#Librerias
library(tidyverse)
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## ✔ tidyr 1.2.0 ✔ stringr 1.4.1
## ✔ readr 2.1.2 ✔ forcats 0.5.2
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library(ggplot2)
library(scatterplot3d)
library(plotly)
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## layout
#Cargar Datos y convertirlos a serie de tiempo
potential_gdp=read.csv("C:/Users/zacar/OneDrive/Documents/UABC/Semestre 1/MicroAplicada/Tarea 1/Datos2/potential_gdp.csv")
real_gdp=read.csv("C:/Users/zacar/OneDrive/Documents/UABC/Semestre 1/MicroAplicada/Tarea 1/Datos2/real_gdp.csv")
potential_gdp_data=data.frame(potential_gdp)
real_gdp_data=data.frame(real_gdp)
potential_gdp_data=ts(potential_gdp_data, frequency = 4,start=c(1985,1))
real_gdp_data=ts(real_gdp_data,frequency = 4, start=c(1985,1))
consumer_price84=read.csv("C:/Users/zacar/OneDrive/Documents/UABC/Semestre 1/MicroAplicada/Tarea 1/Datos2/consumer_price84.csv")
consumer_price84_data=data.frame(consumer_price84)
consumer_price84_data=ts(consumer_price84_data,frequency = 4, start=c(1984,1))
interes_fedfunds=read.csv("C:/Users/zacar/OneDrive/Documents/UABC/Semestre 1/MicroAplicada/Tarea 1/Datos2/interes_fedfunds.csv")
interes_fedfunds_data=data.frame(interes_fedfunds)
interes_fedfunds_data=ts(interes_fedfunds_data,frequency = 4, start=c(1985,1))
persistencia=read.csv("C:/Users/zacar/OneDrive/Documents/UABC/Semestre 1/MicroAplicada/Tarea 1/Datos2/interes_fedfunds_84-4 al 07-3.csv")
persistencia=data.frame(persistencia)
persistencia = c((persistencia[,2]))
persistencia
## [1] 9.2625000 8.4751111 7.9243956 7.9009783 8.1044565 7.8268889 6.9184615
## [8] 6.2094565 6.2667391 6.2225556 6.6500000 6.8395652 6.9196739 6.6659341
## [15] 7.1549451 7.9834783 8.4684783 9.4464444 9.7257143 9.0835870 8.6144565
## [22] 8.2480000 8.2393407 8.1602174 7.7433696 6.4304444 5.8640659 5.6452174
## [29] 4.8184783 4.0242857 3.7740659 3.2592391 3.0348913 3.0423333 2.9972527
## [36] 3.0577174 2.9882609 3.2093333 3.9380220 4.4854348 5.1679348 5.8027778
## [43] 6.0191209 5.7971739 5.7194565 5.3709890 5.2439560 5.3061957 5.2808696
## [50] 5.2784444 5.5221978 5.5346739 5.5073913 5.5193333 5.4974725 5.5316304
## [57] 4.8605435 4.7345556 4.7476923 5.0955435 5.3040217 5.6776923 6.2719780
## [64] 6.5194565 6.4748913 5.5970000 4.3267033 3.5015217 2.1304348 1.7328889
## [71] 1.7515385 1.7408696 1.4442391 1.2496667 1.2467033 1.0168478 0.9967391
## [78] 1.0018681 1.0113187 1.4307609 1.9498913 2.4690000 2.9417582 3.4600000
## [85] 3.9782609 4.4541111 4.9075824 5.2453261 5.2429348 5.2545556 5.2524176
## [92] 5.0743478
##Obtener datos
#1.1 Logaritmo de Real y Potential GDP
#1.1.1 Potential
log_potential_gdp_data= log(potential_gdp_data[,2])
log_potential_gdp_data
## Qtr1 Qtr2 Qtr3 Qtr4
## 1985 8.984566 8.993396 9.002130 9.010733
## 1986 9.019189 9.027534 9.035787 9.043965
## 1987 9.052028 9.059994 9.067866 9.075706
## 1988 9.083443 9.091149 9.098775 9.106337
## 1989 9.113806 9.121175 9.128443 9.135629
## 1990 9.142675 9.149602 9.156338 9.162899
## 1991 9.169324 9.175622 9.181843 9.188063
## 1992 9.194308 9.200616 9.207054 9.213556
## 1993 9.220121 9.226802 9.233537 9.240309
## 1994 9.247089 9.253866 9.260692 9.267525
## 1995 9.274334 9.281164 9.287971 9.294879
## 1996 9.301847 9.309189 9.316992 9.325235
## 1997 9.333895 9.342904 9.352280 9.361904
## 1998 9.371717 9.381751 9.391864 9.402055
## 1999 9.412343 9.422648 9.432980 9.443382
## 2000 9.453773 9.463862 9.473477 9.482590
## 2001 9.491196 9.499302 9.506921 9.514111
## 2002 9.520911 9.527450 9.533830 9.540081
## 2003 9.546276 9.552491 9.558668 9.564884
## 2004 9.571190 9.577547 9.584016 9.590525
## 2005 9.596888 9.603056 9.609101 9.614987
## 2006 9.620704 9.626285 9.631620 9.636713
## 2007 9.641772 9.646837 9.651924 9.656958
#1.1.1 Real
log_real_gdp_data= log(real_gdp_data[,2])
log_real_gdp_data
