# UNIVERSIDAD NACIONAL DEL ALTIPLANO
# INGENIERIA ESTADISTICA E INFORMATICA
# CURSO: SERIES DE TIEMPO
library(readxl)
## Warning: package 'readxl' was built under R version 4.0.2
preciopm <- read_excel("E:/SERIES DE TIEMPO/UNIDAD I/TAREA 01/preciopm.xls")
preciopm
## # A tibble: 352 x 1
## Precio
## <dbl>
## 1 14.9
## 2 13.9
## 3 12.3
## 4 10.9
## 5 10.5
## 6 9.82
## 7 13.2
## 8 20.8
## 9 26.2
## 10 25.5
## # ... with 342 more rows
attach(preciopm)
names(preciopm)
## [1] "Precio"
#file.choose()
#View(Arimar)
library(astsa)
## Warning: package 'astsa' was built under R version 4.0.5
library(tseries)
## Warning: package 'tseries' was built under R version 4.0.5
## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoo
library(lubridate)
## Warning: package 'lubridate' was built under R version 4.0.5
##
## Attaching package: 'lubridate'
## The following objects are masked from 'package:base':
##
## date, intersect, setdiff, union
library(tidyverse)
## Warning: package 'tidyverse' was built under R version 4.0.5
## -- Attaching packages --------------------------------------- tidyverse 1.3.1 --
## v ggplot2 3.3.5 v purrr 0.3.4
## v tibble 3.1.5 v dplyr 1.0.7
## v tidyr 1.1.4 v stringr 1.4.0
## v readr 2.0.2 v forcats 0.5.1
## Warning: package 'ggplot2' was built under R version 4.0.5
## Warning: package 'tibble' was built under R version 4.0.5
## Warning: package 'tidyr' was built under R version 4.0.5
## Warning: package 'readr' was built under R version 4.0.5
## Warning: package 'dplyr' was built under R version 4.0.5
## Warning: package 'forcats' was built under R version 4.0.5
## -- Conflicts ------------------------------------------ tidyverse_conflicts() --
## x lubridate::as.difftime() masks base::as.difftime()
## x lubridate::date() masks base::date()
## x dplyr::filter() masks stats::filter()
## x lubridate::intersect() masks base::intersect()
## x dplyr::lag() masks stats::lag()
## x lubridate::setdiff() masks base::setdiff()
## x lubridate::union() masks base::union()
library(forecast)
## Warning: package 'forecast' was built under R version 4.0.5
##
## Attaching package: 'forecast'
## The following object is masked from 'package:astsa':
##
## gas
#Series de Tiempo Univariadas
#Paso 1. Convertir a objeto de Serie de Tiempo en R
Arimar.ts=ts(preciopm, start=c(1993,1), frequency = 12)
print(Arimar.ts)
## Jan Feb Mar Apr May Jun
## 1993 14.897350 13.856284 12.298178 10.927095 10.452086 9.817348
## 1994 13.795437 10.845017 11.366329 12.068577 11.991099 11.930451
## 1995 10.079426 10.222971 10.928616 12.263161 13.882490 14.717433
## 1996 11.803837 12.505585 12.812625 12.873810 12.220930 11.106039
## 1997 10.227919 9.954569 10.307307 11.943946 12.818879 14.009499
## 1998 14.282580 14.800758 15.121214 16.031652 16.052267 14.611588
## 1999 14.640357 15.096147 16.682205 17.461726 16.069193 15.561163
## 2000 18.060119 15.709637 14.482912 14.259241 14.834376 13.795084
## 2001 9.713509 8.882054 7.631504 9.058311 9.082049 8.297230
## 2002 7.392438 7.126746 9.856138 12.350982 12.237096 13.074408
## 2003 21.348773 23.547154 22.935065 20.260149 23.193243 24.744170
## 2004 18.309991 18.799571 16.851520 16.360149 18.199624 18.789678
## 2005 14.032789 15.278664 19.405427 21.897267 