library(quantmod)
## Warning: package 'quantmod' was built under R version 4.4.1
## Cargando paquete requerido: xts
## Cargando paquete requerido: zoo
##
## Adjuntando el paquete: 'zoo'
## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric
## Cargando paquete requerido: TTR
## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoo
library(tidyverse)
## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr 1.1.4 ✔ readr 2.1.5
## ✔ forcats 1.0.0 ✔ stringr 1.5.1
## ✔ ggplot2 3.5.1 ✔ tibble 3.2.1
## ✔ lubridate 1.9.3 ✔ tidyr 1.3.1
## ✔ purrr 1.0.2
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::first() masks xts::first()
## ✖ dplyr::lag() masks stats::lag()
## ✖ dplyr::last() masks xts::last()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors
library(timeSeries)
## Cargando paquete requerido: timeDate
##
## Adjuntando el paquete: 'timeSeries'
##
## The following object is masked from 'package:dplyr':
##
## lag
##
## The following object is masked from 'package:zoo':
##
## time<-
##
## The following objects are masked from 'package:graphics':
##
## lines, points
library(tseries)
library(zoo)
library(xts)
library(readxl)
library(PerformanceAnalytics)
##
## Adjuntando el paquete: 'PerformanceAnalytics'
##
## The following objects are masked from 'package:timeDate':
##
## kurtosis, skewness
##
## The following object is masked from 'package:graphics':
##
## legend
library(ggplot2)
library(fPortfolio)
## Warning: package 'fPortfolio' was built under R version 4.4.1
## Cargando paquete requerido: fBasics
##
## Adjuntando el paquete: 'fBasics'
##
## The following objects are masked from 'package:PerformanceAnalytics':
##
## kurtosis, skewness
##
## The following object is masked from 'package:TTR':
##
## volatility
##
## Cargando paquete requerido: fAssets
library(PortfolioAnalytics)
## Cargando paquete requerido: foreach
##
## Adjuntando el paquete: 'foreach'
##
## The following objects are masked from 'package:purrr':
##
## accumulate, when
library(copula)
##
## Adjuntando el paquete: 'copula'
##
## The following object is masked from 'package:fPortfolio':
##
## getSigma
##
## The following object is masked from 'package:lubridate':
##
## interval
#install.packages("dygraphs")
library(dygraphs)
library(forecast)
## Warning: package 'forecast' was built under R version 4.4.1
library(ggplot.multistats)
## Warning: package 'ggplot.multistats' was built under R version 4.4.1
library(PerformanceAnalytics)
library(foreign)
library(ggfortify)
## Warning: package 'ggfortify' was built under R version 4.4.1
## Registered S3 methods overwritten by 'ggfortify':
## method from
## autoplot.Arima forecast
## autoplot.acf forecast
## autoplot.ar forecast
## autoplot.bats forecast
## autoplot.decomposed.ts forecast
## autoplot.ets forecast
## autoplot.forecast forecast
## autoplot.stl forecast
## autoplot.ts forecast
## fitted.ar forecast
## fortify.ts forecast
## residuals.ar forecast
library(gridExtra)
## Warning: package 'gridExtra' was built under R version 4.4.1
##
## Adjuntando el paquete: 'gridExtra'
##
## The following object is masked from 'package:dplyr':
##
## combine
library(seasonal)
## Warning: package 'seasonal' was built under R version 4.4.1
##
## Adjuntando el paquete: 'seasonal'
##
## The following objects are masked from 'package:timeSeries':
##
## outlier, series
##
## The following object is masked from 'package:tibble':
##
## view
#install.packages("rugarch")