## Qtr1 Qtr2 Qtr3 Qtr4
## 1985 8.965623 8.974389 8.989545 8.996951
## 1986 9.006243 9.010737 9.020261 9.025616
## 1987 9.033039 9.043770 9.052408 9.069433
## 1988 9.074586 9.087639 9.093481 9.106718
## 1989 9.116833 9.124437 9.131818 9.133787
## 1990 9.144655 9.148278 9.148943 9.139797
## 1991 9.135108 9.142875 9.147915 9.151395
## 1992 9.163295 9.174080 9.183913 9.194288
## 1993 9.195956 9.201760 9.206520 9.220029
## 1994 9.229686 9.243146 9.248974 9.260364
## 1995 9.263905 9.266884 9.275354 9.282122
## 1996 9.289583 9.306125 9.315055 9.325385
## 1997 9.331820 9.348303 9.360734 9.369284
## 1998 9.379228 9.388444 9.400894 9.416927
## 1999 9.426321 9.434636 9.447779 9.464074
## 2000 9.467712 9.485754 9.486751 9.492677
## 2001 9.489429 9.495624 9.491613 9.494382
## 2002 9.502630 9.508766 9.512793 9.514099
## 2003 9.519253 9.528147 9.544679 9.556153
## 2004 9.561866 9.569623 9.578992 9.589160
## 2005 9.600208 9.605062 9.612887 9.618551
## 2006 9.631947 9.634400 9.635903 9.644305
## 2007 9.647237 9.653601 9.659606 9.665684
#1.2 Obtención de la brecha del producto
brechaproducto= log_real_gdp_data -log_potential_gdp_data
brechaproducto
## Qtr1 Qtr2 Qtr3 Qtr4
## 1985 -0.0189431597 -0.0190062261 -0.0125845001 -0.0137820430
## 1986 -0.0129461570 -0.0167969831 -0.0155261642 -0.0183482154
## 1987 -0.0189888396 -0.0162240320 -0.0154580523 -0.0062735260
## 1988 -0.0088573471 -0.0035094116 -0.0052934758 0.0003812393
## 1989 0.0030274620 0.0032616591 0.0033751005 -0.0018426382
## 1990 0.0019807542 -0.0013244000 -0.0073946317 -0.0231013757
## 1991 -0.0342163232 -0.0327472401 -0.0339281454 -0.0366679499
## 1992 -0.0310129741 -0.0265355175 -0.0231411865 -0.0192689266
## 1993 -0.0241654049 -0.0250417682 -0.0270170180 -0.0202795112
## 1994 -0.0174030298 -0.0107205665 -0.0117173625 -0.0071604860
## 1995 -0.0104286162 -0.0142809388 -0.0126169008 -0.0127572464
## 1996 -0.0122632953 -0.0030644389 -0.0019369569 0.0001503957
## 1997 -0.0020746945 0.0053994644 0.0084532688 0.0073801570
## 1998 0.0075112940 0.0066933956 0.0090299088 0.0148714557
## 1999 0.0139776046 0.0119876717 0.0147993390 0.0206917707
## 2000 0.0139390421 0.0218918928 0.0132737150 0.0100871031
## 2001 -0.0017667016 -0.0036774880 -0.0153079725 -0.0197288040
## 2002 -0.0182804390 -0.0186835252 -0.0210368647 -0.0259818418
## 2003 -0.0270226211 -0.0243433748 -0.0139896729 -0.0087306834
## 2004 -0.0093237179 -0.0079242943 -0.0050244294 -0.0013646446
## 2005 0.0033193812 0.0020061371 0.0037865950 0.0035630469
## 2006 0.0112425864 0.0081145725 0.0042833010 0.0075920148
## 2007 0.0054651930 0.0067636321 0.0076814544 0.0087257461
#2.0 Consumer Price o brecha de inflacion
#2.1 Logaritmo de consumer price
log_consumer_price84_data= log(consumer_price84_data[,2])
log_consumer_price84_data
## Qtr1 Qtr2 Qtr3 Qtr4
## 1984 4.630188 4.639572 4.648230 4.656813
## 1985 4.665952 4.675007 4.681205 4.691348
## 1986 4.696533 4.691654 4.697749 4.704714
## 1987 4.716712 4.727978 4.738535 4.747826
## 1988 4.755600 4.767006 4.779123 4.789989
## 1989 4.801285 4.817320 4.825109 4.835223
## 1990 4.852291 4.862135 4.879260 4.896097
## 1991 4.903545 4.909464 4.917057 4.925319
## 1992 4.932073 4.939736 4.947340 4.956062
## 1993 4.963311 4.970508 4.975123 4.983378
## 1994 4.988390 4.994054 5.003275 5.009079
## 1995 5.016396 5.024538 5.029566 5.035003
## 1996 5.043855 5.052417 5.058155 5.066806
## 1997 5.072880 5.075174 5.080161 5.085537
## 1998 5.087596 5.090883 5.095997 5.100679
## 1999 5.104328 5.111787 5.119191 5.126540
## 2000 5.136386 5.144194 5.153292 5.160395
## 2001 5.169916 5.176903 5.179722 5.178971
## 2002 5.182158 5.189989 5.195361 5.201256
## 2003 5.211488 5.209850 5.217288 5.221076
## 2004 5.229503 5.237328 5.243685 5.254365
## 2005 5.259403 5.266138 5.281171 5.290453
## 2006 5.295647 5.304631 5.314027 5.309917
## 2007 5.319673 5.330935 5.337245 5.349437
#2.2 Diferencia de 4 trimestres atrás o tasa de inflacion trimestral
inflacion_tri=diff(log_consumer_price84_data, lag = 4, differences = 1)
inflacion_tri=data.frame(inflacion_tri)
#2.3 Brecha Inflacion
brechainflacion = c((inflacion_tri[,1])-(0.02))