21.987875 21.507413
## 2006 27.074817 27.012354 23.663690 20.458351 21.904876 23.570076
## 2007 25.316733 25.162286 26.962854 28.014928 30.823501 29.251947
## 2008 30.012074 32.092964 36.346343 38.118350 38.912862 43.204432
## 2009 47.779745 46.563260 49.381610 54.956204 55.260986 53.833091
## 2010 42.745920 47.033095 48.943810 52.898664 54.958534 58.682133
## 2011 78.879230 79.714309 87.177370 93.028973 102.884604 112.291047
## 2012 37.230832 37.848297 41.678599 47.490271 56.016166 63.641365
## 2013 70.866452 69.134714 70.093660 72.292077 66.101763 65.540751
## 2014 84.324640 89.161930 99.432700 106.104005 101.835090 100.828631
## 2015 107.455818 108.451418 109.604263 104.893764 100.233358 90.181843
## 2016 97.982782 103.352938 100.770902 97.755385 97.906861 96.993153
## 2017 88.310808 90.822240 91.395224 93.888630 95.086309 97.011046
## 2018 40.451272 45.986060 46.017331 49.325551 52.039105 52.825725
## 2019 23.102382 23.729330 28.326563 31.335818 36.726361 39.807146
## 2020 44.500081 44.174971 41.932428 43.221180 43.850742 41.151050
## 2021 57.453995 56.156762 57.224584 58.159732 62.899289 64.636865
## 2022 54.056660 57.379810 59.464492 62.077030
## Jul Aug Sep Oct Nov Dec
## 1993 13.188972 20.825314 26.238379 25.461774 23.590050 19.221472
## 1994 12.852894 12.724638 13.357160 14.094443 11.643019 10.081917
## 1995 14.694666 14.592165 15.002168 15.047736 13.499847 11.999895
## 1996 11.024373 11.150484 11.278000 11.218994 9.715306 9.101101
## 1997 14.525943 12.763118 12.527938 13.827166 14.100563 13.831668
## 1998 13.256370 13.449261 13.363175 12.991089 13.580205 15.116482
## 1999 15.978825 17.149939 19.308046 20.562573 18.913614 19.316873
## 2000 14.158890 14.821528 14.748565 15.700761 14.316305 11.438379
## 2001 8.804921 8.239905 9.465377 9.128815 7.865962 6.349166
## 2002 15.319650 17.430406 19.077463 18.434955 19.961135 20.140117
## 2003 22.778127 24.355191 25.822586 25.011949 24.065706 17.812948
## 2004 18.433045 19.274814 19.325549 15.571857 13.259511 13.662242
## 2005 22.389223 23.253909 24.514419 22.826465 20.001942 23.282675
## 2006 24.909283 25.174429 22.513946 24.135865 24.170211 24.437509
## 2007 30.770350 32.403355 33.356997 37.293723 30.656835 26.902246
## 2008 44.357927 47.831527 48.880013 45.437368 41.707053 42.989153
## 2009 56.818337 57.866679 49.690903 46.744199 45.794018 47.642082
## 2010 63.212159 62.190669 66.439359 71.018809 78.145548 77.690069
## 2011 118.026634 105.209472 83.841054 58.685407 40.592316 32.916936
## 2012 60.191980 66.404843 64.108802 67.933160 71.534239 68.493029
## 2013 66.923774 68.245485 68.332474 72.942531 75.758392 80.208666
## 2014 102.599593 96.988597 97.634395 99.366005 105.806100 105.126973
## 2015 94.012683 99.512167 100.076628 97.108629 93.682388 94.939944
## 2016 99.672555 99.244140 98.145716 93.873293 88.485898 89.409659
## 2017 93.320166 89.507449 84.128243 72.509358 63.479800 50.181375
## 2018 45.165949 38.419266 36.290362 34.860768 32.508829 26.196096
## 2019 37.971526 37.740903 36.826661 40.668356 38.361623 42.325962
## 2020 43.877714 45.554842 48.162370 48.891135 53.345048 54.055756
## 2021 66.421619 64.265666 68.363482 71.153304 59.825830 51.868669
## 2022
class(Arimar.ts)
## [1] "ts"
start(Arimar.ts)
