# UNIVERSIDAD NACIONAL DEL ALTIPLANO
# INGENIERIA ESTADISTICA E INFORMATICA
# CURSO: SERIES DE TIEMPO
library(readxl)
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library(lubridate)
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library(tidyverse)
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library(car)
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library(tseries)
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library(astsa)
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library(foreign)
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library(timsac)
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library(vars)
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library(lmtest)
library(mFilter)
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library(dynlm)
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library(nlme)
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library(broom)
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library(kableExtra)
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library(knitr)
library(MASS)
library(parallel)
library(car)
library(mlogit)
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library(dplyr)
library(tidyr)
library(forecast)
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library(fpp2)
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library(stats)
library(quantmod)
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## Loading required package: TTR
preciopm <- read_excel("E:\\SERIES DE TIEMPO\\TAREA 04\\preciopm.xls")
# View(preciopm)
attach(preciopm)
names(preciopm)
## [1] "Precio"
precio.ts <- ts(preciopm, start = c(1990,1),end = c(2019,4), frequency = 12)
print(precio.ts)
## Jan Feb Mar Apr May Jun
## 1990 14.897350 13.856284 12.298178 10.927095 10.452086 9.817348
## 1991 13.795437 10.845017 11.366329 12.068577 11.991099 11.930451
## 1992 10.079426 10.222971 10.928616 12.263161 13.882490 14.717433
## 1993 11.803837 12.505585 12.812625 12.873810 12.220930 11.106039
## 1994 10.227919 9.954569 10.307307 11.943946 12.818879 14.009499
## 1995 14.282580 14.800758 15.121214 16.031652 16.052267 14.611588
## 1996 14.640357 15.096147 16.682205 17.461726 16.069193 15.561163
## 1997 18.060119 15.709637 14.482912 14.259241 14.834376 13.795084
## 1998 9.713509 8.882054 7.631504 9.058311 9.082049 8.297230
## 1999 7.392438 7.126746 9.856138 12.350982 12.237096 13.074408
## 2000 21.348773 23.547154 22.935065 20.260149 23.193243 24.744170
## 2001 18.309991 18.799571 16.851520 16.360149 18.199624 18.789678
## 2002 14.032789 15.278664 19.405427 21.897267 21.987875 21.507413
## 2003 27.074817 27.012354 23.663690 20.458351 21.904876 23.570076
## 2004 25.316733 25.162286 26.962854 28.014928 30.823501 29.251947
## 2005 30.012074 32.092964 36.346343 38.118350 38.912862 43.204432
## 2006 47.779745 46.563260 49.381610 54.956204 55.260986 53.833091
## 2007 42.745920 47.033095 48.943810 52.898664 54.958534 58.682133
## 2008 78.879230 79.714309 87.177370 93.028973 102.884604 112.291047
## 2009 37.230832 37.848297 41.678599 47.490271 56.016166 63.641365