brechainflacion = ts (brechainflacion,frequency = 4, start=c(1985,1))
brechainflacion
## Qtr1 Qtr2 Qtr3 Qtr4
## 1985 0.0157637093 0.0154355329 0.0129751968 0.0145344631
## 1986 0.0105815338 -0.0033534997 -0.0034555050 -0.0066340659
## 1987 0.0001783687 0.0163239694 0.0207855308 0.0231126701
## 1988 0.0188881043 0.0190279333 0.0205885951 0.0221621366
## 1989 0.0256853999 0.0303146473 0.0259851132 0.0252345226
## 1990 0.0310055818 0.0248150900 0.0341516986 0.0408738430
## 1991 0.0312542413 0.0273282385 0.0177966422 0.0092224600
## 1992 0.0085280836 0.0102723201 0.0102834966 0.0107423233
## 1993 0.0112377505 0.0107716587 0.0077828071 0.0073165133
## 1994 0.0050789631 0.0035466359 0.0081516888 0.0057002423
## 1995 0.0080067594 0.0104840603 0.0062911421 0.0059241231
## 1996 0.0074586874 0.0078786288 0.0085887283 0.0118029150
## 1997 0.0090243867 0.0027569871 0.0020065467 -0.0012689633
## 1998 -0.0052831834 -0.0042907063 -0.0041641935 -0.0048574966
## 1999 -0.0032683303 0.0009038560 0.0031935374 0.0058609180
## 2000 0.0120584945 0.0124074991 0.0141008938 0.0138553734
## 2001 0.0135291523 0.0127082805 0.0064299061 -0.0014247881
## 2002 -0.0077576397 -0.0069132550 -0.0043601355 0.0022850448
## 2003 0.0093297792 -0.0001391044 0.0019266961 -0.0001793675
## 2004 -0.0019847407 0.0074777097 0.0063971097 0.0132891928
## 2005 0.0099002225 0.0088103733 0.0174860368 0.0160877125
## 2006 0.0162438649 0.0184922604 0.0128554525 -0.0005366891
## 2007 0.0040255713 0.0063038652 0.0032181072 0.0195200601
#3.0 Obtener tasa de interes
interes_fedfunds_data
## DATE DFF
## 1985 Q1 1 8.4751111
## 1985 Q2 2 7.9243956
## 1985 Q3 3 7.9009783
## 1985 Q4 4 8.1044565
## 1986 Q1 5 7.8268889
## 1986 Q2 6 6.9184615
## 1986 Q3 7 6.2094565
## 1986 Q4 8 6.2667391
## 1987 Q1 9 6.2225556
## 1987 Q2 10 6.6500000
## 1987 Q3 11 6.8395652
## 1987 Q4 12 6.9196739
## 1988 Q1 13 6.6659341
## 1988 Q2 14 7.1549451
## 1988 Q3 15 7.9834783
## 1988 Q4 16 8.4684783
## 1989 Q1 17 9.4464444
## 1989 Q2 18 9.7257143
## 1989 Q3 19 9.0835870
## 1989 Q4 20 8.6144565
## 1990 Q1 21 8.2480000
## 1990 Q2 22 8.2393407
## 1990 Q3 23 8.1602174
## 1990 Q4 24 7.7433696
## 1991 Q1 25 6.4304444
## 1991 Q2 26 5.8640659
## 1991 Q3 27 5.6452174
## 1991 Q4 28 4.8184783
## 1992 Q1 29 4.0242857
## 1992 Q2 30 3.7740659
## 1992 Q3 31 3.2592391
## 1992 Q4 32 3.0348913
## 1993 Q1 33 3.0423333
## 1993 Q2 34 2.9972527
## 1993 Q3 35 3.0577174
## 1993 Q4 36 2.9882609
## 1994 Q1 37 3.2093333
## 1994 Q2 38 3.9380220
## 1994 Q3 39 4.4854348
## 1994 Q4 40 5.1679348
## 1995 Q1 41 5.8027778
## 1995 Q2 42 6.0191209
## 1995 Q3 43 5.7971739
## 1995 Q4 44 5.7194565
## 1996 Q1 45 5.3709890
## 1996 Q2 46 5.2439560
## 1996 Q3 47 5.3061957
## 1996 Q4 48 5.2808696
## 1997 Q1 49 5.2784444
## 1997 Q2 50 5.5221978
## 1997 Q3 51 5.5346739
## 1997 Q4 52 5.5073913
## 1998 Q1 53 5.5193333
## 1998 Q2 54 5.4974725
## 1998 Q3 55 5.5316304
## 1998 Q4 56 4.8605435
## 1999 Q1 57 4.7345556
## 1999 Q2 58 4.7476923
## 1999 Q3 59 5.0955435
## 1999 Q4 60 5.3040217
## 2000 Q1 61 5.6776923
## 2000 Q2 62 6.2719780
## 2000 Q3 63 6.5194565
## 2000 Q4 64 6.4748913
## 2001 Q1 65 5.5970000
## 2001 Q2 66 4.3267033
## 2001 Q3 67 3.5015217
## 2001 Q4 68 2.1304348
## 2002 Q1 69 1.7328889
## 2002 Q2 70 1.7515385
## 2002 Q3 71 1.7408696
## 2002 Q4 72 1.4442391
## 2003 Q1 73 1.2496667
## 2003 Q2 74 1.2467033
## 2003 Q3 75 1.0168478
## 2003 Q4 76 0.9967391
## 2004 Q1 77 1.0018681
## 2004 Q2 78 1.0113187
## 2004 Q3 79 1.4307609
## 2004 Q4 80 1.9498913
## 2005 Q1 81 2.4690000
## 2005 Q2 82 2.9417582
## 2005 Q3 83 3.4600000
## 2005 Q4 84 3.9782609
## 2006 Q1 85 4.4541111
## 2006 Q2 86 4.9075824
## 2006 Q3 87 5.2453261
## 2006 Q4 88 5.2429348
## 2007 Q1 89 5.2545556
## 2007 Q2 90 5.2524176
## 2007 Q3 91 5.0743478
## 2007 Q4 92 4.4956522
interes_porcentaje= c((interes_fedfunds_data[,2])/100)
interes_porcentaje=ts (interes_porcentaje,frequency = 4, start=c(1985,1))
interes_porcentaje