library(rugarch)
## Cargando paquete requerido: parallel
##
## Adjuntando el paquete: 'rugarch'
##
## The following objects are masked from 'package:fBasics':
##
## qgh, qnig
##
## The following object is masked from 'package:purrr':
##
## reduce
##
## The following object is masked from 'package:stats':
##
## sigma
library(ggplot2)
library(readxl)
library(tseries)
library(forecast)
library(ggplot.multistats)
library(PerformanceAnalytics)
library(foreign)
library(ggfortify)
library(gridExtra)
library(seasonal)
library(lattice)
library(zoo)
library(urca)
## Warning: package 'urca' was built under R version 4.4.1
library(dynlm)
## Warning: package 'dynlm' was built under R version 4.4.1
# Define el nuevo portafolio
cartera <- c("PM","NEM","KR", "PFE","AMZN","XOM","WMT","PG","CL","IBM")
Precios_i <- NULL
for (Cabecera_i in cartera)
Precios_i <- cbind(Precios_i, getSymbols(Cabecera_i, from = "2010-01-01",to="2024-05-31", auto.assign = FALSE)[, 6])
# Renombra las columnas con los nombres de las acciones
colnames(Precios_i) <- cartera
Retorno_i <- na.omit(Return.calculate(Precios_i,method = "log")) # Calculamos retornos mediante logaritmos
RetPort_i <- as.timeSeries(Retorno_i) # #Convertimos los retornos en series de tiempo
colnames(Retorno_i) <- c("PM","NEM","KR", "PFE","AMZN","XOM","WMT","PG","CL","IBM")
peso_i <-c(0.0612,0.0751,0.0898,0.1168,0.0314,0.0498,0.1868,0.1966,0.1327,0.0598)
Retorno_portafolio_i <- as.numeric(peso_i%*%t(Retorno_i))
Retorno_portafolio_i <- xts(Retorno_portafolio_i,order.by = index(Retorno_i))
names(Retorno_portafolio_i)<- c("Retorno del Portafolio")
ggplot(data = Retorno_portafolio_i, aes(x = index(Retorno_portafolio_i))) +
geom_line(aes(y = `Retorno del Portafolio`, color = "Retorno del Portafolio")) +
labs(x = "Periodos", y = "Retornos", color = "Acción") +
scale_color_manual(values = c("Retorno del Portafolio" = "slategray3")) +
theme_minimal() +
theme(
plot.title = element_text(hjust = 0.6), # Centrar el tÃtulo
) +
ggtitle("Retornos del Portafolio")
#Portafolio con pesos iguales
peso_i <-c(0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1)
Retorno_portafolio_iguales <- as.numeric(peso_i%*%t(Retorno_i))
Retorno_portafolio_iguales <- xts(Retorno_portafolio_iguales,order.by = index(Retorno_i))
names(Retorno_portafolio_iguales)<- c("Retorno del Portafolio con Pesos Iguales")
ggplot(data = Retorno_portafolio_iguales, aes(x = index(Retorno_portafolio_iguales))) +
geom_line(aes(y = Retorno_portafolio_iguales$`Retorno del Portafolio con Pesos Iguales`, color = "Portafolio")) +
labs(x = "Periodos", y = "Retornos", color = "Acción") +
scale_color_manual(values = c("Portafolio" = "#11FFF4")) +
theme_minimal() +
theme(
plot.title = element_text(hjust = 0.5), # Centrar el tÃtulo
) +
ggtitle("Retornos del Portafolio con Pesos Iguales")
## Don't know how to automatically pick scale for object of type <xts/zoo>.
## Defaulting to continuous.
#--------------------------------------------------------------------
mean_portafolio_igual <- mean(Retorno_portafolio_iguales)
sd_portafolio_igual <- sd(Retorno_portafolio_iguales)
cat("Media:", mean_portafolio_igual, "\n")
## Media: 0.000377742
cat("Desviación Estándar:", sd_portafolio_igual, "\n")
## Desviación Estándar: 0.008782236
#ESTIMACION DE LOS MODELOS NO LINEALES TAR, SETAR, STAR y Modelo de Markov Switching del
#Retorno del Portafolio de minima varianza.
