Series Temporais Base Indicadores
1 Passageiros
1.0.1 Dados
1.0.2 Ordenamento Temporal
1.0.3 Série Histórica
1.0.4 Decomposição da Série
Associação com regressão
1.0.5 Correlogramas
1.0.6 Correlações
## jan fev mar abr mai jun jul ago
## 0.8812822 0.8136201 0.9361555 0.9427650 0.9493817 0.9554924 0.9536820 0.9488601
## set out nov dez
## 0.9446244 0.9409552 0.9588498 0.9483952
1.0.7 Forecasting
auto## Series: diff(mensal)
## ARIMA(3,0,2)(1,1,2)[12] with drift
##
## Coefficients:
## ar1 ar2 ar3 ma1 ma2 sar1 sma1 sma2
## -0.3908 -0.0217 0.1167 -0.4612 -0.2670 -0.3766 -0.3103 -0.4182
## s.e. 0.3053 0.1131 0.0866 0.3025 0.2171 0.3139 0.2956 0.2241
## drift
## -225.3197
## s.e. 340.0939
##
## sigma^2 estimated as 1393803581242: log likelihood=-3867.41
## AIC=7754.83 AICc=7755.74 BIC=7790.08sarima## Series: diff(mensal)
## ARIMA(1,0,0)(0,0,1)[12] with non-zero mean
##
## Coefficients:
## ar1 sma1 mean
## -0.3787 0.6761 -32943.58
## s.e. 0.0572 0.0365 166497.74
##
## sigma^2 estimated as 5162366525917: log likelihood=-4224.74
## AIC=8457.47 AICc=8457.63 BIC=8471.761.0.8 AutoArima
fauto <- forecast(auto, h=22)## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Jan 2020 -2087241.17 -3600280.4 -574201.9 -4401235 226752.69
## Feb 2020 -1859499.34 -3847288.9 128290.2 -4899561 1180562.42
## Mar 2020 5769998.89 3781079.5 7758918.3 2728209 8811788.59
## Apr 2020 -422236.77 -2419140.6 1574667.0 -3476238 2631764.02
## May 2020 1126120.20 -883050.8 3135291.2 -1946642 4198882.04
## Jun 2020 -1699983.78 -3711196.4 311228.8 -4775868 1375900.48
## Jul 2020 221939.26 -1789297.1 2233175.6 -2853981 3297859.84
## Aug 2020 1407636.87 -603743.0 3419016.7 -1668503 4483776.88
## Sep 2020 -1625435.34 -3636916.4 386045.7 -4701730 1450859.42
## Oct 2020 1768903.36 -242595.5 3780402.2 -1307419 4845225.32
## Nov 2020 -1505284.85 -3516783.5 506213.8 -4581607 1571036.91
## Dec 2020 -1444030.97 -3455531.2 567469.3 -4520355 1632293.15
## Jan 2021 -3119806.97 -5185892.3 -1053721.7 -6279612 39997.79
## Feb 2021 -2271201.66 -4376203.4 -166200.0 -5490524 948120.62
## Mar 2021 6604791.42 4499684.6 8709898.3 3385308 9824274.52
## Apr 2021 -727216.23 -2833057.0 1378624.6 -3947822 2493389.35
## May 2021 893906.50 -1213071.9 3000884.9 -2328439 4116251.83
## Jun 2021 -1371114.60 -3478283.1 736053.9 -4593751 1851521.53
## Jul 2021 -64778.93 -2171949.7 2042391.8 -3287418 3157860.62
## Aug 2021 1705617.74 -401566.3 3812801.8 -1517042 4928277.68
## Sep 2021 -1794030.57 -3901224.0 313162.9 -5016705 1428643.71
## Oct 2021 1968104.25 -139090.6 4075299.1 -1254572 5190780.721.0.9 Sarima
fsarima <- forecast(sarima, h=22)## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Jan 2020 325740.65 -2586052 3237534 -4127463 4778944
## Feb 2020 270784.87 -2842828 3384397 -4491075 5032644
## Mar 2020 16532.25 -3124963 3158028 -4787971 4821035
## Apr 2020 -216716.62 -3362191 2928758 -5027305 4593872
## May 2020 1802093.77 -1343951 4948139 -3009367 6613554
## Jun 2020 -1793924.64 -4940051 1352202 -6605510 3017661
## Jul 2020 932487.87 -2213651 4078626 -3879116 5744091
## Aug 2020 -697467.68 -3843608 2448672 -5509074 4114138
## Sep 2020 -46801.57 -3192942 3099339 -4858408 4764805
## Oct 2020 -375100.08 -3521240 2771040 -5186707 4436506
## Nov 2020 478687.95 -2667452 3624828 -4332919 5290294
## Dec 2020 -1197858.71 -4343999 1948282 -6009465 3613748
## Jan 2021 408228.92 -3303053 4119510 -5267686 6084144
## Feb 2021 -200022.86 -3985448 3585402 -5989331 5589286
## Mar 2021 30332.09 -3765609 3826273 -5775058 5835723
## Apr 2021 -56907.12 -3854354 3740539 -5864600 5750786
## May 2021 -23868.20 -3821531 3773794 -5831892 5784155
## Jun 2021 -36380.58 -3834074 3761313 -5844452 5771690
## Jul 2021 -31641.93 -3829340 3766056 -5839720 5776436
## Aug 2021 -33436.54 -3831135 3764262 -5841515 5774642
## Sep 2021 -32756.89 -3830456 3764942 -5840836 5775322
## Oct 2021 -33014.28 -3830713 3764684 -5841093 57750651.0.10 Choques
1.1 Change Points
Calcula o posicionamento ideal e (potencialmente) o número de pontos de mudança para dados usando o método especificado pelo usuário.
Há uma grande dificuldade em se trabalhar com séries temporais e, cada vez mais, a necessidade de utilizá-las para a identificação de pontos de mudanças abruptas é crescente. Devido a essa necessidade pertencente às mais variadas áreas de estudo, diversos métodos têm sido utilizdos e descritos pela comunidade científica. Dentre alguns desses métodos, se encontram os seguintes:
- AMOC: Um único ponto de mudança (default)
- Segmentação Binária (o mais utilizado)
- Segmentação por vizinhança
- PELT
Para a utilização da média como método, deve-se utilizar o comando cpt.mean, em casos que se deseja média e variância como como método, deve-se utilizar o comando cpt.meanvar e naqueles casos que se deseja a variância como como método, deve-se utilizar o comando cpt.var. A criação desse comando é derivada do desejo de se identificar o ponto de intervenção através do estudo de mudanças ocorridas na média dos elementos analisados.
Métodos: * AMOC Um único ponto de mudança (default)
Segmentação Binária: “No momento da redação deste artigo, a segmentação binária é sem dúvida o método de pesquisa de ponto de mudança múltiplo mais amplamente usado e se origina do trabalho de Edwards e Cavalli-Sforza (1965), Scott e Knott (1974) e Sen e Srivastava (1975). Por um lado, a segmentação binária primeiro aplica uma estatística de teste de ponto de mudança único a todos os dados, se um ponto de mudança é identificado, os dados são divididos em dois no local do ponto de mudança. O procedimento de ponto de mudança único é repetido nos dois novos conjuntos de dados, antes e depois da mudança. Se os pontos de mudança são identificados em dos novos conjuntos de dados, eles são divididos ainda mais. Esse processo continua até que nenhum ponto de mudança seja encontrado em nenhuma parte dos dados.”
Segmentação por vizinhança: “Proposto por Auger e Lawrence (1989) e mais explorado em Bai e Perron (1998). Embora esse algoritmo seja exato, a complexidade computacional é consideravelmente maior que a da segmentação binária.”
PELT: “O algoritmo PELT proposto por Killick et al. (2012a) é semelhante ao algoritmo de vizinhança de segmento, na medida em que fornece uma segmentação exata. No entanto, devido à construção do algoritmo PELT, ele pode ser mais eficiente em termos computacionais, devido ao uso de métodos dinâmicos. De fato, a principal suposição que controla o tempo computacional é que o número de pontos de mudança aumenta linearmente à medida que o conjunto de dados cresce, ou seja, os pontos de mudança são espalhados pelos dados em vez de confinado a uma porção.”