## Qtr1 Qtr2 Qtr3 Qtr4
## 1985 0.084751111 0.079243956 0.079009783 0.081044565
## 1986 0.078268889 0.069184615 0.062094565 0.062667391
## 1987 0.062225556 0.066500000 0.068395652 0.069196739
## 1988 0.066659341 0.071549451 0.079834783 0.084684783
## 1989 0.094464444 0.097257143 0.090835870 0.086144565
## 1990 0.082480000 0.082393407 0.081602174 0.077433696
## 1991 0.064304444 0.058640659 0.056452174 0.048184783
## 1992 0.040242857 0.037740659 0.032592391 0.030348913
## 1993 0.030423333 0.029972527 0.030577174 0.029882609
## 1994 0.032093333 0.039380220 0.044854348 0.051679348
## 1995 0.058027778 0.060191209 0.057971739 0.057194565
## 1996 0.053709890 0.052439560 0.053061957 0.052808696
## 1997 0.052784444 0.055221978 0.055346739 0.055073913
## 1998 0.055193333 0.054974725 0.055316304 0.048605435
## 1999 0.047345556 0.047476923 0.050955435 0.053040217
## 2000 0.056776923 0.062719780 0.065194565 0.064748913
## 2001 0.055970000 0.043267033 0.035015217 0.021304348
## 2002 0.017328889 0.017515385 0.017408696 0.014442391
## 2003 0.012496667 0.012467033 0.010168478 0.009967391
## 2004 0.010018681 0.010113187 0.014307609 0.019498913
## 2005 0.024690000 0.029417582 0.034600000 0.039782609
## 2006 0.044541111 0.049075824 0.052453261 0.052429348
## 2007 0.052545556 0.052524176 0.050743478 0.044956522
#4.0 Union de los dataframe con "ts.union"
datos_taylor= ts.union(interes_porcentaje, brechaproducto, brechainflacion)
datos_taylor= data.frame(datos_taylor)
cor(datos_taylor)
## interes_porcentaje brechaproducto brechainflacion
## interes_porcentaje 1.0000000 0.22467264 0.56345475
## brechaproducto 0.2246726 1.00000000 -0.05085399
## brechainflacion 0.5634548 -0.05085399 1.00000000
#5.0 Observación de datos
#5.1 Coeficiente de correlacioón.Se calcula el coeficiente de correlación de Pearson entre las variables regresoras.
cor(datos_taylor$brechaproducto, datos_taylor$brechainflacion)
## [1] -0.05085399
#5.2Matriz de Correlación
round(cor(datos_taylor), 2) # Matriz de correlación redondeada a 2 decimales
## interes_porcentaje brechaproducto brechainflacion
## interes_porcentaje 1.00 0.22 0.56
## brechaproducto 0.22 1.00 -0.05
## brechainflacion 0.56 -0.05 1.00
#5.3 Matriz de dispersión. Permite comparar varios subconjuntos de la base de datos para buscar patrones y relacione
plot(datos_taylor, main='Matriz de dispersión', pch = 19, col = "red")
#5.4 Mostramos visualmente la relación de la variable dependiente con cada una de las variables independientes
plot(datos_taylor$brechaproducto,datos_taylor$interes_porcentaje, pch = 19, col = "red", main = "Interes y Producto")
plot(datos_taylor$brechainflacion,datos_taylor$interes_porcentaje, pch = 22, col = "red", main = "Interes e Inflación")
#6.0 Grafico sin ajuste (Posible en 3D Porque solo son 3 variables)
#3D con libraria plotly
scatterplot3d(x=brechaproducto, y=brechainflacion, z=interes_porcentaje, pch=16, cex.lab=1,
highlight.3d=TRUE, type="h", xlab='GDP',
ylab='Inflacion', zlab='Interes')
#Movimiento 3D con libreria scatterplot3d
plot_ly(x=brechaproducto, y=brechainflacion, z=interes_porcentaje, type="scatter3d", color=brechaproducto,) %>%
layout(scene = list(xaxis = list(title = 'GDP'),
yaxis = list(title = 'Inflación'),
zaxis = list(title = 'Interes')))
## No scatter3d mode specifed:
## Setting the mode to markers
## Read more about this attribute -> https://plotly.com/r/reference/#scatter-mode
#7.0 Regresion de Taylor
taylor_reg= lm(interes_porcentaje ~ brechaproducto + brechainflacion, data = datos_taylor)
taylor_reg
##
## Call:
## lm(formula = interes_porcentaje ~ brechaproducto + brechainflacion,
## data = datos_taylor)
##
## Coefficients:
## (Intercept) brechaproducto brechainflacion
## 0.04135 0.39851 1.23923
summary(taylor_reg)
##
## Call:
## lm(formula = interes_porcentaje ~ brechaproducto + brechainflacion,
## data = datos_taylor)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.037774 -0.010219 0.000979 0.011032 0.038686
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.041348 0.002678 15.443 < 2e-16 ***
