -0.44716734 -0.04952975 -0.14052248 -0.06410388
## [21] -0.29333399 -0.66993220  0.12002198  0.49417023  0.67034001
## [26] -0.01243312  0.01090123  0.38154442 -0.44730375 -0.04920149
## [31] -0.14058742 -0.06468019 -0.29239042 -0.67067431  0.12051222
## [36]  0.49390106  0.67060535 -0.01271510  0.01115053  0.38106879
## [41] -0.44708092 -0.04885077 -0.14081023 -0.06510024 -0.29181853
## [46] -0.67073119  0.12041233  0.49401006  0.67047544 -0.01289685
## [51]  0.01141389  0.38088756 -0.44711372 -0.04853882 -0.14119866
## [56] -0.06486267 -0.29181822 -0.67073766
## 
## $ar
##  [1] -0.312339541  0.095735655  0.172772591 -0.054473885 -0.054105010
##  [6] -0.039224799  0.090620044  0.076553115 -0.248436083  0.162997059
## [11]  0.119577596 -0.203108653  0.001704212  0.099252138 -0.037285930
## [16] -0.035715216 -0.059066012  0.110863379  0.120661050 -0.342897292
## [21]  0.129008222  0.364611005 -0.594575306  0.015433913  0.713242192
## [26] -0.483545434 -0.457305295  0.834896587 -0.080854119 -0.819034570
## [31]  0.504710470  0.537244555 -0.791371207 -0.154197085  0.959921349
## [36] -0.507376474 -0.559716298  0.900624397  0.051898354 -0.983046784
## [41]  0.536569621  0.686661890 -0.884777941 -0.167162159  0.977025498
## [46] -0.510671403 -0.472462813  0.810676762 -0.219750323 -0.590359913
## [51]  0.612736331  0.003231171 -0.522031836  0.397399088  0.127051039
## [56] -0.396975836  0.157798402  0.267649186
## 
## $trad
##  [1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [36] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 
## $noise
##  [1] -1.33839649  1.76721880  1.80014815  1.28919792  0.15032836
##  [6] -0.43002331 -0.53738507  1.72962871 -1.38611948  1.70489394
## [11] -0.11623479 -1.24546822 -0.80686392 -0.70656042 -1.08069031
## [16] -0.04471576  0.61196461 -0.45504232  1.02263185 -0.59791393
## [21] -2.15262547 -0.72814297 -1.87981146  1.21090464  1.30792422
## [26]  0.05483548 -0.43093763  0.56656205 -2.13181534 -1.23795547
## [31] -0.11948283 -0.57962639  0.52289122 -2.09142766  2.14665200
## [36]  0.48340158  2.60176171  0.76772975 -0.06403834 -0.75521404
## [41]  1.49759177  1.19414161  0.50298780 -1.84446093  2.38418207
## [46]  0.89712897 -0.08590962 -0.39669572 -1.79747503 -1.89921662
## [51] -0.18344000 -1.10123842 -0.20671977  1.01582096 -0.88110384
## [56]  1.10630210  0.71806133  0.32667523
## 
## $aic
## [1] 263.5171
## 
## $lkhd
## [1] -110.7585
## 
## $sigma2
## [1] 1.730424
## 
## $tau1
## [1] 0.0001000006
## 
## $tau2
## [1] 0.05291096
## 
## $tau3
## [1] 0.0001000005
## 
## $arcoef
## [1] -0.6073534 -0.8721032
## 
## $tdf
## [1] 0 0 0 0 0 0 0

4)沖縄の最高気温の年毎の平均(1960-2017)

maxtemp_o<-ts(x[,2], start=c(1960,1), frequency=1)
ts.plot(maxtemp_o)

decomp(maxtemp_o)

