Actividad 2 - Series de Tiempo
Zujel Enrique Romero Pérez
2024-08-20
#SERIE DE TIEMPO ECONÓMICA
Para el desarrollo de la actividad utilizaremos la serie económica “Reservas Internacionales Brutas - Banco de La República” que fue utilizada en la primera actividad.
## Jan Feb Mar Apr May Jun Jul Aug Sep
## 2014 46099.3 46712.1 47115.1
## 2015 47072.6 47060.3 46920.0 47179.9 47012.7 46981.6 46852.8 46710.2 46732.6
## 2016 46740.5 46852.9 47228.6 47297.8 47538.5 47029.6 47096.7 47043.1 47113.0
## 2017 46989.3 46992.3 46937.4 46941.8 47159.3 47242.5 47540.7 47577.2 47524.6
## 2018 47791.1 47642.5 47614.4 47510.7 47607.0 47497.2 47526.2 47543.5 47520.0
## 2019 49217.2 50503.4 51267.3 51528.3 51978.8 52449.3 52372.4 52998.6 52874.6
## 2020 53469.7 53681.6 53340.7 53868.1 56367.6 56629.2 56978.8 57193.1 56987.1
## 2021 59010.3 58982.0 58908.7 59094.6 59152.9 58925.5 58885.6 58854.4 58730.2
## 2022 58272.9 58289.2 58010.3 57480.5 57634.7 57170.9 57359.7 56989.5 56339.9
## 2023 57802.6 57388.6 57990.1 58058.0 57721.3 57866.2 58152.5 57961.8 57595.4
## 2024 59697.1 59480.3 60023.6 59847.0 60600.5 60931.5
## Oct Nov Dec
## 2014 47373.3 47388.6 47328.1
## 2015 46833.8 46766.4 46740.4
## 2016 46974.3 46751.1 46682.8
## 2017 47416.9 47403.9 47637.2
## 2018 47505.6 47761.2 48401.5
## 2019 53090.5 52957.9 53174.2
## 2020 56928.1 57254.4 59039.3
## 2021 58800.2 58540.2 58587.8
## 2022 56398.9 56991.7 57290.1
## 2023 57488.2 58609.4 59639.2
## 2024## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 46099 47239 52411 52468 57742 60932#FORMULACIÓN DEL MODELO
Para la formulación del modelo se probaron varios valores y combinaciones para las variables de suavización, sin embargo al final se determinó que las que mejor proporcionaban un ajuste del modelo era la optimizada por la función Holtwinters, en este caso no se le pasa a dicha función los argumentos de alpha, beta y gamma dejando a R que trate de buscar la mejor combinacion para dichas constantes.
#alpha <- 0.1
#beta <- 0.2
#gamma <- 0.3
modelholwin <- HoltWinters(reserv_intern_brut_col, seasonal = "multiplicative")
modelholwin## Holt-Winters exponential smoothing with trend and multiplicative seasonal component.
##
## Call:
## HoltWinters(x = reserv_intern_brut_col, seasonal = "multiplicative")
##
## Smoothing parameters:
## alpha: 0.8502186
## beta : 0.1833861
## gamma: 1
##
## Coefficients:
## [,1]
## a 6.070654e+04
## b 2.627820e+02
## s1 1.001776e+00
## s2 9.978404e-01
## s3 9.934207e-01
## s4 9.953627e-01
## s5 1.000440e+00
## s6 1.004025e+00
## s7 1.001939e+00
## s8 9.999714e-01
## s9 1.001952e+00
## s10 9.994722e-01
## s11 1.005799e+00
## s12 1.003706e+00modelholwin$fitted## xhat level trend season
## Jul 2015 47074.51 47075.78 -17.757998 1.0003506
## Aug 2015 46713.53 46869.58 -52.315239 0.9977843
## Sep 2015 46676.16 46814.43 -52.835166 0.9981729
## Oct 2015 46763.57 46809.67 -44.018391 0.9999554
## Nov 2015 46696.17 46825.37 -33.066988 0.9979455
## Dec 2015 46684.06 46852.14 -22.093977 0.9968827
## Jan 2016 46940.75 46878.09 -13.282201 1.0016203
## Feb 2016 46682.69 46694.83 -44.453996 1.0006926
## Mar 2016 46685.79 46795.00 -17.933033 0.9980487
## Apr 2016 