Único Choque
## ints1 ints2 cp
## 26959982 9663672 263
## Jan Feb Mar Apr May Jun Jul Aug
## 1998 27478843 24526792 35962153 34124370 35269092 34212327 34799835 35325684
## 1999 27751396 23861133 35172104 32636140 34548715 33005811 33651748 34964151
## 2000 26751089 25309300 31392157 31833200 35092948 32988592 31609362 35657746
## 2001 27914506 22879205 33627369 31549054 34815087 32112008 31782277 35000511
## 2002 27264442 23106126 30182367 32516494 31953925 29692397 31293706 32696361
## 2003 26009169 22934071 28070340 29063053 30671880 28776699 29421322 29862653
## 2004 23248379 20219110 29672896 26907440 29334946 28426195 27790806 29661938
## 2005 23113974 19910073 28075808 27813307 27984532 29283372 26871749 29747017
## 2006 22529354 19468903 27830012 25266619 28915063 26962968 26113826 29322425
## 2007 22204267 18805822 27321891 25513286 28085823 25830083 25553610 28397216
## 2008 22360968 20989766 26405947 26960207 26574543 26660327 27239337 27647873
## 2009 22304096 19331174 28082216 26763906 27415593 27053746 27070304 26078836
## 2010 22362315 19654325 29148051 26856291 28307157 27097526 26738772 28784607
## 2011 22722294 21439787 27141961 26836944 29108648 27318074 26199808 29937031
## 2012 24008054 21332537 29479178 27287481 30440180 27831557 27382872 30507086
## 2013 24401180 20972680 27441689 29332667 28553224 26984057 26546133 27685102
## 2014 19190831 14475726 25500089 26808421 27940304 24057612 26865944 27496333
## 2015 21595632 19577370 27760586 25564241 25739320 26098840 25636494 26586515
## 2016 20789959 19724698 26640188 25141268 25847848 25476634 23856874 26418346
## 2017 20546321 17415070 24997318 21182091 24595717 22779488 22771542 24334933
## 2018 19250600 16566817 22358483 22036120 20877826 20781648 20255815 22871675
## 2019 17315645 17347332 19492852 20615151 21491553 18936635 20047298 20784505
## 2020 16737175 15446563 13535495 5397173 6436226 7060322 6187968 6955730
## 2021 8539395 7646355 7477617 7956994 9070799 9258598 10268643 10585886
## Sep Oct Nov Dec
## 1998 34914654 37655309 33943184 34914663
## 1999 33140624 33507058 32403406 34434877
## 2000 31990374 32315093 33228302 33094826
## 2001 30009606 34069758 31709544 31024106
## 2002 30239978 34560751 30937177 29853452
## 2003 30610426 30762826 28940569 28751017
## 2004 27813276 30509454 27708938 29302417
## 2005 27061142 28607100 27457718 28154350
## 2006 26601600 29683642 26368036 26325209
## 2007 25651025 27768614 26168047 26346202
## 2008 27941601 30347756 27194737 26906282
## 2009 27778897 28254796 27149958 27479909
## 2010 27488245 29153815 27546736 27700823
## 2011 28187095 28739967 28089457 28268489
## 2012 26286597 30512697 28062071 25576524
## 2013 26978093 29840786 27495122 25692318
## 2014 28117724 29816540 27016007 25261137
## 2015 25435285 26454846 26006491 24767480
## 2016 24508027 25891395 24312775 24122900
## 2017 21598693 22646503 22418313 21257429
## 2018 19816664 23163098 20781444 18914178
## 2019 19482845 21245673 19705649 17180096
## 2020 7641632 8835864 9306813 9197545
## 2021 10260551 11281009Variação da Média
mvalue = cpt.mean(mensal, method="BinSeg")## [1] 48 72 228 263 267
Variação da variância
mvalue = cpt.meanvar(mensal, method="BinSeg")## [1] 60 228 266
1.1.1 BCP
Implementa os métodos de análise de ponto de mudança Bayesianos dados em Wang e Emerson (2015), dos quais o modelo de partição de produto de Barry e Hartigan (1993) para o problema de ponto de mudança de erros normais é um caso específico. 1. Análise de ponto de mudança bayesiana multivariada (ou univariada): Assumimos que existe uma partição desconhecida de uma série de dados y em blocos de forma que a média seja constante dentro de cada bloco. No caso multivariado, uma estrutura de ponto de mudança comum é assumida; as médias são constantes dentro de cada bloco de cada sequência, mas podem diferir entre as sequências dentro de um determinado bloco. Condicional à partição, o modelo assume que as observações são independentes, com distribuição normal idêntica, com médias constantes dentro dos blocos e variância constante ao longo de cada sequência. 2. Análise de ponto de mudança bayesiana de regressão linear: Como no modelo anterior, assumimos que as observações (x, y), onde x pode ser multivariada, são particionadas em blocos e que os modelos lineares são apropriados dentro de cada bloco.
Se uma estrutura de adjacência for fornecida, presume-se que os dados residam em nós de um grafo com a estrutura de adjacência fornecida; parâmetros adicionais são usados neste modelo de ponto de mudança de gráfico. Se nenhuma estrutura de adjacência for fornecida, os dados são considerados sequenciais e os blocos são forçados a serem contíguos.
2 Frota
2.0.1 Ordenamento Temporal
2.0.2 Série Histórica
2.0.3 Decomposição da Série
Associação com regressão
2.0.4 Correlogramas
2.0.5 Correlações
## V1 V2 V3 V4 V5 V6 V7 V8
## 0.9421557 0.9577575 0.9624252 0.9649523 0.9741855 0.9742566 0.9757102 0.9735588
## V9 V10 V11 V12
## 0.9714734 0.9641281 0.9629799 0.91427392.0.6 Forecasting
auto## Series: mensal
## ARIMA(0,2,1)(0,0,1)[12]
##
## Coefficients:
## ma1 sma1
## -0.9498 0.2688
## s.e. 0.0231 0.0804
##
## sigma^2 estimated as 34: log likelihood=-484.07
## AIC=974.15 AICc=974.31 BIC=983.22sarima## Series: mensal
## ARIMA(1,0,0)(0,0,1)[12] with non-zero mean
##
## Coefficients:
## ar1 sma1 mean
## 0.9946 0.3238 1574.2225
## s.e. 0.0053 0.0763 66.0425
##
## sigma^2 estimated as 35.71: log likelihood=-495.51
## AIC=999.01 AICc=999.28 BIC=1011.162.0.7 AutoArima
fauto <- forecast(auto, h=22)## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Nov 2021 1092.190 695.6487 1488.732 485.7324 1698.648
## Dec 2021 1088.410 687.1874 1489.633 474.7928 1702.028
## Jan 2022 1084.631 678.7081 1490.553 463.8258 1705.435
## Feb 2022 1080.851 670.2109 1491.490 452.8314 1708.870
## Mar 2022 1077.071 661.6959 1492.446 441.8097 1712.332
## Apr 2022 1073.291 653.1632 1493.419 430.7609 1715.821
## May 2022 1069.511 644.6127 1494.410 419.6850 1719.337
## Jun 2022 1065.731 636.0446 1495.418 408.5821 1722.881
## Jul 2022 1061.952 627.4589 1496.444 397.4524 1726.451
## Aug 2022 1058.172 618.8557 1497.488 386.2958 1730.048
## Sep 2022 1054.392 610.2350 1498.549 375.1125 1733.671
## Oct 2022 1050.612 601.5969 1499.627 363.9027 1737.321
## Nov 2022 1046.832 592.9415 1500.723 352.6663 1740.998
## Dec 2022 1043.052 584.2688 1501.836 341.4035 1744.701
## Jan 2023 1039.273 575.5789 1502.966 330.1143 1748.431
## Feb 2023 1035.493 566.8718 1504.114 318.7989 1752.186
## Mar 2023 1031.713 558.1477 1505.278 307.4574 1755.968
## Apr 2023 1027.933 549.4064 1506.460 296.0897 1759.776
## May 2023 1024.153 540.6482 1507.658 284.6961 1763.610
## Jun 2023 1020.373 531.8731 1508.874 273.2766 1767.470
## Jul 2023 1016.594 523.0810 1510.106 261.8313 1771.356
## Aug 2023 1012.814 514.2721 1511.355 250.3602 1775.2672.0.8 Sarima
fsarima <- forecast(sarima, h=22)## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Nov 2021 1532.971 1453.385 1612.558 1411.254 1654.688