## $trend
##  [1] 24.88747 24.90276 24.91816 24.93371 24.94940 24.96524 24.98131
##  [8] 24.99765 25.01431 25.03136 25.04879 25.06664 25.08493 25.10368
## [15] 25.12296 25.14281 25.16328 25.18439 25.20612 25.22850 25.25153
## [22] 25.27518 25.29943 25.32423 25.34956 25.37540 25.40170 25.42841
## [29] 25.45544 25.48270 25.51017 25.53778 25.56550 25.59334 25.62128
## [36] 25.64932 25.67746 25.70565 25.73383 25.76188 25.78982 25.81765
## [43] 25.84538 25.87300 25.90051 25.92794 25.95530 25.98260 26.00985
## [50] 26.03707 26.06430 26.09161 26.11905 26.14662 26.17431 26.20210
## [57] 26.22993 26.25776
## 
## $seasonal
##  [1]  0.014726665 -0.006438022 -0.028290932 -0.069873630 -0.052457815
##  [6]  0.003657305 -0.099969022  0.115424325  0.010383456  0.028078265
## [11]  0.065642419  0.019133160  0.014711644 -0.006476724 -0.028231426
## [16] -0.069829775 -0.052625053  0.003819969 -0.100068885  0.115424432
## [21]  0.010496560  0.027970893  0.065687804  0.019166637  0.014622358
## [26] -0.006475968 -0.028171576 -0.069783960 -0.052738084  0.003871968
## [31] -0.100103368  0.115444239  0.010567864  0.027890592  0.065752098
## [36]  0.019109183  0.014611567 -0.006527438 -0.027984792 -0.069859433
## [41] -0.052843029  0.003969659 -0.100147515  0.115399828  0.010715678
## [46]  0.027769362  0.065784217  0.019111732  0.014597931 -0.006470611
## [51] -0.028005060 -0.069888860 -0.052865179  0.004014277 -0.100173487
## [56]  0.115348275  0.010831876  0.027713417
## 
## $ar
##  [1]  0.161618719  0.152249368  0.131266496  0.137810109  0.143743838
##  [6]  0.081984178  0.052049757 -0.001320893 -0.038463021 -0.022004820
## [11] -0.029380067 -0.031823033 -0.044626022 -0.098655386 -0.147131506
## [16] -0.179786346 -0.191457347 -0.184941767 -0.212350336 -0.213432277
## [21] -0.191695196 -0.175082671 -0.149952448 -0.130172636 -0.143798116
## [26] -0.126132991 -0.086206270  0.004194587  0.048217147  0.071594251
## [31]  0.098556329  0.102459261  0.068694971  0.047701000  0.015249503
## [36] -0.011135681  0.020340581  0.096834466  0.190961550  0.175633760
## [41]  0.141186555  0.139289812  0.129027622  0.117510373  0.097741749
## [46]  0.072414386  0.073510396  0.065757358  0.041388204 -0.002719544
## [51] -0.078239090 -0.136108990 -0.147212359 -0.119755239 -0.085272077
## [56] -0.030250863  0.029346470  0.029239422
## 
## $trad
##  [1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [36] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 
## $noise
##  [1]  0.136181566  0.151426276 -0.221139266 -0.001642425  0.659318053
##  [6] -0.350881764  0.266607668 -0.111750793 -0.486232162  0.262568885
## [11] -0.085051895  0.046051915  0.344989359 -0.098545325 -0.147593484
## [16] -0.193197194 -0.219202331  0.296733862 -0.293699065 -0.230492965
## [21]  0.029667469 -0.128070188 -0.015164140  0.286771611 -0.320384275
## [26] -0.142786689 -0.487321278  0.437175298  0.149085558 -0.058167857
## [31]  0.191380683  0.344319275 -0.144763905  0.131069254 -0.002279861
## [36] -0.457291779 -0.312411017 -0.195960998  1.003196973  0.132346808
## [41] -0.278158698  0.139088686  0.025742182  0.094094279  0.091031987
## [46] -0.228121386  0.105404881  0.132530701  0.134165561  0.272120552
## [51] -0.158058186 -0.385614092 -0.318970517 -0.030880789 -0.188866638
## [56] -0.087192912  0.529892810 -0.014713555
## 
## $aic
## [1] 95.6959
## 
## $lkhd
## [1] -26.84795
## 
## $sigma2
## [1] 0.09369196
## 
## $tau1
## [1] 1e-04
## 
## $tau2
## [1] 0.096106
## 
## $tau3
## [1] 0.0001000243
## 
## $arcoef
## [1]  0.94403886 -0.09749391
## 
## $tdf
## [1] 0 0 0 0 0 0 0

