ANALISIS ARIMA DE LA PRODUCCION DE GAS
Paquetes
library(TSA)##
## Attaching package: 'TSA'## The following objects are masked from 'package:stats':
##
## acf, arima## The following object is masked from 'package:utils':
##
## tarlibrary(ggfortify)## Loading required package: ggplot2library(forecast)
library(fpp)## Loading required package: fma## Loading required package: expsmooth## Loading required package: lmtest## Loading required package: zoo##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric## Loading required package: tserieslibrary(seasonal)
library(fpp2)##
## Attaching package: 'fpp2'## The following objects are masked from 'package:fpp':
##
## ausair, ausbeer, austa, austourists, debitcards, departures,
## elecequip, euretail, guinearice, oil, sunspotarea, usmeleclibrary(gridExtra)
library(urca)
library(foreign)
library(vars)## Loading required package: MASS##
## Attaching package: 'MASS'## The following objects are masked from 'package:fma':
##
## cement, housing, petrol## Loading required package: strucchange## Loading required package: sandwichlibrary(zoo)
library(dynlm)
library(lmtest)
library(strucchange)
library(readxl)1. Breve descripcion de la serie elegida, asi como su frecuencia, unidad de medida, fuente, etc.
Serie: PG
2006-2018, incluye serie original, desestacionalizada.
Unidad de medida: Millones de pies cubicos.
Periodicidad: Mensual
Fuente: PEMEX. Dirección Corporativa de Finanzas. (www.inegi.org.mx)
2. Graficar los datos, analizar patrones y observaciones atipicas. Apoye su analisis con una descomposicion clasica.
base<-read_xls("C:/Users/rodar/OneDrive/Escritorio/SERIES/PRODUCCION DE GAS.xls")
PGN <-ts(base$PG, frequency = 12, start=c(2006,1))
autoplot(PGN) + xlab("Year")+ylab("Millones de pies cubicos") +
ggtitle('PRODUCCION NACIONAL DE GAS (PGN ORIGINAL)')
#Graficando para encontrar estacionalidad#
ggseasonplot(PGN)
ggseasonplot(PGN, polar = TRUE)
#Nos apoyamos de una descomposicion clasica#
fit<-decompose(PGN)
autoplot(fit)
3. Si es necesario, utilizar transformacion Box-Cox/logaritmos para estabilizar la varianza.
#No aplica la transformacion Box-Cox#logPGN<- log(PGN)
plot(logPGN)
Se utilizo la aplicacion de un logaritmo, ya que se va a estabilizar la varianza para visualizar el comportamiento de la serie.
4. En caso de estacionalidad, aplicar diferencias estacionales.
PGNdif<-diff(logPGN)
plot(PGNdif)
Demuestra estacionalidad la serie por lo que se aplico la diferencia para que la media se estabilizara.
BoxCox.ar(PGN)## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
PGNdiflog<-diff(logPGN)plot(PGNdiflog)
?? ?? sabemos que contiene un valor= 0 muy cerca de su centro por lo que sugiere este una transformacion logaritmica. el maximo esta al rededor 1.5
plot(PGN^1.5, type="o")
plot(diff(PGN^1.5), type="o")
plot(diff(PGNdiflog))
Se agregaron dos diferencias con logaritmo para estabilizar la serie, aqui se puede observar que se elevo al 1.5 para tener mejoras en la varianza como en la media.
5. Usar preba Dickey-Fuller para evaluar el orden de integracion de la serie. Diferenciar hasta que la serie sea estacionaria.
summary(ur.df(PGN))##
## ###############################################
## # Augmented Dickey-Fuller Test Unit Root Test #
## ###############################################
##
## Test regression none
##
##
## Call:
## lm(formula = z.diff ~ z.lag.1 - 1 + z.diff.lag)
##
## Residuals:
## Min 1Q Median 3Q Max
## -30279 -3129 1791 5072 13343
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## z.lag.1 -0.0003578 0.0034483 -0.104 0.917
## z.diff.lag -0.5865141 0.0673642 -8.707 7.52e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7949 on 141 degrees of freedom
## Multiple R-squared: 0.3499, Adjusted R-squared: 0.3407
## F-statistic: 37.94 on 2 and 141 DF, p-value: 6.535e-14
##
##
## Value of test-statistic is: -0.1038
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau1 -2.58 -1.95 -1.62Como podemos ver, nuestro valor de P= 6.535e-14 que nos indica un valor mayor a 0.5
6. Usar herramientas ACF, PACF, EACF y criterios de Akaike/ Bayes para construir propuestas de modelos.
ggAcf(PGNdiflog)
ggPacf(PGNdiflog)
eacf(PGNdiflog)## AR/MA
## 0 1 2 3 4 5 6 7 8 9 10 11 12 13
## 0 x o o o x x x x o x x x x o
## 1 x x o o o o x o o o o x x x
## 2 o x o o o o x o o o o x o o
## 3 x o o o o o o o o o o x x o
## 4 x o x o o o o o o o o x o o
## 5 x o x o o x o o o o o x o x
## 6 x o o o o x o o o o o x o o
## 7 x o o o o x o o o o o x x oggtsdisplay(PGNdiflog)
con respecto a la pruebas de correlacion y correlacion parcial, podemos observar que se pueden aplicar los siguientes modelos que serian un ar(2) o en su defecto un ma(2).