## 2010 70.866452 69.134714 70.093660 72.292077 66.101763 65.540751
## 2011 84.324640 89.161930 99.432700 106.104005 101.835090 100.828631
## 2012 107.455818 108.451418 109.604263 104.893764 100.233358 90.181843
## 2013 97.982782 103.352938 100.770902 97.755385 97.906861 96.993153
## 2014 88.310808 90.822240 91.395224 93.888630 95.086309 97.011046
## 2015 40.451272 45.986060 46.017331 49.325551 52.039105 52.825725
## 2016 23.102382 23.729330 28.326563 31.335818 36.726361 39.807146
## 2017 44.500081 44.174971 41.932428 43.221180 43.850742 41.151050
## 2018 57.453995 56.156762 57.224584 58.159732 62.899289 64.636865
## 2019 54.056660 57.379810 59.464492 62.077030
## Jul Aug Sep Oct Nov Dec
## 1990 13.188972 20.825314 26.238379 25.461774 23.590050 19.221472
## 1991 12.852894 12.724638 13.357160 14.094443 11.643019 10.081917
## 1992 14.694666 14.592165 15.002168 15.047736 13.499847 11.999895
## 1993 11.024373 11.150484 11.278000 11.218994 9.715306 9.101101
## 1994 14.525943 12.763118 12.527938 13.827166 14.100563 13.831668
## 1995 13.256370 13.449261 13.363175 12.991089 13.580205 15.116482
## 1996 15.978825 17.149939 19.308046 20.562573 18.913614 19.316873
## 1997 14.158890 14.821528 14.748565 15.700761 14.316305 11.438379
## 1998 8.804921 8.239905 9.465377 9.128815 7.865962 6.349166
## 1999 15.319650 17.430406 19.077463 18.434955 19.961135 20.140117
## 2000 22.778127 24.355191 25.822586 25.011949 24.065706 17.812948
## 2001 18.433045 19.274814 19.325549 15.571857 13.259511 13.662242
## 2002 22.389223 23.253909 24.514419 22.826465 20.001942 23.282675
## 2003 24.909283 25.174429 22.513946 24.135865 24.170211 24.437509
## 2004 30.770350 32.403355 33.356997 37.293723 30.656835 26.902246
## 2005 44.357927 47.831527 48.880013 45.437368 41.707053 42.989153
## 2006 56.818337 57.866679 49.690903 46.744199 45.794018 47.642082
## 2007 63.212159 62.190669 66.439359 71.018809 78.145548 77.690069
## 2008 118.026634 105.209472 83.841054 58.685407 40.592316 32.916936
## 2009 60.191980 66.404843 64.108802 67.933160 71.534239 68.493029
## 2010 66.923774 68.245485 68.332474 72.942531 75.758392 80.208666
## 2011 102.599593 96.988597 97.634395 99.366005 105.806100 105.126973
## 2012 94.012683 99.512167 100.076628 97.108629 93.682388 94.939944
## 2013 99.672555 99.244140 98.145716 93.873293 88.485898 89.409659
## 2014 93.320166 89.507449 84.128243 72.509358 63.479800 50.181375
## 2015 45.165949 38.419266 36.290362 34.860768 32.508829 26.196096
## 2016 37.971526 37.740903 36.826661 40.668356 38.361623 42.325962
## 2017 43.877714 45.554842 48.162370 48.891135 53.345048 54.055756
## 2018 66.421619 64.265666 68.363482 71.153304 59.825830 51.868669
## 2019
start(precio.ts);end(precio.ts)
## [1] 1990 1
## [1] 2019 4
boxplot(precio.ts ~ cycle(precio.ts))
cycle(precio.ts)
## Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