時系列解析パッケージ「forecast」「tseries」

まあ、打ったらでてくると思うので調べてみてくださいw

#パッケージのインストール
#install.packages("forecast");install.packages("tseries")
#パッケージの読み込み
library(forecast);library(tseries)
## Warning: package 'forecast' was built under R version 3.4.4
## Warning: package 'tseries' was built under R version 3.4.4

新宿の最高気温データを使ってモデルを作成(単位根だー！笑)

(mdl1<-auto.arima(maxtemp_s, ic="aic", trace=T, stepwise=F, approximation=F,
                 start.p=0, start.q=0, start.P=0, start.Q=0))
## 
##  ARIMA(0,1,0)                    : 251.8039
##  ARIMA(0,1,0) with drift         : 253.7823
##  ARIMA(0,1,1)                    : 221.5897
##  ARIMA(0,1,1) with drift         : Inf
##  ARIMA(0,1,2)                    : 223.5677
##  ARIMA(0,1,2) with drift         : Inf
##  ARIMA(0,1,3)                    : 225.0212
##  ARIMA(0,1,3) with drift         : Inf
##  ARIMA(0,1,4)                    : 226.6869
##  ARIMA(0,1,4) with drift         : Inf
##  ARIMA(0,1,5)                    : 228.6842
##  ARIMA(0,1,5) with drift         : Inf
##  ARIMA(1,1,0)                    : 240.2346
##  ARIMA(1,1,0) with drift         : 242.2046
##  ARIMA(1,1,1)                    : 223.5726
##  ARIMA(1,1,1) with drift         : Inf
##  ARIMA(1,1,2)                    : 225.47
##  ARIMA(1,1,2) with drift         : Inf
##  ARIMA(1,1,3)                    : 226.889
##  ARIMA(1,1,3) with drift         : Inf
##  ARIMA(1,1,4)                    : 228.8585
##  ARIMA(1,1,4) with drift         : 230.4978
##  ARIMA(2,1,0)                    : 229.5674
##  ARIMA(2,1,0) with drift         : 231.5264
##  ARIMA(2,1,1)                    : 224.9685
##  ARIMA(2,1,1) with drift         : 226.5867
##  ARIMA(2,1,2)                    : 226.6699
##  ARIMA(2,1,2) with drift         : 228.2555
##  ARIMA(2,1,3)                    : Inf
##  ARIMA(2,1,3) with drift         : Inf
##  ARIMA(3,1,0)                    : 229.2833
##  ARIMA(3,1,0) with drift         : 231.2461
##  ARIMA(3,1,1)                    : 226.2876
##  ARIMA(3,1,1) with drift         : Inf
##  ARIMA(3,1,2)                    : 228.9394
##  ARIMA(3,1,2) with drift         : 230.5773
##  ARIMA(4,1,0)                    : 231.0991
##  ARIMA(4,1,0) with drift         : 233.0572
##  ARIMA(4,1,1)                    : 228.2669
##  ARIMA(4,1,1) with drift         : Inf
##  ARIMA(5,1,0)                    : 228.4812
##  ARIMA(5,1,0) with drift         : 230.4046
## 
## 
## 
##  Best model: ARIMA(0,1,1)
## Series: maxtemp_s 
## ARIMA(0,1,1) 
## 
## Coefficients:
##           ma1
##       -0.8722
## s.e.   0.0707
## 
## sigma^2 estimated as 2.643:  log likelihood=-108.79
## AIC=221.59   AICc=221.81   BIC=225.68
tsdiag(mdl1)

plot(forecast(mdl1, level = c(50,95), h = 50) )

単位根検定（本当は最初にやんなきゃいけないw）

adf.test(maxtemp_s)
## 
##  Augmented Dickey-Fuller Test
## 
## data:  maxtemp_s
## Dickey-Fuller = -3.7919, Lag order = 3, p-value = 0.02493
## alternative hypothesis: stationary

帰無仮説は「単位根である」->棄却されませんでした。つまり単位根です。