## Dec 2021 1533.196 1453.411 1612.981 1411.175 1655.216
## Jan 2022 1533.419 1453.438 1613.400 1411.099 1655.739
## Feb 2022 1533.641 1453.467 1613.815 1411.026 1656.256
## Mar 2022 1533.862 1453.497 1614.226 1410.955 1656.769
## Apr 2022 1534.081 1453.529 1614.634 1410.887 1657.276
## May 2022 1534.300 1453.561 1615.038 1410.821 1657.779
## Jun 2022 1534.517 1453.595 1615.439 1410.758 1658.276
## Jul 2022 1534.733 1453.631 1615.836 1410.697 1658.769
## Aug 2022 1534.948 1453.667 1616.229 1410.639 1659.257
## Sep 2022 1535.162 1453.705 1616.619 1410.584 1659.740
## Oct 2022 1535.374 1453.743 1617.006 1410.530 1660.218
## Nov 2022 1535.586 1453.783 1617.389 1410.479 1660.692
## Dec 2022 1535.796 1453.824 1617.768 1410.430 1661.162
## Jan 2023 1536.005 1453.866 1618.145 1410.384 1661.627
## Feb 2023 1536.213 1453.909 1618.518 1410.339 1662.087
## Mar 2023 1536.420 1453.952 1618.887 1410.297 1662.543
## Apr 2023 1536.626 1453.997 1619.254 1410.256 1662.995
## May 2023 1536.830 1454.043 1619.618 1410.218 1663.442
## Jun 2023 1537.034 1454.090 1619.978 1410.182 1663.886
## Jul 2023 1537.236 1454.137 1620.335 1410.147 1664.325
## Aug 2023 1537.437 1454.186 1620.689 1410.115 1664.7602.0.9 Choques
2.1 Change Points
Único Choque
## ints1 ints2 cp
## 1667.857 1572.929 126.000
## Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
## 2009 1581 1581 1581 1581 1577 1577 1577 1577 1583 1583 1586 1593
## 2010 1597 1597 1597 1597 1597 1597 1619 1622 1622 1622 1622 1646
## 2011 1655 1656 1656 1656 1656 1657 1657 1657 1657 1661 1656 1662
## 2012 1666 1666 1671 1671 1670 1671 1671 1671 1672 1676 1678 1700
## 2013 1702 1704 1704 1704 1704 1704 1704 1704 1704 1704 1704 1704
## 2014 1703 1703 1703 1702 1703 1702 1703 1703 1703 1702 1702 1696
## 2015 1696 1708 1708 1708 1708 1708 1708 1708 1708 1708 1708 1702
## 2016 1702 1727 1732 1735 1716 1716 1716 1715 1715 1715 1717 1715
## 2017 1715 1715 1718 1715 1689 1686 1681 1680 1678 1678 1677 1671
## 2018 1672 1667 1667 1664 1658 1656 1652 1644 1640 1639 1637 1636
## 2019 1636 1636 1623 1623 1623 1623 1615 1612 1612 1604 1607 1601
## 2020 1601 1601 1600 1598 1597 1597 1598 1593 1593 1570 1570 1570
## 2021 1548 1548 1548 1547 1525 1524 1518 1515 1515 1515Variação da Média
mvalue = cpt.mean(mensal, method="BinSeg")## [1] 23 47 111 126 144
Variação da variância
mvalue = cpt.meanvar(mensal, method="BinSeg")## [1] 4 8 122 126 151
3 Idade Média da Frota
3.0.1 Ordenamento Temporal
3.0.2 Série Histórica
3.0.3 Decomposição da Série
Associação com regressão
3.0.4 Correlogramas
3.0.5 Correlações
## V1 V2 V3 V4 V5 V6 V7 V8
## 0.9219822 0.9624973 0.9543379 0.9657342 0.9745564 0.9745564 0.9654256 0.9784013
## V9 V10 V11 V12
## 0.9784013 0.9784013 0.9784013 0.96731153.0.6 Forecasting
auto## Series: mensal
## ARIMA(0,1,1)(1,0,0)[12] with drift
##
## Coefficients:
## ma1 sar1 drift
## -0.3341 0.0215 0.0262
## s.e. 0.0793 0.0835 0.0158
##
## sigma^2 estimated as 0.08338: log likelihood=-25.59
## AIC=59.18 AICc=59.46 BIC=71.31sarima## Series: mensal
## ARIMA(1,0,0)(0,0,1)[12] with non-zero mean
##
## Coefficients:
## ar1 sma1 mean
## 0.9809 0.1007 5.6898
## s.e. 0.0147 0.0893 1.0772
##
## sigma^2 estimated as 0.09191: log likelihood=-34.99
## AIC=77.97 AICc=78.24 BIC=90.123.0.7 AutoArima
fauto <- forecast(auto, h=22)## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Nov 2021 10.91657 8.254914 13.57823 6.845917 14.98723
## Dec 2021 10.94279 8.269245 13.61634 6.853956 15.03163
## Jan 2022 10.96901 8.283629 13.65439 6.862075 15.07595
## Feb 2022 10.99523 8.298066 13.69239 6.870273 15.12019
## Mar 2022 11.02145 8.312553 13.73034 6.878550 15.16435
## Apr 2022 11.04767 8.327091 13.76824 6.886905 15.20843
## May 2022 11.07389 8.341679 13.80610 6.895335 15.25244
## Jun 2022 11.10011 8.356316 13.84390 6.903841 15.29637
## Jul 2022 11.12633 8.371002 13.88165 6.912422 15.34023
## Aug 2022 11.15254 8.385736 13.91935 6.921076 15.38401
## Sep 2022 11.17876 8.400518 13.95701 6.929803 15.42773
## Oct 2022 11.20498 8.415346 13.99462 6.938601 15.47137
## Nov 2022 11.23120 8.430221 14.03218 6.947470 15.51493
## Dec 2022 11.25742 8.445141 14.06970 6.956410 15.55843
## Jan 2023 11.28364 8.460107 14.10718 6.965418 15.60186
## Feb 2023 11.30986 8.475117 14.14460 6.974495 15.64523
## Mar 2023 11.33608 8.490172 14.18199 6.983639 15.68852
## Apr 2023 11.36230 8.505270 14.21933 6.992850 15.73175
## May 2023 11.38852 8.520411 14.25663 7.002127 15.77491
## Jun 2023 11.41474 8.535595 14.29388 7.011469 15.81801
## Jul 2023 11.44096 8.550821 14.33109 7.020876 15.86104
## Aug 2023 11.46718 8.566089 14.36826 7.030346 15.904013.0.8 Sarima
fsarima <- forecast(sarima, h=22)## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Nov 2021 5.967297 3.824312 8.110281 2.689885 9.244709
## Dec 2021 5.961990 3.818391 8.105590 2.683638 9.240343
## Jan 2022 5.956786 3.812594 8.100977 2.677528 9.236043
## Feb 2022 5.951680 3.806920 8.096440 2.671553 9.231808
## Mar 2022 5.946673 3.801365 8.091980 2.665708 9.227637
## Apr 2022 5.941761 3.795927 8.087595 2.659992 9.223530
## May 2022 5.936943 3.790603 8.083283 2.654399 9.219487
## Jun 2022 5.932217 3.785390 8.079044 2.648929 9.215506
## Jul 2022 5.927582 3.780286 8.074877 2.643577 9.211587
## Aug 2022 5.923035 3.775289 8.070781 2.638341 9.207729
## Sep 2022 5.918575 3.770396 8.066755 2.633218 9.203933
## Oct 2022 5.914201 3.765604 8.062798 2.628206 9.200196
## Nov 2022 5.909910 3.760912 8.058908 2.623302 9.196518
## Dec 2022 5.905701 3.756318 8.055085 2.618503 9.192900
## Jan 2023 5.901573 3.751818 8.051328 2.613807 9.189339
## Feb 2023 5.897524 3.747412 8.047635 2.609212 9.185836
## Mar 2023 5.893552 3.743097 8.044007 2.604715 9.182389
## Apr 2023 5.889656 3.738870 8.040442 2.600313 9.178999
## May 2023 5.885835 3.734731 8.036938 2.596006 9.175663
## Jun 2023 5.882086 3.730677 8.033495 2.591790 9.172383
## Jul 2023 5.878410 3.726706 8.030113 2.587663 9.169156
## Aug 2023 5.874803 3.722817 8.026789 2.583624 9.1659823.0.9 Choques
3.1 Change Points
Único Choque
## ints1 ints2 cp
## 4.463918 7.245614 97.000000
## Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
## 2009 4 4 4 4 4 4 5 4 4 4 4 4
## 2010 4 4 4 4 4 4 4 4 4 4 4 4
## 2011 4 4 4 4 4 4 4 4 4 4 4 3
## 2012 3 4 3 4 4 4 4 4 4 4 4 4
## 2013 4 4 4 4 4 4 4 4 4 4 4 4
## 2014 5 5 5 5 5 5 5 5 5 5 5 5
## 2015 6 5 5 5 6 6 6 6 6 6 6 6
## 2016 6 5 5 5 5 5 5 5 5 5 5 5
## 2017 5 6 6 6 6 6 6 6 6 6 6 6
## 2018 6 6 6 7 7 7 7 7 7 7 7 7
## 2019 7 7 7 7 7 7 8 8 8 8 8 8
## 2020 8 8 8 8 8 8 8 8 8 8 8 8
## 2021 8 8 8 8 8 8 8 8 8 8Variação da Média
mvalue = cpt.mean(mensal, method="BinSeg")## [1] 60 111
Variação da variância
mvalue = cpt.meanvar(mensal, method="BinSeg")## [1] 76 85 97 111 126
4 Reclamação de Pessoal
4.0.1 Ordenamento Temporal
4.0.2 Série Histórica
4.0.3 Decomposição da Série
Associação com regressão
4.0.4 Correlogramas
4.0.5 Correlações
## V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12
## NA NA NA NA NA NA NA NA NA NA NA NA4.0.6 Forecasting
auto## Series: mensal
## ARIMA(1,1,0)(1,0,1)[12]
##
## Coefficients:
## ar1 sar1 sma1
## -0.3386 0.0530 0.4139
## s.e. 0.1231 0.3986 0.3987
##
## sigma^2 estimated as 5691: log likelihood=-338.72
## AIC=685.44 AICc=686.18 BIC=693.75sarima## Series: mensal
## ARIMA(1,0,0)(0,0,1)[12] with non-zero mean
##
## Coefficients:
## ar1 sma1 mean
## 0.9111 0.6037 548.7643
## s.e. 0.0562 0.2169 144.6066
##
## sigma^2 estimated as 5977: log likelihood=-348.24
## AIC=704.48 AICc=705.21 BIC=712.864.0.7 AutoArima
fauto <- forecast(auto, h=22)## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Jan 2021 176.2174 -1342.687 1695.121 -2146.746 2499.181