47514.34 47239.47 66.866554 1.0043969
## May 2016 47244.41 47123.04 33.251253 1.0018686
## Jun 2016 47593.22 47405.87 79.020219 1.0022814
## Jul 2016 46981.30 47006.78 -8.658006 0.9996420
## Aug 2016 47000.74 47096.27 9.341889 0.9977736
## Sep 2016 47080.03 47141.71 15.961340 0.9983536
## Oct 2016 47215.36 47185.75 21.110478 1.0001801
## Nov 2016 46899.49 47001.94 -16.468517 0.9981700
## Dec 2016 46681.91 46859.08 -39.648191 0.9970627
## Jan 2017 46826.43 46820.19 -39.508542 1.0009780
## Feb 2017 46962.92 46919.02 -14.139391 1.0012374
## Mar 2017 46909.46 46929.83 -9.563965 0.9997698
## Apr 2017 47112.89 46944.02 -5.207348 1.0037087
## May 2017 46892.93 46793.88 -31.785480 1.0027979
## Jun 2017 47020.39 46987.94 9.630213 1.0004855
## Jul 2017 47231.00 47186.32 44.245153 1.0000091
## Aug 2017 47486.87 47493.88 92.533295 0.9979082
## Sep 2017 47696.37 47663.37 106.646305 0.9984582
## Oct 2017 47675.52 47623.75 79.823172 0.9994119
## Nov 2017 47413.53 47483.56 39.475803 0.9976957
## Dec 2017 47413.26 47514.83 37.970473 0.9970656
## Jan 2018 47888.37 47743.76 72.989386 1.0014979
## Feb 2018 47855.63 47734.17 57.845350 1.0013312
## Mar 2018 47628.98 47611.05 24.658438 0.9998589
## Apr 2018 47796.29 47623.30 22.384108 1.0031610
## May 2018 47554.43 47403.63 -22.004938 1.0036469
## Jun 2018 47468.77 47426.17 -13.837600 1.0011905
## Jul 2018 47473.81 47436.47 -9.410756 1.0009858
## Aug 2018 47384.48 47471.56 -1.250029 0.9981921
## Sep 2018 47530.17 47605.75 23.588598 0.9979180
## Oct 2018 47575.78 47620.67 21.998890 0.9985961
## Nov 2018 47482.84 47582.91 11.040671 0.9976653
## Dec 2018 47778.84 47831.18 54.543598 0.9977681
## Jan 2019 48626.07 48416.30 151.844133 1.0011927
## Feb 2019 49346.62 49070.13 243.902557 1.0006607
## Mar 2019 50711.57 50296.91 424.147248 0.9998131
## Apr 2019 51821.22 51193.63 510.811515 1.0022586
## May 2019 52119.17 51455.96 465.242325 1.0038130
## Jun 2019 52312.63 51802.30 443.438860 1.0012803
## Jul 2019 52887.32 52361.79 464.720440 1.0011511
## Aug 2019 52704.74 52389.22 384.527492 0.9986924
## Sep 2019 53341.32 53023.92 430.405646 0.9978860
## Oct 2019 53327.36 53056.67 357.480774 0.9983752
## Nov 2019 53454.61 53212.44 320.489837 0.9985370
## Dec 2019 53336.62 53110.00 242.929973 0.9996944
## Jan 2020 53592.53 53214.79 217.597830 1.0029971
## Feb 2020 53746.53 53328.27 198.503713 1.0041055
## Mar 2020 53737.44 53471.80 188.421814 1.0014390
## Apr 2020 53525.19 53323.39 126.652296 1.0014059
## May 2020 54104.94 53741.18 180.043000 1.0034071
## Jun 2020 56464.29 55838.45 531.635161 1.0016712
## Jul 2020 57049.04 56510.06 557.304554 0.9996789
## Aug 2020 57526.49 57007.62 546.349444 0.9995225
## Sep 2020 57566.50 57270.38 494.343086 0.9965684
## Oct 2020 57541.94 57270.41 403.692611 0.9977084
## Nov 2020 57294.22 57151.01 307.763617 0.9971362
## Dec 2020 57682.32 57424.82 301.537216 0.9992372
## Jan 2021 59551.76 58880.96 513.276291 1.0026521
## Feb 2021 59597.10 58935.10 429.076446 1.0039236
## Mar 2021 59196.01 58843.25 333.546088 1.0003246
## Apr 2021 59361.23 58932.60 288.764233 1.0023617
## May 2021 59803.91 58995.21 247.289937 1.0094765
## Jun 2021 58964.99 58694.19 146.738589 