#install.packages(c("TSA", "tsDyn", "MSwM"))
#install.packages("mrstar")
#library(mrstar)
library(TSA)
## Warning: package 'TSA' was built under R version 4.4.1
## Registered S3 methods overwritten by 'TSA':
## method from
## fitted.Arima forecast
## plot.Arima forecast
##
## Adjuntando el paquete: 'TSA'
## The following objects are masked from 'package:fBasics':
##
## kurtosis, skewness
## The following objects are masked from 'package:PerformanceAnalytics':
##
## kurtosis, skewness
## The following objects are masked from 'package:timeDate':
##
## kurtosis, skewness
## The following object is masked from 'package:readr':
##
## spec
## The following objects are masked from 'package:stats':
##
## acf, arima
## The following object is masked from 'package:utils':
##
## tar
library(tsDyn)
## Warning: package 'tsDyn' was built under R version 4.4.1
library(MSwM)
## Warning: package 'MSwM' was built under R version 4.4.1
# Ajustar el modelo TAR
tar_model <- setar(Retorno_portafolio_i, m = 2, thDelay = 1, trim = 0.1, model = "TAR")
summary(tar_model)
##
## Non linear autoregressive model
##
## SETAR model ( 2 regimes)
## Coefficients:
## Low regime:
## const.L phiL.1 phiL.2
## 0.001222685 -0.242885314 0.032053988
##
## High regime:
## const.H phiH.1 phiH.2
## 0.0002197447 -0.0247513436 0.0550748846
##
## Threshold:
## -Variable: Z(t) = + (0) X(t)+ (1)X(t-1)
## -Value: -0.007886
## Proportion of points in low regime: 11.7% High regime: 88.3%
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.08723346 -0.00399807 0.00018547 0.00447199 0.08293141
##
## Fit:
## residuals variance = 7.032e-05, AIC = -34650, MAPE = 357.5%
##
## Coefficient(s):
##
## Estimate Std. Error t value Pr(>|t|)
## const.L 0.00122269 0.00083830 1.4585 0.1448
## phiL.1 -0.24288531 0.03028417 -8.0202 1.413e-15 ***
## phiL.2 0.03205399 0.05211167 0.6151 0.5385
## const.H 0.00021974 0.00015777 1.3928 0.1638
## phiH.1 -0.02475134 0.01976100 -1.2525 0.2105
## phiH.2 0.05507488 0.02310629 2.3835 0.0172 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Threshold
## Variable: Z(t) = + (0) X(t) + (1) X(t-1)
##
## Value: -0.007886
# Ajustar el modelo SETAR
setar_model <- setar(Retorno_portafolio_i, m=2, thDelay=1)
summary(setar_model)
##
## Non linear autoregressive model
##
## SETAR model ( 2 regimes)
## Coefficients:
## Low regime:
## const.L phiL.1 phiL.2
## 0.0009257229 -0.2070494750 0.0234854716
##
## High regime:
## const.H phiH.1 phiH.2
## 0.0001324254 -0.0210747754 0.0675743466
##
## Threshold:
## -Variable: Z(t) = + (0) X(t)+ (1)X(t-1)
## -Value: -0.005496
## Proportion of points in low regime: 17.75% High regime: 82.25%
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.08733226 -0.00402851 0.00019088 0.00453013 0.08239812
##
## Fit:
## residuals variance = 7.045e-05, AIC = -34643, MAPE = 379.5%
##
## Coefficient(s):
##
## Estimate Std. Error t value Pr(>|t|)
## const.L 0.00092572 0.00061949 1.4943 0.135176
## phiL.1 -0.20704947 0.02742111 -7.5507 5.447e-14 ***
## phiL.2 0.02348547 0.04546000 0.5166 0.605454
## const.H 0.00013243 0.00017093 0.7747 0.438549
## phiH.1 -0.02107478 0.02082221 -1.0121 0.311544
## phiH.2 0.06757435 0.02498748 2.7043 0.006876 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Threshold
## Variable: Z(t) = + (0) X(t) + (1) X(t-1)
##
## Value: -0.005496
# Ajustar el modelo STAR
star_model <- lstar(Retorno_portafolio_i, m=2,steps = 1, thDelay=1, trace = TRUE)