## Feb 2021 176.2174 -1346.510 1698.944 -2152.593 2505.027
## Mar 2021 176.2174 -1350.323 1702.758 -2158.425 2510.859
## Apr 2021 176.2174 -1354.127 1706.562 -2164.242 2516.677
## May 2021 176.2174 -1357.921 1710.356 -2170.045 2522.480
## Jun 2021 176.2174 -1361.706 1714.141 -2175.834 2528.269
## Jul 2021 176.2174 -1365.482 1717.917 -2181.609 2534.043
## Aug 2021 176.2174 -1369.249 1721.684 -2187.369 2539.804
## Sep 2021 176.2174 -1373.006 1725.441 -2193.116 2545.550
## Oct 2021 176.2174 -1376.754 1729.189 -2198.848 2551.283
## Nov 2021 176.2174 -1380.494 1732.929 -2204.567 2557.002
## Dec 2021 176.2174 -1384.224 1736.659 -2210.272 2562.707
## Jan 2022 176.2174 -1387.946 1740.380 -2215.963 2568.398
## Feb 2022 176.2174 -1391.658 1744.093 -2221.641 2574.076
## Mar 2022 176.2174 -1395.362 1747.797 -2227.306 2579.741
## Apr 2022 176.2174 -1399.057 1751.492 -2232.957 2585.392
## May 2022 176.2174 -1402.744 1755.178 -2238.595 2591.030
## Jun 2022 176.2174 -1406.421 1758.856 -2244.220 2596.655
## Jul 2022 176.2174 -1410.091 1762.526 -2249.832 2602.266
## Aug 2022 176.2174 -1413.752 1766.186 -2255.430 2607.865
## Sep 2022 176.2174 -1417.404 1769.839 -2261.016 2613.451
## Oct 2022 176.2174 -1421.048 1773.483 -2266.590 2619.0244.0.8 Sarima
fsarima <- forecast(sarima, h=22)## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Jan 2021 548.7643 229.8491 867.6795 61.02561 1036.503
## Feb 2021 548.7643 229.8491 867.6795 61.02561 1036.503
## Mar 2021 548.7643 229.8491 867.6795 61.02561 1036.503
## Apr 2021 548.7643 229.8491 867.6795 61.02561 1036.503
## May 2021 548.7643 229.8491 867.6795 61.02561 1036.503
## Jun 2021 548.7643 229.8491 867.6795 61.02561 1036.503
## Jul 2021 548.7643 229.8491 867.6795 61.02561 1036.503
## Aug 2021 548.7643 229.8491 867.6795 61.02561 1036.503
## Sep 2021 548.7643 229.8491 867.6795 61.02561 1036.503
## Oct 2021 548.7643 229.8491 867.6795 61.02561 1036.503
## Nov 2021 548.7643 229.8491 867.6795 61.02561 1036.503
## Dec 2021 548.7643 229.8491 867.6795 61.02561 1036.503
## Jan 2022 548.7643 229.8491 867.6795 61.02561 1036.503
## Feb 2022 548.7643 229.8491 867.6795 61.02561 1036.503
## Mar 2022 548.7643 229.8491 867.6795 61.02561 1036.503
## Apr 2022 548.7643 229.8491 867.6795 61.02561 1036.503
## May 2022 548.7643 229.8491 867.6795 61.02561 1036.503
## Jun 2022 548.7643 229.8491 867.6795 61.02561 1036.503
## Jul 2022 548.7643 229.8491 867.6795 61.02561 1036.503
## Aug 2022 548.7643 229.8491 867.6795 61.02561 1036.503
## Sep 2022 548.7643 229.8491 867.6795 61.02561 1036.503
## Oct 2022 548.7643 229.8491 867.6795 61.02561 1036.5034.0.9 Choques
4.1 Change Points
Único Choque
## ints1 ints2 cp
## 730.5000 440.9762 18.0000
## Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
## 2016 1022 936 807 882 748 748 712 810 727 731 610 460
## 2017 775 624 656 666 598 637 531 488 539 504 493 424
## 2018 600 578 537 441 427 543 524 505 524 512 493 496
## 2019 533 564 557 500 516 532 486 516 526 476 478 404
## 2020 402 163 226 308 236 235 313 244 338 293 281 235Variação da Média
mvalue = cpt.mean(mensal, method="BinSeg")## [1] 4 10 12 18 49
Variação da variância
mvalue = cpt.meanvar(mensal, method="BinSeg")## [1] 18 47 49
5 Reclamação de Viagens
5.0.1 Ordenamento Temporal
5.0.2 Série Histórica
5.0.3 Decomposição da Série
Associação com regressão
5.0.4 Correlogramas
5.0.5 Correlações
## V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12
## NA NA NA NA NA NA NA NA NA NA NA NA5.0.6 Forecasting
auto## Series: mensal
## ARIMA(1,1,1)(1,1,1)[12]
##
## Coefficients:
## ar1 ma1 sar1 sma1
## 0.1932 -0.5461 -0.0039 -0.7184
## s.e. 0.4610 0.4033 0.4476 0.9448
##
## sigma^2 estimated as 39573: log likelihood=-310.87
## AIC=631.73 AICc=633.23 BIC=640.88sarima## Series: mensal
## ARIMA(1,0,0)(0,0,1)[12] with non-zero mean
##
## Coefficients:
## ar1 sma1 mean
## 0.7235 0.5314 726.3904
## s.e. 0.0870 0.1590 138.2482
##
## sigma^2 estimated as 46917: log likelihood=-401.85
## AIC=811.71 AICc=812.45 BIC=820.025.0.7 AutoArima
fauto <- forecast(auto, h=22)## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Dec 2020 -1237.775 -8718.101 6242.551 -12677.95 10202.396
## Jan 2021 -1515.658 -9042.589 6011.273 -13027.11 9995.790
## Feb 2021 -1639.776 -9212.908 5933.355 -13221.88 9942.328
## Mar 2021 -1756.942 -9375.971 5862.087 -13409.24 9895.357
## Apr 2021 -1956.168 -9620.815 5708.480 -13678.23 9765.899
## May 2021 -1920.239 -9630.233 5789.756 -13711.66 9871.180
## Jun 2021 -1852.792 -9607.869 5902.285 -13713.16 10007.575
## Jul 2021 -1852.814 -9652.713 5947.084 -13781.73 10076.101
## Aug 2021 -1791.698 -9636.162 6052.767 -13788.77 10205.376
## Sep 2021 -1858.102 -9746.884 6030.680 -13922.95 10206.749
## Oct 2021 -1886.609 -9819.474 6046.257 -14018.88 10245.662
## Nov 2021 -1922.388 -9908.628 6063.852 -14136.29 10291.512
## Dec 2021 -1360.537 -9396.930 6675.855 -13651.14 10930.064
## Jan 2022 -1638.420 -9722.482 6445.642 -14001.93 10725.085
## Feb 2022 -1762.538 -9893.875 6368.798 -14198.34 10673.267
## Mar 2022 -1879.704 -10058.019 6298.611 -14387.36 10627.950
## Apr 2022 -2078.930 -10303.951 6146.092 -14658.01 10500.155
## May 2022 -2043.001 -10314.464 6228.463 -14693.11 10607.111
## Jun 2022 -1975.554 -10293.200 6342.092 -14696.30 10745.188
## Jul 2022 -1975.576 -10339.150 6387.997 -14766.56 10815.406
## Aug 2022 -1914.460 -10323.710 6494.791 -14775.30 10946.379
## Sep 2022 -1980.864 -10435.548 6473.820 -14911.19 10949.4595.0.8 Sarima
fsarima <- forecast(sarima, h=22)## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Dec 2020 726.3904 267.1855 1185.595 24.09718 1428.684
## Jan 2021 726.3904 267.1855 1185.595 24.09718 1428.684
## Feb 2021 726.3904 267.1855 1185.595 24.09718 1428.684
## Mar 2021 726.3904 267.1855 1185.595 24.09718 1428.684
## Apr 2021 726.3904 267.1855 1185.595 24.09718 1428.684
## May 2021 726.3904 267.1855 1185.595 24.09718 1428.684
## Jun 2021 726.3904 267.1855 1185.595 24.09718 1428.684
## Jul 2021 726.3904 267.1855 1185.595 24.09718 1428.684
## Aug 2021 726.3904 267.1855 1185.595 24.09718 1428.684
## Sep 2021 726.3904 267.1855 1185.595 24.09718 1428.684
## Oct 2021 726.3904 267.1855 1185.595 24.09718 1428.684
## Nov 2021 726.3904 267.1855 1185.595 24.09718 1428.684
## Dec 2021 726.3904 267.1855 1185.595 24.09718 1428.684
## Jan 2022 726.3904 267.1855 1185.595 24.09718 1428.684
## Feb 2022 726.3904 267.1855 1185.595 24.09718 1428.684
## Mar 2022 726.3904 267.1855 1185.595 24.09718 1428.684
## Apr 2022 726.3904 267.1855 1185.595 24.09718 1428.684
## May 2022 726.3904 267.1855 1185.595 24.09718 1428.684
## Jun 2022 726.3904 267.1855 1185.595 24.09718 1428.684
## Jul 2022 726.3904 267.1855 1185.595 24.09718 1428.684
## Aug 2022 726.3904 267.1855 1185.595 24.09718 1428.684
## Sep 2022 726.3904 267.1855 1185.595 24.09718 1428.6845.0.9 Choques
5.1 Change Points
Único Choque
## ints1 ints2 cp
## 931.4872 438.4000 39.0000
## Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
## 2016 1524 1148 840 762 709 681 728 848 665 685 898 721
## 2017 1936 1538 1316 1245 745 823 976 934 963 770 638 576
## 2018 1094 1042 970 630 622 667 823 769 1019 931 881 825
## 2019 1215 1231 940 671 535 567 487 582 446 422 435 494
## 2020 811 279 378 467 190 231 325 253 474 412 309Variação da Média
mvalue = cpt.mean(mensal, method="BinSeg")## [1] 2 12 16 39 49
Variação da variância
mvalue = cpt.meanvar(mensal, method="BinSeg")## [1] 40
6 Acidentes
6.0.1 Ordenamento Temporal
6.0.2 Série Histórica
6.0.3 Decomposição da Série
Associação com regressão
6.0.4 Correlogramas
6.0.5 Correlações
## V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12
## NA NA NA NA NA NA NA NA NA NA NA NA6.0.6 Forecasting
auto## Series: mensal
## ARIMA(0,1,1)
##
## Coefficients:
## ma1
## -0.6876
## s.e. 0.0978
##
## sigma^2 estimated as 0.00004746: log likelihood=210.16
## AIC=-416.32 AICc=-416.1 BIC=-412.16sarima## Series: mensal
## ARIMA(1,0,0)(0,0,1)[12] with non-zero mean
##
## Coefficients:
## ar1 sma1 mean
## 0.5470 -0.1335 0.0348
## s.e. 0.1115 0.1565 0.0017
##
## sigma^2 estimated as 0.0000513: log likelihood=212.45
## AIC=-416.9 AICc=-416.17 BIC=-408.526.0.7 AutoArima
fauto <- forecast(auto, h=22)## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Jan 2021 0.02958835 -0.01078295 0.06995964 -0.03215423 0.09133092