## brechaproducto 0.398515 0.130937 3.044 0.00307 **
## brechainflacion 1.239233 0.179422 6.907 7.11e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.01732 on 89 degrees of freedom
## Multiple R-squared: 0.3818, Adjusted R-squared: 0.3679
## F-statistic: 27.49 on 2 and 89 DF, p-value: 5.065e-10
anova(taylor_reg)
## Analysis of Variance Table
##
## Response: interes_porcentaje
## Df Sum Sq Mean Sq F value Pr(>F)
## brechaproducto 1 0.0021796 0.0021796 7.2674 0.008396 **
## brechainflacion 1 0.0143073 0.0143073 47.7041 7.107e-10 ***
## Residuals 89 0.0266927 0.0002999
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
fitted(taylor_reg)
## 1 2 3 4 5 6 7
## 0.05333406 0.05290224 0.05241246 0.05386752 0.04930203 0.03049866 0.03087870
## 8 9 10 11 12 13 14
## 0.02581509 0.03400198 0.05511196 0.06094613 0.06749017 0.06122526 0.06352977
## 15 16 17 18 19 20 21
## 0.06475281 0.06896426 0.07438496 0.08021501 0.07489491 0.07188541 0.08056078
## 22 23 24 25 26 27 28
## 0.07157216 0.08072332 0.08279425 0.06644386 0.06216407 0.04988160 0.03816434
## 29 30 31 32 33 34 35
## 0.03955743 0.04350328 0.04486982 0.04698157 0.04564420 0.04471736 0.04022631
## 36 37 38 39 40 41 42
## 0.04233346 0.04070693 0.04147108 0.04678058 0.04555865 0.04711456 0.04864931
## 43 44 45 46 47 48 49
## 0.04411645 0.04360569 0.04570422 0.04989051 0.05121981 0.05603477 0.05170480
## 50 51 52 53 54 55 56
## 0.04691659 0.04720361 0.04271684 0.03779454 0.03869851 0.03978642 0.04125520
## 57 58 59 60 61 62 63
## 0.04286833 0.04724563 0.05120357 0.05685729 0.06184647 0.06544830 0.06411234
## 64 65 66 67 68 69 70
## 0.06253817 0.05740999 0.05563126 0.04321598 0.03172041 0.02444973 0.02533548
## 71 72 73 74 75 76 77
## 0.02756155 0.03382583 0.04214113 0.03147470 0.03816081 0.03764669 0.03517308
## 78 79 80 81 82 83 84
## 0.04745695 0.04727348 0.05727285 0.05493978 0.05306586 0.06452656 0.06270463
## 85 86 87 88 89 90 91
## 0.06595855 0.06749827 0.05898614 0.04370872 0.04851486 0.05185564 0.04839743
## 92
## 0.06901552
#8 Graficas SOLO del interes (Federal Fund Rate) vs valores ajustados del FFR
#valores ajustados
interes_calculado=(taylor_reg$fitted.values)
#Valores ajustados a serie de tiempo
interes_calculado=ts(interes_calculado, freq = 4, start = c(1985, 1))
#Grafica con plot
plot(interes_porcentaje, main="Tasa de interés observada y ajustada
1985-2007 (Trimestral)",xlab="Periodo",ylab="Tasa de interés",col=1)
lines(interes_calculado,col=2)
# *** Obtain and save standardized residuals
taylor_reg$stdres <- rstandard(taylor_reg)
taylor_reg$stdre
## 1 2 3 4 5 6
## 1.83441202 1.53784965 1.54624439 1.58153635 1.68352333 2.27589744
## 7 8 9 10 11 12
## 1.83532229 2.18270376 1.65509425 0.66409426 0.43600793 0.10002154
## 13 14 15 16 17 18
## 0.31686295 0.46790422 0.88113775 0.92192041 1.18594690 1.01645989
## 19 20 21 22 23 24
## 0.94224966 0.83940013 0.11456136 0.63669314 0.05271576 -0.33069169
## 25 26 27 28 29 30
## -0.12999972 -0.21180796 0.39072975 0.59724852 0.04048657 -0.33831979
## 31 32 33 34 35 36
## -0.71823712 -0.96990087 -0.89133036 -0.86422057 -0.56708659 -0.72699892
## 37 38 39 40 41 42
## -0.50244794 -0.12173238 -0.11193293 0.35572686 0.63398787 0.67114266
## 43 44 45 46 47 48
## 0.80584334 0.79051671 0.46536843 0.14809471 0.10704234 -0.18762326
## 49 50 51 52 53 54
## 0.06272980 0.48559131 0.47753284 0.72639431 1.02875521 0.96023396
## 55 56 57 58 59 60
## 0.91780105 0.43762172 0.26563308 0.01362424 -0.01463758 -0.22681104
## 61 62 63 64 65 66
## -0.29825780 -0.16248151 0.06367373 0.12959087 -0.08373330 -0.71839491
## 67 68 69 70 71 72
## -0.47747737 -0.61238100 -0.42268178 -0.46354257 -0.60021012 -1.14178289
## 73 74 75 76 77 78
## -1.74157537 -1.12051784 -1.63373347 -1.61646095 -1.47241876 -2.16899418
## 79 80 81 82 83 84
## -1.91550828 -2.19658118 -1.76170607 -1.37628413 -1.74928713 -1.33818570
## 85 86 87 88 89 90
## -1.25889994 -1.08156557 -0.38091396 0.51228503 0.23547098 0.03905055
## 91 92
## 0.13736062 -1.41484539
#Datos ajustados Fitted values are also called predicted values.