## Using maximum autoregressive order for low regime: mL = 2
## Using maximum autoregressive order for high regime: mH = 2
## Performing grid search for starting values...
## Starting values fixed: gamma = 41.61538 , th = -0.008876243 ; SSE = 0.2508577
## Optimization algorithm converged
## Optimized values fixed for regime 2 : gamma = 41.61539 , th = -0.07661486 ; SSE = -0.8524603
summary(star_model)
##
## Non linear autoregressive model
##
## LSTAR model
## Coefficients:
## Low regime:
## const.L phiL.1 phiL.2
## 0.2202097 -1.9361530 1.9513001
##
## High regime:
## const.H phiH.1 phiH.2
## -0.2291959 1.9910027 -1.6262140
##
## Smoothing parameter: gamma = 41.62
##
## Threshold
## Variable: Z(t) = + (0) X(t) + (1) X(t-1)
##
## Value: -0.07661
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.08634338 -0.00395042 0.00028234 0.00448395 0.07761158
##
## Fit:
## residuals variance = 6.843e-05, AIC = -34747, MAPE = 379.3%
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|z|)
## const.L 0.220210 0.201837 1.0910 0.2752616
## phiL.1 -1.936153 0.168405 -11.4970 < 2.2e-16 ***
## phiL.2 1.951300 1.702487 1.1461 0.2517343
## const.H -0.229196 0.215251 -1.0648 0.2869746
## phiH.1 1.991003 0.372216 5.3491 8.841e-08 ***
## phiH.2 -1.626214 1.414243 -1.1499 0.2501920
## gamma 41.615386 11.601404 3.5871 0.0003344 ***
## th -0.076615 0.017455 -4.3893 1.137e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Non-linearity test of full-order LSTAR model against full-order AR model
## F = 34.038 ; p-value = 2.2632e-15
##
## Threshold
## Variable: Z(t) = + (0) X(t) + (1) X(t-1)
# Ajustar el modelo de Cambio de Régimen de Markov
mod <- lm(Retorno_portafolio_i ~ lag(Retorno_portafolio_i, -1))
msm_model <- msmFit(mod, k = 2, sw = c(TRUE,TRUE,TRUE))
summary(msm_model)
## Markov Switching Model
##
## Call: msmFit(object = mod, k = 2, sw = c(TRUE, TRUE, TRUE))
##
## AIC BIC logLik
## -25291.75 -25234.18 12649.87
##
## Coefficients:
##
## Regime 1
## ---------
## Estimate Std. Error t value Pr(>|t|)
## (Intercept)(S) -0.0011 0.0008 -1.3750 0.1691314
## lag(Retorno_portafolio_i, -1)(S) -0.1541 0.0458 -3.3646 0.0007665 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.01649121
## Multiple R-squared: 0.02269
##
## Standardized Residuals:
## Min Q1 Med Q3 Max
## -7.231060e-02 -1.697820e-04 8.766519e-05 4.295236e-04 8.646552e-02
##
## Regime 2
## ---------
## Estimate Std. Error t value Pr(>|t|)
## (Intercept)(S) 0.0006 0.0001 6.0000 1.973e-09 ***
## lag(Retorno_portafolio_i, -1)(S) -0.0354 0.0190 -1.8632 0.06243 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.006165375
## Multiple R-squared: 0.001324
##
## Standardized Residuals:
## Min Q1 Med Q3 Max
## -0.0187846640 -0.0033700469 -0.0000130112 0.0034884972 0.0187803078
##
## Transition probabilities:
## Regime 1 Regime 2
## Regime 1 0.92171466 0.01263725
## Regime 2 0.07828534 0.98736275
plot(tar_model)
plot(setar_model)
plot(star_model)
par(mar=c(3,3,3,3))
plotProb(msm_model, which=1)
plotProb(msm_model, which=2)
plotDiag(msm_model, regime=1, which=1)
plotDiag(msm_model, regime=1, which=2)
plotDiag(msm_model, regime=1, which=3)
plotProb(msm_model, which=3)
plot(msm_model)
AIC(tar_model)
## [1] -34649.86
AIC(setar_model)
## [1] -34643.41
AIC(star_model)
## [1] -34746.74
AIC(msm_model)
## [1] -25287.75
#---------------------
BIC(tar_model)
## [1] -34606.5
BIC(setar_model)
## [1] -34600.04
BIC(star_model)
## [1] -34697.17
#BIC(msm_model)
#ESTIMACION DE LOS MODELOS NO LINEALES TAR, SETAR, STAR y Modelo de Markov Switching del
#Retorno del Portafolio de Pesos Iguales.