## Feb 2021 0.02958835 -0.01087706 0.07005375 -0.03229815 0.09147484
## Mar 2021 0.02958835 -0.01097095 0.07014764 -0.03244174 0.09161843
## Apr 2021 0.02958835 -0.01106462 0.07024131 -0.03258500 0.09176169
## May 2021 0.02958835 -0.01115808 0.07033477 -0.03272793 0.09190462
## Jun 2021 0.02958835 -0.01125132 0.07042801 -0.03287054 0.09204723
## Jul 2021 0.02958835 -0.01134435 0.07052104 -0.03301281 0.09218950
## Aug 2021 0.02958835 -0.01143717 0.07061386 -0.03315477 0.09233146
## Sep 2021 0.02958835 -0.01152978 0.07070647 -0.03329641 0.09247310
## Oct 2021 0.02958835 -0.01162219 0.07079888 -0.03343772 0.09261441
## Nov 2021 0.02958835 -0.01171438 0.07089107 -0.03357872 0.09275541
## Dec 2021 0.02958835 -0.01180637 0.07098306 -0.03371941 0.09289610
## Jan 2022 0.02958835 -0.01189816 0.07107485 -0.03385978 0.09303647
## Feb 2022 0.02958835 -0.01198974 0.07116643 -0.03399985 0.09317654
## Mar 2022 0.02958835 -0.01208112 0.07125781 -0.03413961 0.09331630
## Apr 2022 0.02958835 -0.01217230 0.07134899 -0.03427906 0.09345575
## May 2022 0.02958835 -0.01226329 0.07143998 -0.03441820 0.09359489
## Jun 2022 0.02958835 -0.01235407 0.07153076 -0.03455705 0.09373374
## Jul 2022 0.02958835 -0.01244466 0.07162135 -0.03469560 0.09387229
## Aug 2022 0.02958835 -0.01253506 0.07171175 -0.03483384 0.09401053
## Sep 2022 0.02958835 -0.01262526 0.07180195 -0.03497179 0.09414848
## Oct 2022 0.02958835 -0.01271527 0.07189196 -0.03510945 0.094286146.0.8 Sarima
fsarima <- forecast(sarima, h=22)## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Jan 2021 0.03478775 0.02372684 0.04584867 0.01787155 0.05170396
## Feb 2021 0.03478775 0.02372684 0.04584867 0.01787155 0.05170396
## Mar 2021 0.03478775 0.02372684 0.04584867 0.01787155 0.05170396
## Apr 2021 0.03478775 0.02372684 0.04584867 0.01787155 0.05170396
## May 2021 0.03478775 0.02372684 0.04584867 0.01787155 0.05170396
## Jun 2021 0.03478775 0.02372684 0.04584867 0.01787155 0.05170396
## Jul 2021 0.03478775 0.02372684 0.04584867 0.01787155 0.05170396
## Aug 2021 0.03478775 0.02372684 0.04584867 0.01787155 0.05170396
## Sep 2021 0.03478775 0.02372684 0.04584867 0.01787155 0.05170396
## Oct 2021 0.03478775 0.02372684 0.04584867 0.01787155 0.05170396
## Nov 2021 0.03478775 0.02372684 0.04584867 0.01787155 0.05170396
## Dec 2021 0.03478775 0.02372684 0.04584867 0.01787155 0.05170396
## Jan 2022 0.03478775 0.02372684 0.04584867 0.01787155 0.05170396
## Feb 2022 0.03478775 0.02372684 0.04584867 0.01787155 0.05170396
## Mar 2022 0.03478775 0.02372684 0.04584867 0.01787155 0.05170396
## Apr 2022 0.03478775 0.02372684 0.04584867 0.01787155 0.05170396
## May 2022 0.03478775 0.02372684 0.04584867 0.01787155 0.05170396
## Jun 2022 0.03478775 0.02372684 0.04584867 0.01787155 0.05170396
## Jul 2022 0.03478775 0.02372684 0.04584867 0.01787155 0.05170396
## Aug 2022 0.03478775 0.02372684 0.04584867 0.01787155 0.05170396
## Sep 2022 0.03478775 0.02372684 0.04584867 0.01787155 0.05170396
## Oct 2022 0.03478775 0.02372684 0.04584867 0.01787155 0.051703966.0.9 Choques
6.1 Change Points
Único Choque
## ints
## 0.03476551
## Jan Feb Mar Apr May Jun
## 2016 0.04810776 0.05131495 0.05003207 0.04874920 0.04618345 0.04682489
## 2017 0.04227213 0.04227213 0.03368560 0.03038309 0.03896962 0.03896962
## 2018 0.02920723 0.02781641 0.03616134 0.03616134 0.03198887 0.03824757
## 2019 0.02777778 0.03632479 0.03133903 0.03774929 0.03561254 0.04131054
## 2020 0.03544304 0.01198402 0.02023121 0.02325581 0.03202329 0.02919708
## Jul Aug Sep Oct Nov Dec
## 2016 0.04490058 0.05003207 0.04554201 0.04041052 0.03143040 0.02694035
## 2017 0.03104359 0.02708058 0.03632761 0.03038309 0.02708058 0.02179657
## 2018 0.02712100 0.02990264 0.03616134 0.03337969 0.04659249 0.02503477
## 2019 0.02991453 0.04629630 0.03133903 0.03133903 0.03205128 0.04059829
## 2020 0.03478261 0.02439024 0.02970297 0.03776224 0.03203343 0.02496533Variação da Média
mvalue = cpt.mean(mensal, method="BinSeg")## numeric(0)
Variação da variância
mvalue = cpt.meanvar(mensal, method="BinSeg")## [1] 9
7 Autuações
7.0.1 Ordenamento Temporal
7.0.2 Série Histórica
7.0.3 Decomposição da Série
Associação com regressão
7.0.4 Correlogramas
7.0.5 Correlações
## V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12
## NA NA NA NA NA NA NA NA NA NA NA NA7.0.6 Forecasting
auto## Series: mensal
## ARIMA(1,0,0) with non-zero mean
##
## Coefficients:
## ar1 mean
## 0.3696 0.2998
## s.e. 0.1188 0.0434
##
## sigma^2 estimated as 0.04742: log likelihood=7.27
## AIC=-8.54 AICc=-8.11 BIC=-2.26sarima## Series: mensal
## ARIMA(1,0,0)(0,0,1)[12] with non-zero mean
##
## Coefficients:
## ar1 sma1 mean
## 0.3595 0.1166 0.2972
## s.e. 0.1202 0.1330 0.0465
##
## sigma^2 estimated as 0.04749: log likelihood=7.67
## AIC=-7.34 AICc=-6.61 BIC=1.047.0.7 AutoArima
fauto <- forecast(auto, h=22)## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Jan 2021 0.2997585 -0.0005656663 0.6000827 -0.1595477 0.7590647
## Feb 2021 0.2997585 -0.0005656663 0.6000827 -0.1595477 0.7590647
## Mar 2021 0.2997585 -0.0005656663 0.6000827 -0.1595477 0.7590647
## Apr 2021 0.2997585 -0.0005656663 0.6000827 -0.1595477 0.7590647
## May 2021 0.2997585 -0.0005656663 0.6000827 -0.1595477 0.7590647
## Jun 2021 0.2997585 -0.0005656663 0.6000827 -0.1595477 0.7590647
## Jul 2021 0.2997585 -0.0005656663 0.6000827 -0.1595477 0.7590647
## Aug 2021 0.2997585 -0.0005656663 0.6000827 -0.1595477 0.7590647
## Sep 2021 0.2997585 -0.0005656663 0.6000827 -0.1595477 0.7590647
## Oct 2021 0.2997585 -0.0005656663 0.6000827 -0.1595477 0.7590647
## Nov 2021 0.2997585 -0.0005656663 0.6000827 -0.1595477 0.7590647
## Dec 2021 0.2997585 -0.0005656663 0.6000827 -0.1595477 0.7590647
## Jan 2022 0.2997585 -0.0005656663 0.6000827 -0.1595477 0.7590647
## Feb 2022 0.2997585 -0.0005656663 0.6000827 -0.1595477 0.7590647
## Mar 2022 0.2997585 -0.0005656663 0.6000827 -0.1595477 0.7590647
## Apr 2022 0.2997585 -0.0005656663 0.6000827 -0.1595477 0.7590647
## May 2022 0.2997585 -0.0005656663 0.6000827 -0.1595477 0.7590647
## Jun 2022 0.2997585 -0.0005656663 0.6000827 -0.1595477 0.7590647
## Jul 2022 0.2997585 -0.0005656663 0.6000827 -0.1595477 0.7590647
## Aug 2022 0.2997585 -0.0005656663 0.6000827 -0.1595477 0.7590647
## Sep 2022 0.2997585 -0.0005656663 0.6000827 -0.1595477 0.7590647
## Oct 2022 0.2997585 -0.0005656663 0.6000827 -0.1595477 0.75906477.0.8 Sarima
fsarima <- forecast(sarima, h=22)## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Jan 2021 0.297233 -0.004070886 0.5985368 -0.1635715 0.7580374
## Feb 2021 0.297233 -0.004070886 0.5985368 -0.1635715 0.7580374
## Mar 2021 0.297233 -0.004070886 0.5985368 -0.1635715 0.7580374
## Apr 2021 0.297233 -0.004070886 0.5985368 -0.1635715 0.7580374
## May 2021 0.297233 -0.004070886 0.5985368 -0.1635715 0.7580374
## Jun 2021 0.297233 -0.004070886 0.5985368 -0.1635715 0.7580374
## Jul 2021 0.297233 -0.004070886 0.5985368 -0.1635715 0.7580374
## Aug 2021 0.297233 -0.004070886 0.5985368 -0.1635715 0.7580374
## Sep 2021 0.297233 -0.004070886 0.5985368 -0.1635715 0.7580374
## Oct 2021 0.297233 -0.004070886 0.5985368 -0.1635715 0.7580374
## Nov 2021 0.297233 -0.004070886 0.5985368 -0.1635715 0.7580374
## Dec 2021 0.297233 -0.004070886 0.5985368 -0.1635715 0.7580374
## Jan 2022 0.297233 -0.004070886 0.5985368 -0.1635715 0.7580374
## Feb 2022 0.297233 -0.004070886 0.5985368 -0.1635715 0.7580374
## Mar 2022 0.297233 -0.004070886 0.5985368 -0.1635715 0.7580374
## Apr 2022 0.297233 -0.004070886 0.5985368 -0.1635715 0.7580374
## May 2022 0.297233 -0.004070886 0.5985368 -0.1635715 0.7580374
## Jun 2022 0.297233 -0.004070886 0.5985368 -0.1635715 0.7580374
## Jul 2022 0.297233 -0.004070886 0.5985368 -0.1635715 0.7580374
## Aug 2022 0.297233 -0.004070886 0.5985368 -0.1635715 0.7580374
## Sep 2022 0.297233 -0.004070886 0.5985368 -0.1635715 0.7580374
## Oct 2022 0.297233 -0.004070886 0.5985368 -0.1635715 0.75803747.0.9 Choques
7.1 Change Points