## [1] 1993 1
end(Arimar.ts)
## [1] 2022 4
plot(Arimar.ts, main="Serie de tiempo", ylab="Precio", col="red")
serielog=log(Arimar.ts)
serielog
## Jan Feb Mar Apr May Jun Jul Aug
## 1993 2.701183 2.628739 2.509451 2.391245 2.346802 2.284151 2.579381 3.036169
## 1994 2.624338 2.383706 2.430655 2.490605 2.484165 2.479094 2.553569 2.543540
## 1995 2.310496 2.324637 2.391385 2.506600 2.630628 2.689033 2.687485 2.680485
## 1996 2.468425 2.526175 2.550431 2.555195 2.503150 2.407489 2.400109 2.411483
## 1997 2.325121 2.298032 2.332853 2.480225 2.550919 2.639736 2.675936 2.546560
## 1998 2.659041 2.694678 2.716099 2.774565 2.775850 2.681815 2.584478 2.598924
## 1999 2.683782 2.714440 2.814343 2.860011 2.776904 2.744778 2.771264 2.841995
## 2000 2.893706 2.754274 2.672969 2.657405 2.696947 2.624312 2.650343 2.696081
## 2001 2.273518 2.184033 2.032285 2.203683 2.206300 2.115922 2.175311 2.108989
## 2002 2.000458 1.963855 2.288094 2.513736 2.504472 2.570657 2.729136 2.858216
## 2003 3.060994 3.159005 3.132667 3.008656 3.143861 3.208590 3.125801 3.192745
## 2004 2.907447 2.933834 2.824441 2.794848 2.901401 2.933308 2.914145 2.958799
## 2005 2.641397 2.726457 2.965553 3.086362 3.090491 3.068398 3.108580 3.146473
## 2006 3.298604 3.296294 3.163942 3.018391 3.086709 3.159978 3.215241 3.225829
## 2007 3.231466 3.225346 3.294460 3.332738 3.428277 3.375946 3.426552 3.478262
## 2008 3.401600 3.468637 3.593094 3.640696 3.661325 3.765943 3.792291 3.867685
## 2009 3.866602 3.840812 3.899578 4.006537 4.012067 3.985888 4.039859 4.058142
## 2010 3.755274 3.850852 3.890673 3.968378 4.006579 4.072135 4.146497 4.130205
## 2011 4.367918 4.378449 4.467945 4.532911 4.633608 4.721094 4.770910 4.655953
## 2012 3.617137 3.633586 3.729988 3.860525 4.025640 4.153264 4.097539 4.195770
## 2013 4.260797 4.236057 4.249832 4.280715 4.191195 4.182672 4.203554 4.223111
## 2014 4.434674 4.490454 4.599481 4.664420 4.623355 4.613422 4.630834 4.574593
## 2015 4.677080 4.686302 4.696876 4.652948 4.607501 4.501828 4.543430 4.600280
## 2016 4.584792 4.638150 4.612850 4.582468 4.584017 4.574640 4.601890 4.597583
## 2017 4.480862 4.508904 4.515193 4.542109 4.554785 4.574825 4.536036 4.494322
## 2018 3.700098 3.828338 3.829018 3.898442 3.951995 3.966998 3.810343 3.648559
## 2019 3.139936 3.166712 3.343800 3.444762 3.603495 3.684046 3.636837 3.630744
## 2020 3.795491 3.788158 3.736059 3.766331 3.780792 3.717249 3.781407 3.818917
## 2021 4.050985 4.028147 4.046984 4.063193 4.141535 4.168785 4.196023 4.163026
## 2022 3.990033 4.049692 4.085379 4.128376
## Sep Oct Nov Dec
## 1993 3.267223 3.237178 3.160825 2.956028
## 1994 2.592053 2.645781 2.454707 2.310743
## 1995 2.708195 2.711228 2.602678 2.484898
## 1996 2.422854 2.417608 2.273703 2.208395
## 1997 2.527961 2.626635 2.646215 2.626961
## 1998 2.592503 2.564264 2.608613 2.715786
## 1999 2.960522 3.023473 2.939882 2.960979
## 2000 2.691146 2.753709 2.661399 2.436974
## 2001 2.247641 2.211436 2.062545 1.848323
## 2002 2.948508 2.914249 2.993787 3.002714
## 2003 3.251250 3.219354 3.180788 2.879926
## 2004 2.961428 2.745465 2.584715 2.614636
## 2005 3.199261 3.127921 2.995829 3.147710
## 2006 3.114135 3.183699 3.185121 3.196119
## 2007 3.507268 3.618825 3.422856 3.292210
## 2008 