#install.packages(c("TSA", "tsDyn", "MSwM"))
# Ajustar el modelo TAR
tar_model_i <- setar(Retorno_portafolio_iguales, m = 2, thDelay = 1, trim = 0.1, model = "TAR")
summary(tar_model_i)
##
## Non linear autoregressive model
##
## SETAR model ( 2 regimes)
## Coefficients:
## Low regime:
## const.L phiL.1 phiL.2
## 0.002884967 -0.237233034 0.132927059
##
## High regime:
## const.H phiH.1 phiH.2
## 0.0002575588 -0.0239210353 0.0534432117
##
## Threshold:
## -Variable: Z(t) = + (0) X(t)+ (1)X(t-1)
## -Value: -0.009195
## Proportion of points in low regime: 9.99% High regime: 90.01%
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.08906605 -0.00425449 0.00036649 0.00460666 0.07770229
##
## Fit:
## residuals variance = 7.56e-05, AIC = -34388, MAPE = 144.9%
##
## Coefficient(s):
##
## Estimate Std. Error t value Pr(>|t|)
## const.L 0.00288497 0.00096361 2.9939 0.002773 **
## phiL.1 -0.23723303 0.03226452 -7.3528 2.389e-13 ***
## phiL.2 0.13292706 0.05384023 2.4689 0.013598 *
## const.H 0.00025756 0.00016044 1.6054 0.108499
## phiH.1 -0.02392104 0.01924399 -1.2430 0.213934
## phiH.2 0.05344321 0.02271903 2.3524 0.018708 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Threshold
## Variable: Z(t) = + (0) X(t) + (1) X(t-1)
##
## Value: -0.009195
# Ajustar el modelo SETAR
setar_model_i <- setar(Retorno_portafolio_iguales, m=2, thDelay=1)
summary(setar_model_i)
##
## Non linear autoregressive model
##
## SETAR model ( 2 regimes)
## Coefficients:
## Low regime:
## const.L phiL.1 phiL.2
## 0.001969767 -0.207054660 0.101077577
##
## High regime:
## const.H phiH.1 phiH.2
## 0.0001602632 -0.0167137786 0.0678435545
##
## Threshold:
## -Variable: Z(t) = + (0) X(t)+ (1)X(t-1)
## -Value: -0.006659
## Proportion of points in low regime: 15.62% High regime: 84.38%
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.08907846 -0.00430010 0.00038814 0.00462364 0.07748062
##
## Fit:
## residuals variance = 7.567e-05, AIC = -34384, MAPE = 148%
##
## Coefficient(s):
##
## Estimate Std. Error t value Pr(>|t|)
## const.L 0.00196977 0.00070944 2.7765 0.005523 **
## phiL.1 -0.20705466 0.02909570 -7.1163 1.33e-12 ***
## phiL.2 0.10107758 0.04703699 2.1489 0.031709 *
## const.H 0.00016026 0.00017293 0.9268 0.354117
## phiH.1 -0.01671378 0.02014409 -0.8297 0.406757
## phiH.2 0.06784355 0.02471327 2.7452 0.006077 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Threshold
## Variable: Z(t) = + (0) X(t) + (1) X(t-1)
##
## Value: -0.006659
# Ajustar el modelo STAR
star_model_i <- lstar(Retorno_portafolio_iguales, m=2, thDelay=1,trace = TRUE)