Único Choque
## ints
## 0.3011886
## Jan Feb Mar Apr May Jun
## 2016 0.148171905 0.295702373 0.190506735 0.212957024 0.114175754 0.204618345
## 2017 0.505284016 1.128797886 1.513210040 0.126816380 0.404887715 0.167107001
## 2018 0.506258693 0.509735744 0.682197497 0.435326843 0.087621697 0.328929068
## 2019 0.270655271 0.234330484 0.267094017 0.258547009 0.202279202 0.195156695
## 2020 0.394508671 0.208776596 0.394508671 0.416545718 0.400291121 0.312408759
## Jul Aug Sep Oct Nov Dec
## 2016 0.153944836 0.264271969 0.262989096 0.214239897 0.260423348 0.181526620
## 2017 0.291281374 0.331571995 0.027741083 0.421400264 0.439233818 0.130779392
## 2018 0.151599444 0.280945758 0.259388039 0.155076495 0.168984701 0.161335188
## 2019 0.175213675 0.236467236 0.381054131 0.187321937 0.226495726 0.180199430
## 2020 0.482608696 0.263988522 0.008486563 0.149650350 0.200557103 0.305131761Variação da Média
mvalue = cpt.mean(mensal, method="BinSeg")## numeric(0)
Variação da variância
mvalue = cpt.meanvar(mensal, method="BinSeg")## [1] 12 15 28
8 Índide de Quebras
8.0.1 Ordenamento Temporal
8.0.2 Série Histórica
8.0.3 Decomposição da Série
Associação com regressão
8.0.4 Correlogramas
8.0.5 Correlações
## V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12
## NA NA NA NA NA NA NA NA NA NA NA NA8.0.6 Forecasting
auto## Series: mensal
## ARIMA(0,1,0)
##
## sigma^2 estimated as 0.000006318: log likelihood=269.46
## AIC=-536.92 AICc=-536.85 BIC=-534.84sarima## Series: mensal
## ARIMA(1,0,0)(0,0,1)[12] with non-zero mean
##
## Coefficients:
## ar1 sma1 mean
## 0.5575 0.0901 0.0123
## s.e. 0.1048 0.1277 0.0007
##
## sigma^2 estimated as 0.000005069: log likelihood=281.94
## AIC=-555.88 AICc=-555.15 BIC=-547.58.0.7 AutoArima
fauto <- forecast(auto, h=22)## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Jan 2021 0.01198732 -0.03413509 0.05810973 -0.05855082 0.08252546
## Feb 2021 0.01198732 -0.03424745 0.05822209 -0.05872265 0.08269729
## Mar 2021 0.01198732 -0.03435953 0.05833417 -0.05889407 0.08286871
## Apr 2021 0.01198732 -0.03447135 0.05844598 -0.05906508 0.08303972
## May 2021 0.01198732 -0.03458289 0.05855753 -0.05923567 0.08321031
## Jun 2021 0.01198732 -0.03469417 0.05866881 -0.05940586 0.08338050
## Jul 2021 0.01198732 -0.03480518 0.05877982 -0.05957564 0.08355028
## Aug 2021 0.01198732 -0.03491594 0.05889057 -0.05974502 0.08371966
## Sep 2021 0.01198732 -0.03502643 0.05900107 -0.05991400 0.08388864
## Oct 2021 0.01198732 -0.03513666 0.05911130 -0.06008259 0.08405722
## Nov 2021 0.01198732 -0.03524663 0.05922127 -0.06025078 0.08422542
## Dec 2021 0.01198732 -0.03535635 0.05933099 -0.06041858 0.08439322
## Jan 2022 0.01198732 -0.03546582 0.05944046 -0.06058599 0.08456063
## Feb 2022 0.01198732 -0.03557503 0.05954967 -0.06075302 0.08472766
## Mar 2022 0.01198732 -0.03568399 0.05965863 -0.06091966 0.08489430
## Apr 2022 0.01198732 -0.03579271 0.05976735 -0.06108593 0.08506057
## May 2022 0.01198732 -0.03590118 0.05987581 -0.06125181 0.08522645
## Jun 2022 0.01198732 -0.03600940 0.05998404 -0.06141733 0.08539197
## Jul 2022 0.01198732 -0.03611738 0.06009202 -0.06158247 0.08555711
## Aug 2022 0.01198732 -0.03622512 0.06019975 -0.06174724 0.08572188
## Sep 2022 0.01198732 -0.03633261 0.06030725 -0.06191164 0.08588628
## Oct 2022 0.01198732 -0.03643987 0.06041451 -0.06207568 0.086050328.0.8 Sarima
fsarima <- forecast(sarima, h=22)## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Jan 2021 0.01233925 0.00884934 0.01582916 0.007001894 0.0176766
## Feb 2021 0.01233925 0.00884934 0.01582916 0.007001894 0.0176766
## Mar 2021 0.01233925 0.00884934 0.01582916 0.007001894 0.0176766
## Apr 2021 0.01233925 0.00884934 0.01582916 0.007001894 0.0176766
## May 2021 0.01233925 0.00884934 0.01582916 0.007001894 0.0176766
## Jun 2021 0.01233925 0.00884934 0.01582916 0.007001894 0.0176766
## Jul 2021 0.01233925 0.00884934 0.01582916 0.007001894 0.0176766
## Aug 2021 0.01233925 0.00884934 0.01582916 0.007001894 0.0176766
## Sep 2021 0.01233925 0.00884934 0.01582916 0.007001894 0.0176766
## Oct 2021 0.01233925 0.00884934 0.01582916 0.007001894 0.0176766
## Nov 2021 0.01233925 0.00884934 0.01582916 0.007001894 0.0176766
## Dec 2021 0.01233925 0.00884934 0.01582916 0.007001894 0.0176766
## Jan 2022 0.01233925 0.00884934 0.01582916 0.007001894 0.0176766
## Feb 2022 0.01233925 0.00884934 0.01582916 0.007001894 0.0176766
## Mar 2022 0.01233925 0.00884934 0.01582916 0.007001894 0.0176766
## Apr 2022 0.01233925 0.00884934 0.01582916 0.007001894 0.0176766
## May 2022 0.01233925 0.00884934 0.01582916 0.007001894 0.0176766
## Jun 2022 0.01233925 0.00884934 0.01582916 0.007001894 0.0176766
## Jul 2022 0.01233925 0.00884934 0.01582916 0.007001894 0.0176766
## Aug 2022 0.01233925 0.00884934 0.01582916 0.007001894 0.0176766
## Sep 2022 0.01233925 0.00884934 0.01582916 0.007001894 0.0176766
## Oct 2022 0.01233925 0.00884934 0.01582916 0.007001894 0.01767668.0.9 Choques
8.1 Change Points
Único Choque
## ints
## 0.01238554
## Jan Feb Mar Apr May Jun
## 2016 0.012368365 0.012051093 0.007841625 0.006991254 0.006496755 0.008172670
## 2017 0.013359185 0.010523998 0.011590744 0.013496257 0.008458687 0.012869135
## 2018 0.015837409 0.015020862 0.011934138 0.012911451 0.012248194 0.012360357
## 2019 0.011143277 0.011324786 0.004870876 0.012820513 0.013969304 0.015003217
## 2020 0.014917653 0.009942299 0.010674995 0.013275194 0.013147392 0.011773016
## Jul Aug Sep Oct Nov Dec
## 2016 0.008338192 0.010407223 0.013341108 0.015228064 0.012372802 0.010491462
## 2017 0.013408190 0.014893254 0.013870542 0.010610645 0.007819491 0.010520853
## 2018 0.010802040 0.012046301 0.013745943 0.013930638 0.015052268 0.014032386
## 2019 0.015598291 0.017691389 0.016286800 0.016749380 0.015876298 0.014957265
## 2020 0.010917874 0.010829824 0.013767091 0.015068802 0.015095696 0.011987319Variação da Média
mvalue = cpt.mean(mensal, method="BinSeg")## numeric(0)
Variação da variância
mvalue = cpt.meanvar(mensal, method="BinSeg")## numeric(0)
9 Frequência de Acidentes
9.0.1 Ordenamento Temporal
9.0.2 Série Histórica
9.0.3 Decomposição da Série
Associação com regressão
9.0.4 Correlogramas
9.0.5 Correlações
## V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12
## NA NA NA NA NA NA NA NA NA NA NA NA9.0.6 Forecasting
auto## Series: mensal
## ARIMA(0,1,1) with drift
##
## Coefficients:
## ma1 drift
## -0.5906 -0.9850
## s.e. 0.1252 0.5395
##
## sigma^2 estimated as 100.9: log likelihood=-219.02
## AIC=444.05 AICc=444.48 BIC=450.28sarima## Series: mensal
## ARIMA(1,0,0)(0,0,1)[12] with non-zero mean
##
## Coefficients:
## ar1 sma1 mean
## 0.8264 -0.0842 47.5708
## s.e. 0.0769 0.1515 6.7974
##
## sigma^2 estimated as 117.4: log likelihood=-227.18
## AIC=462.35 AICc=463.08 BIC=470.739.0.7 AutoArima
fauto <- forecast(auto, h=22)## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Jan 2021 -182.3521 -258.7008 -106.0035 -299.1173 -65.58692
