library(lubridate)
## 
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library(tidyverse)
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## v readr   2.0.2     v forcats 0.5.1
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library(tseries)
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library(forecast)
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library(lmtest)
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library(quantmod)
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library(rugarch)
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library(fGarch)
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library(timsac)
library(FinTS)
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library(dynlm)
## Warning: package 'dynlm' was built under R version 4.1.3
library(tidyr)
library(dplyr)
library(readxl)

Data_base_research <- read_excel("C:/Users/rchang/Downloads/Data_base_research.xlsx")
head(Data_base_research)
inciso1 <- ts(Data_base_research$CO2_Emission_Percapita, start = c(1966, 1), end = c(2013, 1), frequency = 1  )
plot(inciso1)

acf(inciso1)

pacf(inciso1)

adf.test(inciso1)
## Warning in adf.test(inciso1): p-value greater than printed p-value
## 
##  Augmented Dickey-Fuller Test
## 
## data:  inciso1
## Dickey-Fuller = -0.10263, Lag order = 3, p-value = 0.99
## alternative hypothesis: stationary

La serie de emisiones de CO2 percapita de Honduras No es estacionaria.

modelosarima1=auto.arima(inciso1,stepwise = FALSE,approximation = FALSE)
modelosarima1
## Series: inciso1 
## ARIMA(1,1,0) with drift 
## 
## Coefficients:
##           ar1   drift
##       -0.2691  0.0185
## s.e.   0.1682  0.0063
## 
## sigma^2 = 0.003131:  log likelihood = 69.8
## AIC=-133.6   AICc=-133.05   BIC=-128.05

El mejor modelo es un autoregresivo 0, integrado 1 y media móvil 1.

residuossarima1=residuals(modelosarima1)
plot(residuossarima1)

Box.test(residuossarima1,type="Ljung-Box")
## 
##  Box-Ljung test
## 
## data:  residuossarima1
## X-squared = 0.0003934, df = 1, p-value = 0.9842

LA hipótesis nula no se rechaza y nos muestra ausencia de autocorrelación. EN otras palabras, los residuos se distribuyen independientemente.

Proyección a 10 datos

forecast_data <- forecast(modelosarima1, 10, level=c(80,95) ) 


print(forecast_data)
##      Point Forecast    Lo 80    Hi 80    Lo 95    Hi 95
## 2014       1.191553 1.119839 1.263267 1.081876 1.301230
## 2015       1.225350 1.136524 1.314177 1.089502 1.361199
## 2016       1.239705 1.133833 1.345577 1.077788 1.401622
## 2017       1.259292 1.139424 1.379161 1.075969 1.442616
## 2018       1.277471 1.144918 1.410025 1.074748 1.480195
## 2019       1.296030 1.151942 1.440117 1.075667 1.516392
## 2020       1.314486 1.159712 1.469259 1.077780 1.551191
## 2021       1.332969 1.168203 1.497735 1.080982 1.584956
## 2022       1.351445 1.177259 1.525631 1.085051 1.617840
## 2023       1.369923 1.186801 1.553046 1.089862 1.649985
plot(forecast_data)

dataframe<-data.frame(forecast_data)
chartSeries(inciso1)

model1=auto.arima(inciso1,stepwise = FALSE,approximation = FALSE)
summary(model1)
## Series: inciso1 
## ARIMA(1,1,0) with drift 
## 
## Coefficients:
##           ar1   drift
##       -0.2691  0.0185
## s.e.   0.1682  0.0063
## 
## sigma^2 = 0.003131:  log likelihood = 69.8
## AIC=-133.6   AICc=-133.05   BIC=-128.05
## 
## Training set error measures:
##                        ME       RMSE        MAE       MPE     MAPE      MASE
## Training set 0.0001588804 0.05418177 0.04110976 -1.250726 7.132555 0.9379411
##                      ACF1
## Training set -0.002775629

Claramente observamos que estamos ante un modelo ARIMA (0,1,1).

Revisar si hay efectos ARCH El primer paso es conocer el orden de nuestro modelo ARMA, de esta forma crearemos nuestro mejor ARIMA y checar el orden de nuestro modelo.

checkresiduals(model1)

## 
##  Ljung-Box test
## 
## data:  Residuals from ARIMA(1,1,0) with drift
## Q* = 5.0716, df = 8, p-value = 0.7499
## 
## Model df: 2.   Total lags used: 10
residuosmodel1=residuals(model1)
chartSeries(residuosmodel1)

acf(residuosmodel1)

pacf(residuosmodel1)

La serie no es estacionaria, lo cual nos indica el test de Dickey-Fuller

adf.test(residuosmodel1)
## 
##  Augmented Dickey-Fuller Test
## 
## data:  residuosmodel1
## Dickey-Fuller = -2.6737, Lag order = 3, p-value = 0.3051
## alternative hypothesis: stationary

Observamos que nuestra varianza no es constante, ya que los errores al cuadrado muestran que al pasar los días la varianza llega a ser heterocedastica, por lo que ahora haremos nuestra regresión. Esto para observar si nos enfrentamos a un modelo ARCH o no.

residuosmodel1cuad=residuosmodel1*residuosmodel1
chartSeries(residuosmodel1cuad)

acf(residuosmodel1cuad)

pacf(residuosmodel1cuad)

adf.test(residuosmodel1cuad)
## 
##  Augmented Dickey-Fuller Test
## 
## data:  residuosmodel1cuad
## Dickey-Fuller = -0.30417, Lag order = 3, p-value = 0.9867
## alternative hypothesis: stationary

No es estacionaria la serie de tiempo con los residuos al cuadrado.

La siguiente prueba nos indica si hay efectos ARCH, por lo que corraboramos de que no hay efectos ARCH.

#model1reg=dynlm(residuosmodel1cuad~L(residuosmodel1cuad),data=retornosdiaWMT)
#summary(model1reg)