## Using maximum autoregressive order for low regime: mL = 2
## Using maximum autoregressive order for high regime: mH = 2
## Performing grid search for starting values...
## Starting values fixed: gamma = 41.61538 , th = -0.009165186 ; SSE = 0.2688339
## Optimization algorithm converged
## Optimized values fixed for regime 2 : gamma = 41.61539 , th = -0.06347237 ; SSE = 0.2671526
summary(star_model_i)
## Warning in vcov.lstar(object): Hessian negative-semi definite
## Warning in sqrt(diag(vc)): Se han producido NaNs
##
## Non linear autoregressive model
##
## LSTAR model
## Coefficients:
## Low regime:
## const.L phiL.1 phiL.2
## 0.1688292 -1.4183783 1.9368088
##
## High regime:
## const.H phiH.1 phiH.2
## -0.1807432 1.4978238 -1.5526125
##
## Smoothing parameter: gamma = 41.62
##
## Threshold
## Variable: Z(t) = + (0) X(t) + (1) X(t-1)
##
## Value: -0.06347
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.08800104 -0.00420335 0.00041312 0.00462213 0.07591407
##
## Fit:
## residuals variance = 7.37e-05, AIC = -34478, MAPE = 136.1%
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|z|)
## const.L 0.168829 NaN NaN NaN
## phiL.1 -1.418378 0.126803 -11.186 < 2.2e-16 ***
## phiL.2 1.936809 NaN NaN NaN
## const.H -0.180743 NaN NaN NaN
## phiH.1 1.497824 0.083439 17.951 < 2.2e-16 ***
## phiH.2 -1.552613 NaN NaN NaN
## gamma 41.615385 NaN NaN NaN
## th -0.063472 NaN NaN NaN
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Non-linearity test of full-order LSTAR model against full-order AR model
## F = 32.095 ; p-value = 1.5258e-14
##
## Threshold
## Variable: Z(t) = + (0) X(t) + (1) X(t-1)
# Ajustar el modelo de Cambio de Régimen de Markov
mod_i <- lm(Retorno_portafolio_iguales ~ lag(Retorno_portafolio_iguales, -1))
msm_model_i <- msmFit(mod_i, k = 2, sw = c(TRUE, TRUE, TRUE))
summary(msm_model_i)
## Markov Switching Model
##
## Call: msmFit(object = mod_i, k = 2, sw = c(TRUE, TRUE, TRUE))
##
## AIC BIC logLik
## -25022.14 -24964.58 12515.07
##
## Coefficients:
##
## Regime 1
## ---------
## Estimate Std. Error t value Pr(>|t|)
## (Intercept)(S) -0.0011 0.0007 -1.5714 0.116090
## lag(Retorno_portafolio_iguales, -1)(S) -0.1317 0.0408 -3.2279 0.001247 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.01575909
## Multiple R-squared: 0.01685
##
## Standardized Residuals:
## Min Q1 Med Q3 Max
## -7.745831e-02 -1.883186e-04 8.387469e-05 4.629094e-04 7.909368e-02
##
## Regime 2
## ---------
## Estimate Std. Error t value Pr(>|t|)
## (Intercept)(S) 0.0007 0.0001 7.0000 2.56e-12 ***
## lag(Retorno_portafolio_iguales, -1)(S) -0.0348 0.0199 -1.7487 0.08034 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.006271084
## Multiple R-squared: 0.001268
##
## Standardized Residuals:
## Min Q1 Med Q3 Max
## -1.994376e-02 -3.328413e-03 3.271578e-08 3.341198e-03 1.978669e-02
##
## Transition probabilities:
## Regime 1 Regime 2
## Regime 1 0.94703814 0.01121435
## Regime 2 0.05296186 0.98878565
plot(tar_model_i)
plot(setar_model_i)
plot(star_model_i)
par(mar=c(3,3,3,3))
plotProb(msm_model_i, which=1)
plotProb(msm_model_i, which=2)
plotDiag(msm_model_i, regime=1, which=1)
plotDiag(msm_model_i, regime=1, which=2)
plotDiag(msm_model_i, regime=1, which=3)
plotProb(msm_model_i, which=3)
plot(msm_model_i)
AIC(tar_model_i)
## [1] -34387.66
AIC(setar_model_i)
## [1] -34384.11
AIC(star_model_i)