#Residual Standard Error (RSE)
sigma(taylor_reg)
## [1] 0.01731813
# This finds the R Squared value of a linear regression model named model.
summary(taylor_reg)$r.squared
## [1] 0.381822
# Para regresion con 3 valores. Para incluir el plano de regresión que representa el modelo ajustado anterior se puede usar el siguiente código.
##Se crea el grafico 3d y se guarda en un objeto, por ejemplo mi_3d
taylor_3d <- scatterplot3d(x=brechaproducto, y=brechainflacion, z=interes_porcentaje, pch=16, cex.lab=1,
highlight.3d=TRUE, type="h", xlab='GDP',
ylab='Inflacion', zlab='Interes')
# Para agregar el plano usamos $plane3d( ) con argumento modelo ajustado
taylor_3d$plane3d(taylor_reg, lty.box="solid", col='mediumblue')
#plot predicción vs. Valores actuales
plot(x=predict(taylor_reg), y=datos_taylor$interes_porcentaje,
xlab='Prediccion',
ylab='Valores Actuales',
main='Prediccion vs Valores Actuales')
abline(a=0, b=1)
#9.0 Estima la regla de Taylor con Persistencia
##Persistencia en porcentaje
persistencia_porcentaje= c((persistencia/100))
persistencia_porcentaje
## [1] 0.092625000 0.084751111 0.079243956 0.079009783 0.081044565 0.078268889
## [7] 0.069184615 0.062094565 0.062667391 0.062225556 0.066500000 0.068395652
## [13] 0.069196739 0.066659341 0.071549451 0.079834783 0.084684783 0.094464444
## [19] 0.097257143 0.090835870 0.086144565 0.082480000 0.082393407 0.081602174
## [25] 0.077433696 0.064304444 0.058640659 0.056452174 0.048184783 0.040242857
## [31] 0.037740659 0.032592391 0.030348913 0.030423333 0.029972527 0.030577174
## [37] 0.029882609 0.032093333 0.039380220 0.044854348 0.051679348 0.058027778
## [43] 0.060191209 0.057971739 0.057194565 0.053709890 0.052439560 0.053061957
## [49] 0.052808696 0.052784444 0.055221978 0.055346739 0.055073913 0.055193333
## [55] 0.054974725 0.055316304 0.048605435 0.047345556 0.047476923 0.050955435
## [61] 0.053040217 0.056776923 0.062719780 0.065194565 0.064748913 0.055970000
## [67] 0.043267033 0.035015217 0.021304348 0.017328889 0.017515385 0.017408696
## [73] 0.014442391 0.012496667 0.012467033 0.010168478 0.009967391 0.010018681
## [79] 0.010113187 0.014307609 0.019498913 0.024690000 0.029417582 0.034600000
## [85] 0.039782609 0.044541111 0.049075824 0.052453261 0.052429348 0.052545556
## [91] 0.052524176 0.050743478
interes_porcentaje=ts (interes_porcentaje,frequency = 4, start=c(1985,1))
interes_porcentaje
## Qtr1 Qtr2 Qtr3 Qtr4
## 1985 0.084751111 0.079243956 0.079009783 0.081044565
## 1986 0.078268889 0.069184615 0.062094565 0.062667391
## 1987 0.062225556 0.066500000 0.068395652 0.069196739
## 1988 0.066659341 0.071549451 0.079834783 0.084684783
## 1989 0.094464444 0.097257143 0.090835870 0.086144565
## 1990 0.082480000 0.082393407 0.081602174 0.077433696
## 1991 0.064304444 0.058640659 0.056452174 0.048184783
## 1992 0.040242857 0.037740659 0.032592391 0.030348913
## 1993 0.030423333 0.029972527 0.030577174 0.029882609
## 1994 0.032093333 0.039380220 0.044854348 0.051679348
## 1995 0.058027778 0.060191209 0.057971739 0.057194565
## 1996 0.053709890 0.052439560 0.053061957 0.052808696
## 1997 0.052784444 0.055221978 0.055346739 0.055073913
## 1998 0.055193333 0.054974725 0.055316304 0.048605435
## 1999 0.047345556 0.047476923 0.050955435 0.053040217
## 2000 0.056776923 0.062719780 0.065194565 0.064748913
## 2001 0.055970000 0.043267033 0.035015217 0.021304348
## 2002 0.017328889 0.017515385 0.017408696 0.014442391
## 2003 0.012496667 0.012467033 0.010168478 0.009967391
## 2004 0.010018681 0.010113187 0.014307609 0.019498913
## 2005 0.024690000 0.029417582 0.034600000 0.039782609
## 2006 0.044541111 0.049075824 0.052453261 0.052429348
## 2007 0.052545556 0.052524176 0.050743478 0.044956522
##9.1 Union de los dataframe con "ts.union"
datos_taylor2= ts.union(interes_porcentaje, brechaproducto, brechainflacion, persistencia_porcentaje)
datos_taylor2= data.frame(datos_taylor2)
datos_taylor2