1.0021083
## Jul 2021 58918.22 58807.43 140.594374 0.9994944
## Aug 2021 58976.09 58920.28 135.506081 0.9986505
## Sep 2021 58776.48 58952.18 116.506844 0.9950531
## Oct 2021 58907.74 59029.14 109.255216 0.9960997
## Nov 2021 58963.52 59046.61 92.421832 0.9970323
## Dec 2021 58962.39 58778.04 26.221336 1.0026891
## Jan 2022 58529.19 58486.63 -32.027708 1.0012760
## Feb 2022 58302.19 58236.98 -71.937066 1.0023579
## Mar 2022 58056.51 58154.02 -73.957739 0.9995944
## Apr 2022 58057.24 58040.76 -81.165217 1.0016847
## May 2022 57746.93 57470.06 -170.938806 1.0078152
## Jun 2022 57130.62 57204.45 -188.301444 1.0020078
## Jul 2022 56834.82 57050.32 -182.033642 0.9994115
## Aug 2022 57119.77 57314.82 -100.147176 0.9983414
## Sep 2022 56694.65 57103.73 -120.492241 0.9949356
## Oct 2022 56268.20 56680.08 -176.085950 0.9958269
## Nov 2022 56231.50 56615.59 -155.622049 0.9959536
## Dec 2022 57171.03 57108.92 -36.612119 1.0017298
## Jan 2023 57190.54 57173.37 -18.079564 1.0006168
## Feb 2023 57886.89 57675.35 77.292394 1.0023245
## Mar 2023 57299.66 57329.97 -0.219457 0.9994752
## Apr 2023 58035.11 57917.08 107.488769 1.0001816
## May 2023 58592.49 58044.03 111.057325 1.0075213
## Jun 2023 57517.46 57419.91 -23.763278 1.0021135
## Jul 2023 57767.73 57692.03 30.497204 1.0007831
## Aug 2023 58023.55 58049.41 90.442317 0.9979997
## Sep 2023 57818.92 58087.24 80.794757 0.9939982
## Oct 2023 57800.51 57976.85 45.732781 0.9961727
## Nov 2023 57634.34 57756.03 -3.148707 0.9979474
## Dec 2023 58852.71 58583.60 149.194301 1.0020417
## Jan 2024 59803.35 59400.12 271.572085 1.0022063
## Feb 2024 59897.79 59581.56 255.042600 1.0010226
## Mar 2024 59747.25 59482.00 190.014455 1.0012607
## Apr 2024 60154.20 59906.68 233.048566 1.0002407
## May 2024 60379.03 59878.60 185.161354 1.0052488
## Jun 2024 60653.15 60251.08 219.512795 1.0030189#Suavizacuion Holwinters#VALORES REALES VS VALORES AJUSTADOS
Se puede nbotar graficamente un ajuste suave de los valores ajustados a los valores reales dispuestos en la serie de tiempo.
#ERROR CUADRADO Y RAIZ DEL ERROR CUADRADO
En este caso se logró un mejor modelo mediante la herramienta Excel y su optimización mediante el Add-in Solver:
## [1] 190272.4## [1] 436.2023## Modelo Multiplicativo en R - ECM: 190272.4 RMSE: 436.2023## En el modelo construido en Excel y utilizando la herramienta Solver:## Modelo Multiplicativo en Excel - ECM: 17334, RMSE: 131.66 ,#PRONOSTICOS
Utilizando la funcion predict de la libreria stats de R podemos utilizar el modelo para hacer predicciones de periodos futuros. en este caso hacemos una pronostico del año siguiente:
## fit upr lwr
## Jul 2024 61077.60 61935.91 60219.29
## Aug 2024 61099.87 62315.03 59884.71
## Sep 2024 61090.29 62656.87 59523.72
## Oct 2024 61471.28 63404.83 59537.74
## Nov 2024 62047.76 64367.55 59727.97
## Dec 2024 62533.92 65252.93 59814.90
## Jan 2025 62667.30 65785.74 59548.87
## Feb 2025 62807.00 66338.19 59275.81
## Mar 2025 63194.67 67166.46 59222.89
## Apr 2025 63300.93 67710.08 58891.79
## May 2025 63965.97 68866.01 59065.92
## Jun 2025 64096.57 69393.55 58799.59El gráfico nos muestra las lineas de predicción a un intervalo de confianza del 95%