## 1990 1 2 3 4 5 6 7 8 9 10 11 12
## 1991 1 2 3 4 5 6 7 8 9 10 11 12
## 1992 1 2 3 4 5 6 7 8 9 10 11 12
## 1993 1 2 3 4 5 6 7 8 9 10 11 12
## 1994 1 2 3 4 5 6 7 8 9 10 11 12
## 1995 1 2 3 4 5 6 7 8 9 10 11 12
## 1996 1 2 3 4 5 6 7 8 9 10 11 12
## 1997 1 2 3 4 5 6 7 8 9 10 11 12
## 1998 1 2 3 4 5 6 7 8 9 10 11 12
## 1999 1 2 3 4 5 6 7 8 9 10 11 12
## 2000 1 2 3 4 5 6 7 8 9 10 11 12
## 2001 1 2 3 4 5 6 7 8 9 10 11 12
## 2002 1 2 3 4 5 6 7 8 9 10 11 12
## 2003 1 2 3 4 5 6 7 8 9 10 11 12
## 2004 1 2 3 4 5 6 7 8 9 10 11 12
## 2005 1 2 3 4 5 6 7 8 9 10 11 12
## 2006 1 2 3 4 5 6 7 8 9 10 11 12
## 2007 1 2 3 4 5 6 7 8 9 10 11 12
## 2008 1 2 3 4 5 6 7 8 9 10 11 12
## 2009 1 2 3 4 5 6 7 8 9 10 11 12
## 2010 1 2 3 4 5 6 7 8 9 10 11 12
## 2011 1 2 3 4 5 6 7 8 9 10 11 12
## 2012 1 2 3 4 5 6 7 8 9 10 11 12
## 2013 1 2 3 4 5 6 7 8 9 10 11 12
## 2014 1 2 3 4 5 6 7 8 9 10 11 12
## 2015 1 2 3 4 5 6 7 8 9 10 11 12
## 2016 1 2 3 4 5 6 7 8 9 10 11 12
## 2017 1 2 3 4 5 6 7 8 9 10 11 12
## 2018 1 2 3 4 5 6 7 8 9 10 11 12
## 2019 1 2 3 4
# Para Graficar la Serie de Tiempo
plot(precio.ts, ylab = "precio", main = "Precio del Petroleo Maya")
# Modelo Aditivo
modeloaditivo <- decompose(precio.ts)
plot(modeloaditivo)
# Modelo Multiplicativo
modelomultiplicativo <- decompose(precio.ts, type = "mult")
plot(modelomultiplicativo)
# Estimar Tendencia
tendencia <- modelomultiplicativo$trend
print(tendencia)
## Jan Feb Mar Apr May Jun
## 1990 NA NA NA NA NA NA
## 1991 16.696236 16.344704 15.470459 14.460103 13.488671 12.610063
## 1992 12.314088 12.468642 12.614998 12.723260 12.840348 12.997632
## 1993 13.027013 12.730681 12.432104 12.117399 11.800179 11.521707
## 1994 11.208430 11.421522 11.540796 11.701551 11.992943 12.372769
## 1995 14.320139 14.295830 14.359220 14.359185 14.302667 14.334520
## 1996 14.885717 15.153347 15.555245 16.118427 16.656130 17.053372
## 1997 16.788439 16.615591 16.328596 15.936042 15.541912 15.022087
## 1998 11.264342 10.767025 10.272658 9.778694 9.236099 8.755284
## 1999 9.595777 10.250161 11.033602 11.821862 12.713583 13.792172
## 2000 20.843460 21.442762 22.012342 22.567430 23.012495 23.086554
## 2001 20.415375 20.022647 19.540255 18.876208 18.032613 17.409409
## 2002 17.967879 18.298515 18.680513 19.198992 19.782202 20.463988
## 2003 23.434402 23.619426 23.616095 23.587300 23.815537 24.037332
## 2004 26.150335 26.695752 27.448751 28.448789 29.267309 29.640282
## 2005 34.738693 35.947683 37.237316 38.223426 39.023171 40.153884
## 2006 48.767345 49.704660 50.156579 50.244817 50.469558 50.833721
## 2007 51.084607 51.531183 52.409201 54.118496 56.477918 59.077898
## 2008 83.339949 87.416335 89.933856 90.145035 88.066425 84.636160
## 2009 57.855002 53.828365 51.389329 50.952474 52.627044 55.398628
## 2010 68.005114 68.362299 68.614979 68.999689 69.384419 70.048577
## 2011 85.994686 88.678808 91.097351 93.419242 95.772208 98.062459
## 2012 102.004056 101.751417 101.958325 101.966028 101.366816 100.437201
## 2013 98.077033 98.301693 98.210071 97.994810 97.643484 97.196535
## 2014 93.514110 92.843732 91.853975 90.379750 88.447665 85.771233
## 2015 59.641194 55.506094 51.384175 47.822238 44.963090 42.673246
## 2016 32.739305 32.411272 32.405353 32.669681 33.155531 34.071475
## 2017 41.306548 41.878220 42.676122 43.491059 44.457984 45.571035
## 2018 55.140837 56.859784 58.481115 60.250418 61.448041 61.626945
## 2019 NA