## [1] -34477.85
AIC(msm_model_i)
## [1] -25018.14
#---------------------
BIC(tar_model_i)
## [1] -34344.29
BIC(setar_model_i)
## [1] -34340.74
BIC(star_model_i)
## [1] -34428.29
#BIC(msm_model_i)
#-----------------------------------------------------------------------------------------------------------------
#--------------APLICACION DE LOS MODELOS NO LINEALES A LOS PRECIOS DE LA ACCION DE PM ----------------------------
#-----------------------------------------------------------------------------------------------------------------
PM <- c("PM")
Precios_PM <- NULL
for (Cabecera_PM in PM)
Precios_PM <- cbind(Precios_PM, getSymbols(Cabecera_PM, from = "2023-01-01",to="2024-05-31", auto.assign = FALSE)[, 6])
# Renombra las columnas con los nombres de las acciones
colnames(Precios_PM) <- PM
dygraph(Precios_PM,main = "Precio de la Accion ",ylab = "Precio Ajustado",xlab = "Periodo") %>% dyRangeSelector()
# Ajustar el modelo TAR
tar_model_pm <- setar(Precios_PM, m = 2, thDelay = 1, trim = 0.1, model = "TAR")
## Warning: Possible unit root in the high regime. Roots are: 0.939 4.0577
summary(tar_model_pm)
##
## Non linear autoregressive model
##
## SETAR model ( 2 regimes)
## Coefficients:
## Low regime:
## const.L phiL.1 phiL.2
## 2.65861474 1.03180727 -0.06100659
##
## High regime:
## const.H phiH.1 phiH.2
## -8.0270815 0.8185734 0.2624684
##
## Threshold:
## -Variable: Z(t) = + (0) X(t)+ (1)X(t-1)
## -Value: 92.68
## Proportion of points in low regime: 84.94% High regime: 15.06%
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.968210 -0.561759 -0.011703 0.528850 3.519580
##
## Fit:
## residuals variance = 0.83, AIC = -52, MAPE = 0.7815%
##
## Coefficient(s):
##
## Estimate Std. Error t value Pr(>|t|)
## const.L 2.658615 2.088844 1.2728 0.20395
## phiL.1 1.031807 0.059436 17.3600 < 2.2e-16 ***
## phiL.2 -0.061007 0.062066 -0.9829 0.32632
## const.H -8.027081 6.581935 -1.2196 0.22346
## phiH.1 0.818573 0.119572 6.8459 3.446e-11 ***
## phiH.2 0.262468 0.142362 1.8437 0.06608 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Threshold
## Variable: Z(t) = + (0) X(t) + (1) X(t-1)
##
## Value: 92.68
# Ajustar el modelo SETAR
setar_model_pm <- setar(Precios_PM, m=2, thDelay=1)
summary(setar_model_pm)
##
## Non linear autoregressive model
##
## SETAR model ( 2 regimes)
## Coefficients:
## Low regime:
## const.L phiL.1 phiL.2
## 3.4177523 0.7849597 0.1787806
##
## High regime:
## const.H phiH.1 phiH.2
## 1.75283877 1.04561098 -0.06550739
##
## Threshold:
## -Variable: Z(t) = + (0) X(t)+ (1)X(t-1)
## -Value: 87.25
## Proportion of points in low regime: 21.59% High regime: 78.41%
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.333270 -0.548468 0.016512 0.524379 3.569873
##
## Fit:
## residuals variance = 0.8313, AIC = -51, MAPE = 0.7792%
##
## Coefficient(s):
##
## Estimate Std. Error t value Pr(>|t|)
## const.L 3.417752 8.406634 0.4066 0.6846
## phiL.1 0.784960 0.120118 6.5349 2.265e-10 ***
## phiL.2 0.178781 0.142403 1.2555 0.2102
## const.H 1.752839 1.959415 0.8946 0.3716
## phiH.1 1.045611 0.059416 17.5981 < 2.2e-16 ***
## phiH.2 -0.065507 0.061861 -1.0589 0.2904
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Threshold
## Variable: Z(t) = + (0) X(t) + (1) X(t-1)
##
## Value: 87.25
# Ajustar el modelo STAR
star_model_pm <- lstar(Precios_PM, m=2,steps = 1, thDelay=1,trace = TRUE)