## Feb 2021 -183.3371 -259.8674 -106.8069 -300.3800 -66.29419
## Mar 2021 -184.3221 -261.0335 -107.6107 -301.6421 -67.00212
## Apr 2021 -185.3071 -262.1993 -108.4150 -302.9035 -67.71071
## May 2021 -186.2921 -263.3646 -109.2196 -304.1643 -68.41994
## Jun 2021 -187.2771 -264.5295 -110.0247 -305.4244 -69.12981
## Jul 2021 -188.2621 -265.6939 -110.8303 -306.6839 -69.84033
## Aug 2021 -189.2471 -266.8580 -111.6362 -307.9427 -70.55147
## Sep 2021 -190.2321 -268.0216 -112.4425 -309.2009 -71.26325
## Oct 2021 -191.2171 -269.1849 -113.2493 -310.4585 -71.97566
## Nov 2021 -192.2021 -270.3477 -114.0565 -311.7155 -72.68868
## Dec 2021 -193.1871 -271.5101 -114.8640 -312.9718 -73.40233
## Jan 2022 -194.1721 -272.6721 -115.6720 -314.2276 -74.11659
## Feb 2022 -195.1571 -273.8338 -116.4804 -315.4827 -74.83145
## Mar 2022 -196.1421 -274.9950 -117.2891 -316.7372 -75.54693
## Apr 2022 -197.1271 -276.1558 -118.0983 -317.9912 -76.26300
## May 2022 -198.1121 -277.3163 -118.9079 -319.2445 -76.97967
## Jun 2022 -199.0971 -278.4764 -119.7178 -320.4972 -77.69693
## Jul 2022 -200.0821 -279.6360 -120.5281 -321.7494 -78.41478
## Aug 2022 -201.0671 -280.7953 -121.3388 -323.0009 -79.13322
## Sep 2022 -202.0521 -281.9542 -122.1499 -324.2519 -79.85224
## Oct 2022 -203.0371 -283.1128 -122.9614 -325.5023 -80.571849.0.8 Sarima
fsarima <- forecast(sarima, h=22)## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Jan 2021 47.57077 23.03553 72.10601 10.04736 85.09419
## Feb 2021 47.57077 23.03553 72.10601 10.04736 85.09419
## Mar 2021 47.57077 23.03553 72.10601 10.04736 85.09419
## Apr 2021 47.57077 23.03553 72.10601 10.04736 85.09419
## May 2021 47.57077 23.03553 72.10601 10.04736 85.09419
## Jun 2021 47.57077 23.03553 72.10601 10.04736 85.09419
## Jul 2021 47.57077 23.03553 72.10601 10.04736 85.09419
## Aug 2021 47.57077 23.03553 72.10601 10.04736 85.09419
## Sep 2021 47.57077 23.03553 72.10601 10.04736 85.09419
## Oct 2021 47.57077 23.03553 72.10601 10.04736 85.09419
## Nov 2021 47.57077 23.03553 72.10601 10.04736 85.09419
## Dec 2021 47.57077 23.03553 72.10601 10.04736 85.09419
## Jan 2022 47.57077 23.03553 72.10601 10.04736 85.09419
## Feb 2022 47.57077 23.03553 72.10601 10.04736 85.09419
## Mar 2022 47.57077 23.03553 72.10601 10.04736 85.09419
## Apr 2022 47.57077 23.03553 72.10601 10.04736 85.09419
## May 2022 47.57077 23.03553 72.10601 10.04736 85.09419
## Jun 2022 47.57077 23.03553 72.10601 10.04736 85.09419
## Jul 2022 47.57077 23.03553 72.10601 10.04736 85.09419
## Aug 2022 47.57077 23.03553 72.10601 10.04736 85.09419
## Sep 2022 47.57077 23.03553 72.10601 10.04736 85.09419
## Oct 2022 47.57077 23.03553 72.10601 10.04736 85.094199.0.9 Choques
9.1 Change Points
Único Choque
## ints1 ints2 cp
## 53.85714 19.18182 49.00000
## Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
## 2016 75 80 78 76 72 73 70 78 71 63 49 42
## 2017 64 64 51 46 59 59 47 41 55 46 41 33
## 2018 42 40 52 52 46 55 39 43 52 48 67 36
## 2019 39 51 44 53 50 58 42 65 44 44 45 57
## 2020 42 9 14 16 22 20 24 17 21 27 23 18Variação da Média
mvalue = cpt.mean(mensal, method="BinSeg")## [1] 10 12 18 26 49
Variação da variância
mvalue = cpt.meanvar(mensal, method="BinSeg")## [1] 9 49
10 Índice de Cumprimento de Viagens
10.0.1 Ordenamento Temporal
10.0.2 Série Histórica
10.0.3 Decomposição da Série
Associação com regressão
10.0.4 Correlogramas
10.0.5 Correlações
## V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12
## NA NA NA NA NA NA NA NA NA NA NA NA10.0.6 Forecasting
auto## Series: mensal
## ARIMA(1,0,0)(1,0,0)[12] with non-zero mean
##
## Coefficients:
## ar1 sar1 mean
## 0.7038 0.5290 0.8928
## s.e. 0.0986 0.1372 0.0098
##
## sigma^2 estimated as 0.0001636: log likelihood=157.99
## AIC=-307.98 AICc=-307.16 BIC=-300.02sarima## Series: mensal
## ARIMA(1,0,0)(0,0,1)[12] with non-zero mean
##
## Coefficients:
## ar1 sma1 mean
## 0.6379 0.4528 0.8912
## s.e. 0.1027 0.1606 0.0065
##
## sigma^2 estimated as 0.0001761: log likelihood=156.68
## AIC=-305.36 AICc=-304.54 BIC=-297.410.0.7 AutoArima
fauto <- forecast(auto, h=22)## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Jul 2020 0.8928010 0.8653988 0.9202033 0.8508930 0.9347091
## Aug 2020 0.8928006 0.8653984 0.9202029 0.8508926 0.9347087
## Sep 2020 0.8928012 0.8653989 0.9202034 0.8508931 0.9347093
## Oct 2020 0.8928012 0.8653990 0.9202035 0.8508932 0.9347093
## Nov 2020 0.8928013 0.8653991 0.9202035 0.8508932 0.9347094
## Dec 2020 0.8928014 0.8653992 0.9202036 0.8508933 0.9347095
## Jan 2021 0.8928014 0.8653991 0.9202036 0.8508933 0.9347094
## Feb 2021 0.8928013 0.8653991 0.9202036 0.8508933 0.9347094
## Mar 2021 0.8928012 0.8653990 0.9202035 0.8508932 0.9347093
## Apr 2021 0.8928012 0.8653989 0.9202034 0.8508931 0.9347093
## May 2021 0.8928013 0.8653991 0.9202035 0.8508932 0.9347094
## Jun 2021 0.8928013 0.8653991 0.9202035 0.8508932 0.9347094
## Jul 2021 0.8928011 0.8653989 0.9202033 0.8508930 0.9347092
## Aug 2021 0.8928009 0.8653987 0.9202031 0.8508928 0.9347090
## Sep 2021 0.8928012 0.8653990 0.9202034 0.8508931 0.9347093
## Oct 2021 0.8928012 0.8653990 0.9202034 0.8508931 0.9347093
## Nov 2021 0.8928012 0.8653990 0.9202035 0.8508932 0.9347093
## Dec 2021 0.8928013 0.8653991 0.9202035 0.8508932 0.9347094
## Jan 2022 0.8928013 0.8653991 0.9202035 0.8508932 0.9347094
## Feb 2022 0.8928013 0.8653990 0.9202035 0.8508932 0.9347093
## Mar 2022 0.8928012 0.8653990 0.9202034 0.8508931 0.9347093
## Apr 2022 0.8928012 0.8653990 0.9202034 0.8508931 0.934709310.0.8 Sarima
fsarima <- forecast(sarima, h=22)## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Jul 2020 0.8912073 0.8669234 0.9154912 0.8540683 0.9283463
## Aug 2020 0.8912073 0.8669234 0.9154912 0.8540683 0.9283463
## Sep 2020 0.8912073 0.8669234 0.9154912 0.8540683 0.9283463
## Oct 2020 0.8912073 0.8669234 0.9154912 0.8540683 0.9283463
## Nov 2020 0.8912073 0.8669234 0.9154912 0.8540683 0.9283463
## Dec 2020 0.8912073 0.8669234 0.9154912 0.8540683 0.9283463
## Jan 2021 0.8912073 0.8669234 0.9154912 0.8540683 0.9283463
## Feb 2021 0.8912073 0.8669234 0.9154912 0.8540683 0.9283463
## Mar 2021 0.8912073 0.8669234 0.9154912 0.8540683 0.9283463
## Apr 2021 0.8912073 0.8669234 0.9154912 0.8540683 0.9283463
## May 2021 0.8912073 0.8669234 0.9154912 0.8540683 0.9283463
## Jun 2021 0.8912073 0.8669234 0.9154912 0.8540683 0.9283463
## Jul 2021 0.8912073 0.8669234 0.9154912 0.8540683 0.9283463
## Aug 2021 0.8912073 0.8669234 0.9154912 0.8540683 0.9283463
## Sep 2021 0.8912073 0.8669234 0.9154912 0.8540683 0.9283463
## Oct 2021 0.8912073 0.8669234 0.9154912 0.8540683 0.9283463
## Nov 2021 0.8912073 0.8669234 0.9154912 0.8540683 0.9283463
## Dec 2021 0.8912073 0.8669234 0.9154912 0.8540683 0.9283463
## Jan 2022 0.8912073 0.8669234 0.9154912 0.8540683 0.9283463
## Feb 2022 0.8912073 0.8669234 0.9154912 0.8540683 0.9283463
## Mar 2022 0.8912073 0.8669234 0.9154912 0.8540683 0.9283463
## Apr 2022 0.8912073 0.8669234 0.9154912 0.8540683 0.928346310.0.9 Choques
10.1 Change Points
Único Choque
## ints
## 0.8888666
## Jan Feb Mar Apr May Jun Jul
## 2016 0.8827335 0.8776801 0.9027446 0.9125972 0.9124977 0.9054000 0.9070000
## 2017 0.8506129 0.8537572 0.8673598 0.8688000 0.8882000 0.8805756 0.8707413
## 2018 0.8755505 0.8731658 0.8883367 0.8891990 0.9039887 0.8741908 0.8737465
## 2019 0.8812731 0.8873276 0.9091145 0.9038493 0.9107488 0.9037230 0.9030742
## 2020 0.8763443 0.8392885 0.8901889 0.8967959 0.9025271 0.9139159
## Aug Sep Oct Nov Dec
## 2016 0.9047000 0.9012108 0.8907000 0.8904000 0.8763706
## 2017 0.8664865 0.8641245 0.8715402 0.8897519 0.8831091
## 2018 0.8818683 0.8958630 0.8807812 0.9097256 0.9088713
## 2019 0.9053730 0.8936046 0.8834719 0.9127924 0.9110038
## 2020Variação da Média
mvalue = cpt.mean(mensal, method="BinSeg")## numeric(0)
Variação da variância
mvalue = cpt.meanvar(mensal, method="BinSeg")## numeric(0)
11 Índice de Passageiros por Quilômetro
11.0.1 Ordenamento Temporal
11.0.2 Série Histórica
11.0.3 Decomposição da Série
Associação com regressão