NA NA NA
## Jul Aug Sep Oct Nov Dec
## 1990 16.685279 16.513896 16.349600 16.358334 16.470022 16.622193
## 1991 12.074415 11.893662 11.849506 11.839375 11.926291 12.121223
## 1992 13.149398 13.316358 13.489967 13.593911 13.550123 13.330417
## 1993 11.335260 11.163305 10.952624 10.809492 10.795662 10.941554
## 1994 12.738821 13.109689 13.512193 13.883094 14.188139 14.347951
## 1995 14.402961 14.430176 14.507525 14.632153 14.692445 14.732715
## 1996 17.370878 17.538931 17.472855 17.247781 17.062894 16.937856
## 1997 14.346041 13.713783 13.143825 12.641644 12.185258 11.716501
## 1998 8.446522 8.276673 8.296228 8.526116 8.794771 9.125280
## 1999 14.948308 16.214006 17.443145 18.317649 19.103704 20.046450
## 2000 22.862972 22.538541 22.087244 21.671263 21.300695 20.844524
## 2001 17.058246 16.733325 16.693033 17.030159 17.418716 17.689799
## 2002 21.408257 22.440578 23.106910 23.224383 23.160969 23.243455
## 2003 24.012197 23.861857 23.922236 24.374559 25.061026 25.669380
## 2004 29.938619 30.423036 31.102793 31.914748 32.672780 33.591191
## 2005 41.564492 42.907740 44.053806 45.298519 46.681268 47.805301
## 2006 50.817850 50.627684 50.629019 50.525046 50.426713 50.616154
## 2007 61.835452 64.702724 67.657506 70.922667 74.591683 78.822307
## 2008 81.035263 77.555496 73.915297 70.122069 66.271771 62.291849
## 2009 58.282450 60.987534 63.475096 65.692465 67.146107 67.645481
## 2010 71.097486 72.492711 74.549639 77.180929 80.078648 83.037865
## 2011 100.064521 101.832049 103.059592 103.432981 103.315815 102.805460
## 2012 99.618032 99.010886 98.430392 97.764903 97.370533 97.557400
## 2013 96.563108 95.637996 94.725231 94.173463 93.894825 93.778048
## 2014 82.142573 78.280252 74.521332 70.773792 67.123363 63.488675
## 2015 40.950989 39.300755 37.636276 36.149588 34.761985 33.581513
## 2016 35.635123 37.378596 38.797409 39.859543 40.651616 41.004461
## 2017 46.599523 47.638510 48.774925 50.034538 51.450667 53.222932
## 2018 61.394261 61.303665 61.447955 61.704506 NA NA
## 2019
# Estimar la Estacionalidad
estacionalidad <- modelomultiplicativo$seasonal
print(estacionalidad)
## Jan Feb Mar Apr May Jun Jul
## 1990 0.9230576 0.9264216 0.9568760 1.0005568 1.0322156 1.0402198 1.0421301
## 1991 0.9230576 0.9264216 0.9568760 1.0005568 1.0322156 1.0402198 1.0421301
## 1992 0.9230576 0.9264216 0.9568760 1.0005568 1.0322156 1.0402198 1.0421301
## 1993 0.9230576 0.9264216 0.9568760 1.0005568 1.0322156 1.0402198 1.0421301
## 1994 0.9230576 0.9264216 0.9568760 1.0005568 1.0322156 1.0402198 1.0421301
## 1995 0.9230576 0.9264216 0.9568760 1.0005568 1.0322156 1.0402198 1.0421301
## 1996 0.9230576 0.9264216 0.9568760 1.0005568 1.0322156 1.0402198 1.0421301
## 1997 0.9230576 0.9264216 0.9568760 1.0005568 1.0322156 1.0402198 1.0421301
## 1998 0.9230576 0.9264216 0.9568760 1.0005568 1.0322156 1.0402198 1.0421301
## 1999 0.9230576 0.9264216 0.9568760 1.0005568 1.0322156 1.0402198 1.0421301
## 2000 0.9230576 0.9264216 0.9568760 1.0005568 1.0322156 1.0402198 1.0421301
## 2001 0.9230576 0.9264216 0.9568760 1.0005568 1.0322156 1.0402198 1.0421301
## 2002 0.9230576 0.9264216 0.9568760 