3.889369 3.816335 3.730670 3.760948
## 2009 3.905822 3.844690 3.824153 3.863716
## 2010 4.196290 4.262945 4.358573 4.352727
## 2011 4.428923 4.072191 3.703579 3.493987
## 2012 4.160582 4.218524 4.270176 4.226732
## 2013 4.224385 4.289672 4.327549 4.384632
## 2014 4.581230 4.598810 4.661608 4.655169
## 2015 4.605936 4.575830 4.539910 4.553245
## 2016 4.586453 4.541946 4.482843 4.493229
## 2017 4.432342 4.283716 4.150722 3.915644
## 2018 3.591552 3.551362 3.481512 3.265610
## 2019 3.606222 3.705450 3.647058 3.745401
## 2020 3.874578 3.889596 3.976781 3.990016
## 2021 4.224839 4.264837 4.091438 3.948715
## 2022
plot(serielog)
#Stationarity: To know the number of differences that are required to achieve that the series
#be stationary
ndiffs(Arimar.ts)
## [1] 1
#Paso 2.Prueba de DickeyFuller
adf.test(Arimar.ts)
##
## Augmented Dickey-Fuller Test
##
## data: Arimar.ts
## Dickey-Fuller = -2.2091, Lag order = 7, p-value = 0.4886
## alternative hypothesis: stationary
seriedif=diff(Arimar.ts)
plot(seriedif)
acf(seriedif)
ndiffs(seriedif)
## [1] 0
adf.test(seriedif)
## Warning in adf.test(seriedif): p-value smaller than printed p-value
##
## Augmented Dickey-Fuller Test
##
## data: seriedif
## Dickey-Fuller = -7.452, Lag order = 7, p-value = 0.01
## alternative hypothesis: stationary
#Prueba de Dickey Fuller con dos diferencias
seriedif2=diff(Arimar.ts, differences =2)
plot(seriedif2)
adf.test(seriedif2)
## Warning in adf.test(seriedif2): p-value smaller than printed p-value
##
## Augmented Dickey-Fuller Test
##
## data: seriedif2
## Dickey-Fuller = -11.192, Lag order = 7, p-value = 0.01
## alternative hypothesis: stationary
#Paso 4: Analisis visual de as graficas
plot(seriedif2, type="o", lty="dashed",main="Serie de Tiempo",col="red")
par(mfrow=c(2,1), mar=c(2,2,2,1)+.1)
acf(seriedif2)
pacf(seriedif2)
acf(ts(seriedif2, frequency=1))
pacf(ts(seriedif2, frequency=1))
#Modelo Arima
modelo1=arima(Arimar.ts,order=c(1,2,1))
summary(modelo1)
##
## Call:
## arima(x = Arimar.ts, order = c(1, 2, 1))
##
## Coefficients:
## ar1 ma1
## 0.5335 -1.0000
## s.e. 0.0454 0.0077
##
## sigma^2 estimated as 10.76: log likelihood = -914.68, aic = 1835.36
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set 0.03286225 3.270376 2.232341 0.2781591 6.525319 0.8900024
## ACF1
## Training set 0.0383441
tsdiag(modelo1)
Box.test(residuals(modelo1),type="Ljung-Box")
##
## Box-Ljung test
##
## data: residuals(modelo1)
## X-squared = 0.52196, df = 1, p-value = 0.47
error=residuals(modelo1)
plot(error)
#Pronosticos Arima
pronostico=forecast::forecast(modelo1,h=10)
pronostico
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## May 2022 63.53557 59.32651 67.74463 57.09837 69.97277
## Jun 2022 64.37841 56.66265 72.09417 52.57817 76.17865
## Jul 2022 64.89276 54.00425 75.78128 48.24021 81.54531
## Aug 2022 65.23185 51.51413 78.94958 44.25240 86.21131
## Sep 2022 65.47744 49.22923 81.72564 40.62795 90.32692
## Oct 2022 65.67313 47.14035 84.20591 37.32969 94.01658
## Nov 2022 65.84221 45.22406 86.46035 34.30948 97.37494
## Dec 2022 65.99708 43.45509 88.53908 31.52208 100.47209
## Jan 2023 66.14438 41.81057 90.47820 28.92903 103.35974
## Feb 2023 66.28764 40.27120 92.30408 26.49893 106.07635
plot(pronostico)