11.0.4 Correlogramas
11.0.5 Correlações
## V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12
## 1 1 1 1 1 1 1 1 1 1 1 111.0.6 Forecasting
auto## Series: mensal
## ARIMA(0,1,0)
##
## sigma^2 estimated as 0.05348: log likelihood=1.36
## AIC=-0.72 AICc=-0.57 BIC=0.69sarima## Series: mensal
## ARIMA(1,0,0)(0,0,1)[12] with non-zero mean
##
## Coefficients:
## ar1 sma1 mean
## 0.7014 -0.0104 2.1251
## s.e. 0.1224 0.1837 0.1199
##
## sigma^2 estimated as 0.04955: log likelihood=3.82
## AIC=0.35 AICc=1.89 BIC=6.0911.0.7 AutoArima
fauto <- forecast(auto, h=22)## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Aug 2021 2.268075 -2.265602 6.801751 -4.665585 9.201735
## Sep 2021 2.268075 -2.275279 6.811428 -4.680385 9.216534
## Oct 2021 2.268075 -2.284935 6.821085 -4.695153 9.231303
## Nov 2021 2.268075 -2.294571 6.830721 -4.709890 9.246040
## Dec 2021 2.268075 -2.304187 6.840336 -4.724596 9.260746
## Jan 2022 2.268075 -2.313783 6.849932 -4.739271 9.275421
## Feb 2022 2.268075 -2.323358 6.859507 -4.753916 9.290065
## Mar 2022 2.268075 -2.332914 6.869063 -4.768530 9.304679
## Apr 2022 2.268075 -2.342449 6.878599 -4.783113 9.319263
## May 2022 2.268075 -2.351965 6.888115 -4.797667 9.333816
## Jun 2022 2.268075 -2.361462 6.897611 -4.812191 9.348340
## Jul 2022 2.268075 -2.370939 6.907088 -4.826685 9.362834
## Aug 2022 2.268075 -2.380397 6.916546 -4.841149 9.377298
## Sep 2022 2.268075 -2.389835 6.925985 -4.855584 9.391733
## Oct 2022 2.268075 -2.399255 6.935404 -4.869990 9.406139
## Nov 2022 2.268075 -2.408655 6.944804 -4.884366 9.420516
## Dec 2022 2.268075 -2.418037 6.954186 -4.898714 9.434864
## Jan 2023 2.268075 -2.427400 6.963549 -4.913034 9.449183
## Feb 2023 2.268075 -2.436744 6.972893 -4.927324 9.463474
## Mar 2023 2.268075 -2.446070 6.982219 -4.941587 9.477736
## Apr 2023 2.268075 -2.455377 6.991526 -4.955821 9.491970
## May 2023 2.268075 -2.464666 7.000815 -4.970027 9.50617711.0.8 Sarima
fsarima <- forecast(sarima, h=22)## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Aug 2021 2.125134 1.724901 2.525367 1.51303 2.737238
## Sep 2021 2.125134 1.724901 2.525367 1.51303 2.737238
## Oct 2021 2.125134 1.724901 2.525367 1.51303 2.737238
## Nov 2021 2.125134 1.724901 2.525367 1.51303 2.737238
## Dec 2021 2.125134 1.724901 2.525367 1.51303 2.737238
## Jan 2022 2.125134 1.724901 2.525367 1.51303 2.737238
## Feb 2022 2.125134 1.724901 2.525367 1.51303 2.737238
## Mar 2022 2.125134 1.724901 2.525367 1.51303 2.737238
## Apr 2022 2.125134 1.724901 2.525367 1.51303 2.737238
## May 2022 2.125134 1.724901 2.525367 1.51303 2.737238
## Jun 2022 2.125134 1.724901 2.525367 1.51303 2.737238
## Jul 2022 2.125134 1.724901 2.525367 1.51303 2.737238
## Aug 2022 2.125134 1.724901 2.525367 1.51303 2.737238
## Sep 2022 2.125134 1.724901 2.525367 1.51303 2.737238
## Oct 2022 2.125134 1.724901 2.525367 1.51303 2.737238
## Nov 2022 2.125134 1.724901 2.525367 1.51303 2.737238
## Dec 2022 2.125134 1.724901 2.525367 1.51303 2.737238
## Jan 2023 2.125134 1.724901 2.525367 1.51303 2.737238
## Feb 2023 2.125134 1.724901 2.525367 1.51303 2.737238
## Mar 2023 2.125134 1.724901 2.525367 1.51303 2.737238
## Apr 2023 2.125134 1.724901 2.525367 1.51303 2.737238
## May 2023 2.125134 1.724901 2.525367 1.51303 2.73723811.0.9 Choques
11.1 Change Points
Único Choque
## ints
## 2.114174
## Jan Feb Mar Apr May Jun Jul Aug
## 2019 2.144558 2.320669 2.363991 2.486471 2.502773 2.390995 2.283880 2.402042
## 2020 2.081333 2.127794 1.793405 1.152548 1.727204 1.887959 1.548418 1.808161
## 2021 2.068674 2.030732 1.664123 1.929501 2.125682 2.176482 2.268075
## Sep Oct Nov Dec
## 2019 2.425602 2.448309 2.441354 2.223925
## 2020 2.024949 2.249646 2.299580 2.140556
## 2021Variação da Média
mvalue = cpt.mean(mensal, method="BinSeg")## numeric(0)
Variação da variância
mvalue = cpt.meanvar(mensal, method="BinSeg")## [1] 12
11.1.1 Referências
Daniel Barry and J. A. Hartigan (1993), A Bayesian Analysis for Change Point Problems, Journal of The American Statistical Association, 88, 309-19.
Change in Normal mean: Hinkley, D. V. (1970) Inference About the Change-Point in a Sequence of Random Variables, Biometrika 57, 1–17
CUSUM Test: M. Csorgo, L. Horvath (1997) Limit Theorems in Change-Point Analysis, Wiley
PELT Algorithm: Killick R, Fearnhead P, Eckley IA (2012) Optimal detection of changepoints with a linear computational cost, JASA 107(500), 1590–1598
CROPS: Haynes K, Eckley IA, Fearnhead P (2014) Efficient penalty search for multiple changepoint problems (in submission), arXiv:1412.3617
Binary Segmentation: Scott, A. J. and Knott, M. (1974) A Cluster Analysis Method for Grouping Means in the Analysis of Variance, Biometrics 30(3), 507–512
Segment Neighbourhoods: Auger, I. E. And Lawrence, C. E. (1989) Algorithms for the Optimal Identification of Segment Neighborhoods, Bulletin of Mathematical Biology 51(1), 39–54
MBIC: Zhang, N. R. and Siegmund, D. O. (2007) A Modified Bayes Information Criterion with Applications to the Analysis of Comparative Genomic Hybridization Data. Biometrics 63, 22-32.
12 Apêndice
Autocorrelação é simplesmente a correlação entre uma série e ela mesma defasada. Ou seja, é a correlação entre os valores da série em um determinado período de tempo, e os valores da mesma série em um outro momento no tempo.
Um exemplo simples seria tomar os valores de um processo de Fevereiro a Dezembro de um ano e calcular a correlação desses valores com as realizações do mesmo processo de Janeiro a Novembro desse mesmo ano (comparar t com t-1). Essa é uma autocorrelação de defasagem igual a 1 (lag=1). Para defasagem 2 bastaria pular dois meses. Quando a série for aleatória, observaremos autocorrelações próximas de zero. No entanto, quando temos uma tendência ou uma sazonalidade, observamos uma tendência de queda ou picos positivos nos valores. Uma forma de analisar a autocorrelação é através de um correlograma. O correlograma é o gráfico utilizado em séries temporais para traçar as autocorrelações (também chamadas em inglês de ACF = autocorrelation function) em diversas defasagens. A análise desse gráfico permite entender se a série é aleatória ou possui alguma tendência ou sazonalidade. Para traçar esse gráfico no R, podemos utilizar a função ggACF() do pacote forecast. Vamos ver alguns exemplos e interpretá-los No gráfico abaixo, o eixo vertical indica a autocorrelação e o horizontal a defasagem. A linha tracejada azul indica onde é significativamente diferente de zero. Como é possível ver na imagem, praticamente todos os valores ACF estão dentro do limite da linha tracejada azul. Ou seja, autocorrelação igual a zero, indicando que a série é aleatória – conforme o esperado.
y <- ts(rnorm(50))
A série beer2 contém os dados trimestrais para a produção de cerveja na Austrália, iniciando no ano de 1992. Para cada linha você terá o valor de um trimestre. É possível observar aqui que o maior valor está em 4. Isso ocorre porque a série tem sazonalidade trimestral. Obviamente, os valores múltiplos de 4 também serão altos, mas vão diminuindo com o passar do tempo.
Na série beer é possível observar aqui que o maior valor está em 12. Isso ocorre porque a série tem comportamento cíclico.
Utilizando dados do varejo dos EUA como exemplo, podemos ver que o maior valor está em 12, além de valores positivos altos em múltiplos de 12. Isso porque a sazonalidade aqui é mensal. É possível observar inclusive um padrão sendo seguido a cada 12 defasagens. Os picos são causados pela sazonalidade, enquanto que o comportamento decrescente dos valores de autocorrelação ocorrem por conta de uma tendência nas vendas.