1.0005568 1.0322156 1.0402198 1.0421301
## 2003 0.9230576 0.9264216 0.9568760 1.0005568 1.0322156 1.0402198 1.0421301
## 2004 0.9230576 0.9264216 0.9568760 1.0005568 1.0322156 1.0402198 1.0421301
## 2005 0.9230576 0.9264216 0.9568760 1.0005568 1.0322156 1.0402198 1.0421301
## 2006 0.9230576 0.9264216 0.9568760 1.0005568 1.0322156 1.0402198 1.0421301
## 2007 0.9230576 0.9264216 0.9568760 1.0005568 1.0322156 1.0402198 1.0421301
## 2008 0.9230576 0.9264216 0.9568760 1.0005568 1.0322156 1.0402198 1.0421301
## 2009 0.9230576 0.9264216 0.9568760 1.0005568 1.0322156 1.0402198 1.0421301
## 2010 0.9230576 0.9264216 0.9568760 1.0005568 1.0322156 1.0402198 1.0421301
## 2011 0.9230576 0.9264216 0.9568760 1.0005568 1.0322156 1.0402198 1.0421301
## 2012 0.9230576 0.9264216 0.9568760 1.0005568 1.0322156 1.0402198 1.0421301
## 2013 0.9230576 0.9264216 0.9568760 1.0005568 1.0322156 1.0402198 1.0421301
## 2014 0.9230576 0.9264216 0.9568760 1.0005568 1.0322156 1.0402198 1.0421301
## 2015 0.9230576 0.9264216 0.9568760 1.0005568 1.0322156 1.0402198 1.0421301
## 2016 0.9230576 0.9264216 0.9568760 1.0005568 1.0322156 1.0402198 1.0421301
## 2017 0.9230576 0.9264216 0.9568760 1.0005568 1.0322156 1.0402198 1.0421301
## 2018 0.9230576 0.9264216 0.9568760 1.0005568 1.0322156 1.0402198 1.0421301
## 2019 0.9230576 0.9264216 0.9568760 1.0005568
## Aug Sep Oct Nov Dec
## 1990 1.0577040 1.0672579 1.0489735 0.9801718 0.9244152
## 1991 1.0577040 1.0672579 1.0489735 0.9801718 0.9244152
## 1992 1.0577040 1.0672579 1.0489735 0.9801718 0.9244152
## 1993 1.0577040 1.0672579 1.0489735 0.9801718 0.9244152
## 1994 1.0577040 1.0672579 1.0489735 0.9801718 0.9244152
## 1995 1.0577040 1.0672579 1.0489735 0.9801718 0.9244152
## 1996 1.0577040 1.0672579 1.0489735 0.9801718 0.9244152
## 1997 1.0577040 1.0672579 1.0489735 0.9801718 0.9244152
## 1998 1.0577040 1.0672579 1.0489735 0.9801718 0.9244152
## 1999 1.0577040 1.0672579 1.0489735 0.9801718 0.9244152
## 2000 1.0577040 1.0672579 1.0489735 0.9801718 0.9244152
## 2001 1.0577040 1.0672579 1.0489735 0.9801718 0.9244152
## 2002 1.0577040 1.0672579 1.0489735 0.9801718 0.9244152
## 2003 1.0577040 1.0672579 1.0489735 0.9801718 0.9244152
## 2004 1.0577040 1.0672579 1.0489735 0.9801718 0.9244152
## 2005 1.0577040 1.0672579 1.0489735 0.9801718 0.9244152
## 2006 1.0577040 1.0672579 1.0489735 0.9801718 0.9244152
## 2007 1.0577040 1.0672579 1.0489735 0.9801718 0.9244152
## 2008 1.0577040 1.0672579 1.0489735 0.9801718 0.9244152
## 2009 1.0577040 1.0672579 1.0489735 0.9801718 0.9244152
## 2010 1.0577040 1.0672579 1.0489735 0.9801718 0.9244152
## 2011 1.0577040 1.0672579 1.0489735 0.9801718 0.9244152
## 2012 1.0577040 1.0672579 1.0489735 0.9801718 0.9244152
## 2013 1.0577040 1.0672579 1.0489735 0.9801718 0.9244152
## 2014 1.0577040 1.0672579 1.0489735 0.9801718 0.9244152
## 2015 1.0577040 1.0672579 1.0489735 0.9801718 0.9244152
## 2016 1.0577040 1.0672579 1.0489735 0.9801718 0.9244152
## 2017 1.0577040 1.0672579 1.0489735 0.9801718 0.9244152
## 2018 1.0577040 1.0672579 1.0489735 0.9801718 0.9244152
## 2019
ts.plot(cbind(tendencia,tendencia*estacionalidad), lty = 1:2)