## interes_porcentaje brechaproducto brechainflacion persistencia_porcentaje
## 1 0.084751111 -0.0189431597 0.0157637093 0.092625000
## 2 0.079243956 -0.0190062261 0.0154355329 0.084751111
## 3 0.079009783 -0.0125845001 0.0129751968 0.079243956
## 4 0.081044565 -0.0137820430 0.0145344631 0.079009783
## 5 0.078268889 -0.0129461570 0.0105815338 0.081044565
## 6 0.069184615 -0.0167969831 -0.0033534997 0.078268889
## 7 0.062094565 -0.0155261642 -0.0034555050 0.069184615
## 8 0.062667391 -0.0183482154 -0.0066340659 0.062094565
## 9 0.062225556 -0.0189888396 0.0001783687 0.062667391
## 10 0.066500000 -0.0162240320 0.0163239694 0.062225556
## 11 0.068395652 -0.0154580523 0.0207855308 0.066500000
## 12 0.069196739 -0.0062735260 0.0231126701 0.068395652
## 13 0.066659341 -0.0088573471 0.0188881043 0.069196739
## 14 0.071549451 -0.0035094116 0.0190279333 0.066659341
## 15 0.079834783 -0.0052934758 0.0205885951 0.071549451
## 16 0.084684783 0.0003812393 0.0221621366 0.079834783
## 17 0.094464444 0.0030274620 0.0256853999 0.084684783
## 18 0.097257143 0.0032616591 0.0303146473 0.094464444
## 19 0.090835870 0.0033751005 0.0259851132 0.097257143
## 20 0.086144565 -0.0018426382 0.0252345226 0.090835870
## 21 0.082480000 0.0019807542 0.0310055818 0.086144565
## 22 0.082393407 -0.0013244000 0.0248150900 0.082480000
## 23 0.081602174 -0.0073946317 0.0341516986 0.082393407
## 24 0.077433696 -0.0231013757 0.0408738430 0.081602174
## 25 0.064304444 -0.0342163232 0.0312542413 0.077433696
## 26 0.058640659 -0.0327472401 0.0273282385 0.064304444
## 27 0.056452174 -0.0339281454 0.0177966422 0.058640659
## 28 0.048184783 -0.0366679499 0.0092224600 0.056452174
## 29 0.040242857 -0.0310129741 0.0085280836 0.048184783
## 30 0.037740659 -0.0265355175 0.0102723201 0.040242857
## 31 0.032592391 -0.0231411865 0.0102834966 0.037740659
## 32 0.030348913 -0.0192689266 0.0107423233 0.032592391
## 33 0.030423333 -0.0241654049 0.0112377505 0.030348913
## 34 0.029972527 -0.0250417682 0.0107716587 0.030423333
## 35 0.030577174 -0.0270170180 0.0077828071 0.029972527
## 36 0.029882609 -0.0202795112 0.0073165133 0.030577174
## 37 0.032093333 -0.0174030298 0.0050789631 0.029882609
## 38 0.039380220 -0.0107205665 0.0035466359 0.032093333
## 39 0.044854348 -0.0117173625 0.0081516888 0.039380220
## 40 0.051679348 -0.0071604860 0.0057002423 0.044854348
## 41 0.058027778 -0.0104286162 0.0080067594 0.051679348
## 42 0.060191209 -0.0142809388 0.0104840603 0.058027778
## 43 0.057971739 -0.0126169008 0.0062911421 0.060191209
## 44 0.057194565 -0.0127572464 0.0059241231 0.057971739
## 45 0.053709890 -0.0122632953 0.0074586874 0.057194565
## 46 0.052439560 -0.0030644389 0.0078786288 0.053709890
## 47 0.053061957 -0.0019369569 0.0085887283 0.052439560
## 48 0.052808696 0.0001503957 0.0118029150 0.053061957
## 49 0.052784444 -0.0020746945 0.0090243867 0.052808696
## 50 0.055221978 0.0053994644 0.0027569871 0.052784444
## 51 0.055346739 0.0084532688 0.0020065467 0.055221978
## 52 0.055073913 0.0073801570 -0.0012689633 0.055346739
## 53 0.055193333 0.0075112940 -0.0052831834 0.055073913
## 54 0.054974725 0.0066933956 -0.0042907063 0.055193333
## 55 0.055316304 0.0090299088 -0.0041641935 0.054974725
## 56 0.048605435 0.0148714557 -0.0048574966 0.055316304
## 57 0.047345556 0.0139776046 -0.0032683303 0.048605435
## 58 0.047476923 0.0119876717 0.0009038560 0.047345556
## 59 0.050955435 0.0147993390 0.0031935374 0.047476923
## 60 0.053040217 0.0206917707 0.0058609180 0.050955435
## 61 0.056776923 0.0139390421 0.0120584945 0.053040217
## 62 0.062719780 0.0218918928 0.0124074991 0.056776923
## 63 0.065194565 0.0132737150 0.0141008938 0.062719780
## 64 0.064748913 0.0100871031 0.0138553734 0.065194565
## 65 0.055970000 -0.0017667016 0.0135291523 0.064748913
## 66 0.043267033 -0.0036774880 0.0127082805 0.055970000
## 67 0.035015217 -0.0153079725 0.0064299061 0.043267033
## 68 0.021304348 -0.0197288040 -0.0014247881 0.035015217
## 69 0.017328889 -0.0182804390 -0.0077576397 0.021304348
## 70 0.017515385 -0.0186835252 -0.0069132550 0.017328889
## 71 0.017408696 -0.0210368647 -0.0043601355 0.017515385
## 72 0.014442391 -0.0259818418 0.0022850448 0.017408696
## 73 0.012496667 -0.0270226211 0.0093297792 0.014442391
## 74 0.012467033 -0.0243433748 -0.0001391044 0.012496667
## 75 0.010168478 -0.0139896729 0.0019266961 0.012467033
## 76 0.009967391 -0.0087306834 -0.0001793675 0.010168478
## 77 0.010018681 -0.0093237179 -0.0019847407 0.009967391
## 78 0.010113187 -0.0079242943 0.0074777097 0.010018681
## 79 0.014307609 -0.0050244294 