## Using maximum autoregressive order for low regime: mL = 2
## Using maximum autoregressive order for high regime: mH = 2
## Performing grid search for starting values...
## Starting values fixed: gamma = 100 , th = 92.70527 ; SSE = 294.254
## Grid search selected lower/upper bound gamma (was: 1 100 ]).
## Might try to widen bound with arg: 'starting.control=list(gammaInt=c(1,200))'
## Optimization algorithm converged
## Optimized values fixed for regime 2 : gamma = 100.0007 , th = 92.70195 ; SSE = 294.2382
summary(star_model_pm)
##
## Non linear autoregressive model
##
## LSTAR model
## Coefficients:
## Low regime:
## const.L phiL.1 phiL.2
## 2.74101231 1.03169360 -0.06183473
##
## High regime:
## const.H phiH.1 phiH.2
## -10.5067511 -0.2130023 0.3214743
##
## Smoothing parameter: gamma = 100
##
## Threshold
## Variable: Z(t) = + (0) X(t) + (1) X(t-1)
##
## Value: 92.7
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.9757000 -0.5578334 -0.0095117 0.5221244 3.5234265
##
## Fit:
## residuals variance = 0.8312, AIC = -49, MAPE = 0.7826%
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|z|)
## const.L 2.741012 2.083541 1.3156 0.18832
## phiL.1 1.031694 0.059005 17.4847 < 2e-16 ***
## phiL.2 -0.061835 0.061627 -1.0034 0.31568
## const.H -10.506751 6.938040 -1.5144 0.12993
## phiH.1 -0.213002 0.134452 -1.5842 0.11314
## phiH.2 0.321474 0.157131 2.0459 0.04077 *
## gamma 100.000715 117.572233 0.8505 0.39502
## th 92.701949 0.024361 3805.2696 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Non-linearity test of full-order LSTAR model against full-order AR model
## F = 0.47338 ; p-value = 0.62329
##
## Threshold
## Variable: Z(t) = + (0) X(t) + (1) X(t-1)
# Ajustar el modelo de Cambio de Régimen de Markov
mod_pm <- lm(Precios_PM ~ lag(Precios_PM, -1))
msm_model_pm <- msmFit(mod_pm, k = 2, sw = c(TRUE, TRUE,TRUE))
summary(msm_model_pm)
## Markov Switching Model
##
## Call: msmFit(object = mod_pm, k = 2, sw = c(TRUE, TRUE, TRUE))
##
## AIC BIC logLik
## 931.8599 970.7917 -461.93
##
## Coefficients:
##
## Regime 1
## ---------
## Estimate Std. Error t value Pr(>|t|)
## (Intercept)(S) 6.9012 8.8572 0.7792 0.4359
## lag(Precios_PM, -1)(S) 0.9230 0.0976 9.4570 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.324246
## Multiple R-squared: 0.8355
##
## Standardized Residuals:
## Min Q1 Med Q3 Max
## -3.07663523 -0.22617953 -0.01568988 0.22841093 4.41334362
##
## Regime 2
## ---------
## Estimate Std. Error t value Pr(>|t|)
## (Intercept)(S) 3.5767 2.6752 1.337 0.1812
## lag(Precios_PM, -1)(S) 0.9599 0.0294 32.650 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7127481
## Multiple R-squared: 0.9457
##
## Standardized Residuals:
## Min Q1 Med Q3 Max
## -1.227027742 -0.471963274 -0.009326425 0.497600194 1.289352030
##
## Transition probabilities:
## Regime 1 Regime 2
## Regime 1 0.4875134 0.1812671
## Regime 2 0.5124866 0.8187329
plot(tar_model_pm)
plot(setar_model_pm)
plot(star_model_pm)
par(mar=c(3,3,3,3))
plotProb(msm_model_pm, which=1)
plotProb(msm_model_pm, which=2)
plotDiag(msm_model_pm, regime=1, which=1)
plotDiag(msm_model_pm, regime=1, which=2)
plotDiag(msm_model_pm, regime=1, which=3)
plotProb(msm_model_pm, which=3)
plotDiag(msm_model_pm, regime=2, which=1)
plotDiag(msm_model_pm, regime=2, which=2)
plotDiag(msm_model_pm, regime=2, which=3)
plot(msm_model_pm)
AIC(tar_model_pm)
## [1] -51.95331
AIC(setar_model_pm)
## [1] -51.40942
AIC(star_model_pm)
## [1] -49.45712
AIC(msm_model_pm)
## [1] 935.8599
#---------------------
BIC(tar_model_pm)
## [1] -24.86823
BIC(setar_model_pm)
## [1] -24.32434
BIC(star_model_pm)
## [1] -18.50275
#BIC(msm_model_i)