0.0063971097 0.010113187
## 80 0.019498913 -0.0013646446 0.0132891928 0.014307609
## 81 0.024690000 0.0033193812 0.0099002225 0.019498913
## 82 0.029417582 0.0020061371 0.0088103733 0.024690000
## 83 0.034600000 0.0037865950 0.0174860368 0.029417582
## 84 0.039782609 0.0035630469 0.0160877125 0.034600000
## 85 0.044541111 0.0112425864 0.0162438649 0.039782609
## 86 0.049075824 0.0081145725 0.0184922604 0.044541111
## 87 0.052453261 0.0042833010 0.0128554525 0.049075824
## 88 0.052429348 0.0075920148 -0.0005366891 0.052453261
## 89 0.052545556 0.0054651930 0.0040255713 0.052429348
## 90 0.052524176 0.0067636321 0.0063038652 0.052545556
## 91 0.050743478 0.0076814544 0.0032181072 0.052524176
## 92 0.044956522 0.0087257461 0.0195200601 0.050743478
#9.2Matriz de Correlación
round(cor(datos_taylor2), 2) # Matriz de correlación redondeada a 2 decimales
## interes_porcentaje brechaproducto brechainflacion
## interes_porcentaje 1.00 0.22 0.56
## brechaproducto 0.22 1.00 -0.05
## brechainflacion 0.56 -0.05 1.00
## persistencia_porcentaje 0.98 0.13 0.55
## persistencia_porcentaje
## interes_porcentaje 0.98
## brechaproducto 0.13
## brechainflacion 0.55
## persistencia_porcentaje 1.00
#9.3 Matriz de dispersión. Permite comparar varios subconjuntos de la base de datos para buscar patrones y relacione
plot(datos_taylor2, main='Matriz de dispersión', pch = 19, col = "red")
#9.4 Modelo 2 o segunda regresión
taylor_reg_2= lm(interes_porcentaje ~ persistencia+ brechaproducto + brechainflacion, data = datos_taylor2)
taylor_reg_2
##
## Call:
## lm(formula = interes_porcentaje ~ persistencia + brechaproducto +
## brechainflacion, data = datos_taylor2)
##
## Coefficients:
## (Intercept) persistencia brechaproducto brechainflacion
## 0.003794 0.009126 0.160450 0.131002
summary(taylor_reg_2)
##
## Call:
## lm(formula = interes_porcentaje ~ persistencia + brechaproducto +
## brechainflacion, data = datos_taylor2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.012679 -0.001909 0.000296 0.001742 0.009538
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.0037939 0.0011513 3.295 0.00142 **
## persistencia 0.0091258 0.0002341 38.975 < 2e-16 ***
## brechaproducto 0.1604496 0.0314135 5.108 1.87e-06 ***
## brechainflacion 0.1310015 0.0509057 2.573 0.01174 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.004076 on 88 degrees of freedom
## Multiple R-squared: 0.9661, Adjusted R-squared: 0.965
## F-statistic: 837.2 on 3 and 88 DF, p-value: < 2.2e-16
#10 Graficas SOLO del interes (Federal Fund Rate) vs valorescon persistencia
#valores ajustados
interes_calculado_2=(taylor_reg_2$fitted.values)
#Valores ajustados a serie de tiempo
interes_calculado_2=ts(interes_calculado_2, freq = 4, start = c(1985, 1))#aqui pongo 1985-1 pero la persistencia tiempo menos 1, 1984-4
interes_calculado_2
## Qtr1 Qtr2 Qtr3 Qtr4
## 1985 0.08734747 0.08010878 0.07579110 0.07558952
## 1986 0.07706271 0.07208630 0.06398669 0.05664724
## 1987 0.05795964 0.06011514 0.06472330 0.06823175
## 1988 0.06799481 0.06655561 0.07093644 0.07961413
## 1989 0.08492630 0.09449506 0.09649465 0.08969920
## 1990 0.08678748 0.08210198 0.08227210 0.07991051
## 1991 0.07306286 0.06080273 0.05419593 0.05063592
## 1992 0.04390762 0.03760686 0.03586948 0.03185267
## 1993 0.02908458 0.02895082 0.02783095 0.02940269
## 1994 0.02893725 0.03182618 0.03891940 0.04432500
## 1995 0.05033116 0.05583105 0.05752308 0.05542703
## 1996 0.05499808 0.05334899 0.05246364 0.05378761
## 1997 0.05283548 0.05319153 0.05580766 0.05532023
## 1998 0.05456643 0.05467420 0.05486616 0.05602433
## 1999 0.04996488 0.04904241 0.04991338 0.05438268
## 2000 0.05601363 0.06074544 0.06500784 0.06672283
## 2001 0.06437146 0.05594586 0.04166477 0.03239601
## 2002 0.01928648 0.01570449 0.01583155 0.01581130
## 2003 0.01386018 0.01127399 0.01317882 0.01164910
## 2004 0.01113393 0.01264487 0.01305484 0.01837268
## 2005 0.02341776 0.02780158 0.03353809 0.03804842
## 2006 0.04403061 0.04816579 0.05095094 0.05280962
## 2007 0.05304421 0.05365705 0.05338057 0.05405867
#Grafica con plot
plot(interes_porcentaje, main="Tasa de interés observada y ajustada
(Trimestral) con Persistencia",xlab="Periodo",ylab="Tasa de interés",col=1)
lines(interes_calculado_2,col=2)