CRITERIO DE BAYES
PGN.2 <-armasubsets(y=PGNdiflog,nar= 12, nma=12, y.name="test", ar.method="ols")plot(PGN.2)
se puede aplicar una ar(2) o un ma(2)
propuesta <- Arima(PGNdiflog, order = c(2,1,2),method = "ML")
propuesta## Series: PGNdiflog
## ARIMA(2,1,2)
##
## Coefficients:
## ar1 ar2 ma1 ma2
## -0.0538 0.1592 -1.7584 0.7932
## s.e. 0.1422 0.1294 0.1080 0.1020
##
## sigma^2 estimated as 0.0017: log likelihood=252.57
## AIC=-495.14 AICc=-494.7 BIC=-480.32En la aplicacion de un ar(2) podemos ver que en el criterio de akaike es -497.7 y esto no esta diciendo que tan bien estan ajustados los datos para este modelo de ar.
propuesta2 <- Arima(PGNdiflog, order = c(1,1,1),method = "ML")
propuesta2## Series: PGNdiflog
## ARIMA(1,1,1)
##
## Coefficients:
## ar1 ma1
## -0.5993 -0.9672
## s.e. 0.0682 0.0208
##
## sigma^2 estimated as 0.001933: log likelihood=242.83
## AIC=-479.66 AICc=-479.48 BIC=-470.77De las dos propuestas se escoge el AR(2) por que la prueba de akakike ajustada es menor que el de la propuesta de AR(1) entonces se aprecia que la prueba de akaike ajustada tiene un valor de -479.48 y nos esta diciendo que en relacion con el AR(2) los datos se estan ajustando de una mejor manera ya que es mas pequeño el valor en el AR(1).
7. Como parte del diagnostico del modelo, analizar los residuos y aplicar la prueba Ljung-Box.
tsdiag(propuesta,gof=12, omit.initial=F)
tsdiag(propuesta2,gof=12, omit.initial=F)
Se ajustan mas los residuos en la propuesta dos que en la uno, porque en la pruebas de la ljung-box y la ACF se ven la variaciones mas estables, los valores de p son arriba de 0.5.
8. Usar la funcion auto.arima () y compare sus resultados con el inciso anterior.
propuesta.auto<-auto.arima(PGNdiflog)
propuesta.auto## Series: PGNdiflog
## ARIMA(1,0,1)(0,1,1)[12] with drift
##
## Coefficients:
## ar1 ma1 sma1 drift
## 0.3541 -0.6215 -0.8771 -1e-04
## s.e. 0.1867 0.1500 0.1474 1e-04
##
## sigma^2 estimated as 0.0006228: log likelihood=293.3
## AIC=-576.59 AICc=-576.12 BIC=-562.18checkresiduals(propuesta.auto)
##
## Ljung-Box test
##
## data: Residuals from ARIMA(1,0,1)(0,1,1)[12] with drift
## Q* = 14.063, df = 20, p-value = 0.8273
##
## Model df: 4. Total lags used: 24propuest.auto2 <- auto.arima(PGNdiflog, stepwise = FALSE, approximation = FALSE)
propuest.auto2## Series: PGNdiflog
## ARIMA(1,0,1)(0,1,1)[12] with drift
##
## Coefficients:
## ar1 ma1 sma1 drift
## 0.3541 -0.6215 -0.8771 -1e-04
## s.e. 0.1867 0.1500 0.1474 1e-04
##
## sigma^2 estimated as 0.0006228: log likelihood=293.3
## AIC=-576.59 AICc=-576.12 BIC=-562.18checkresiduals(propuest.auto2)
##
## Ljung-Box test
##
## data: Residuals from ARIMA(1,0,1)(0,1,1)[12] with drift
## Q* = 14.063, df = 20, p-value = 0.8273
##
## Model df: 4. Total lags used: 24Se puede observar que en las dos propuestas,la media ya es estable asi como los residuales.
9. Presente la ecuacion final y describa.
\[ Yt= 0.3541 e_1-0.6215e_{t-1}+et \] Tiene correlacion.
10. Crear un pronostico a dos años.
pronostico<- plot(forecast(propuesta.auto, h=24))
pronostico## $mean
## Jan Feb Mar Apr May
## 2018 -0.11331309 0.07759195 -0.05026112 0.01834441
## 2019 -0.01045285 -0.10360933 0.07994103 -0.05051619 0.01716726
## 2020 -0.01213535
## Jun Jul Aug Sep Oct
## 2018 -0.03545813 0.02092041 -0.01227701 -0.06848575 0.03743088
## 2019 -0.03696178 0.01930116 -0.01393720 -0.07016043 0.03575107
## 2020
## Nov Dec
## 2018 -0.04045739 0.02432303
## 2019 -0.04213901 0.02264076
## 2020
##
## $lower
## 80% 95%
## Feb 2018 -0.145463820 -0.16248339
## Mar 2018 0.044314856 0.02669903
## Apr 2018 -0.083676747 -0.10136591
## May 2018 -0.015088543 -0.03278688
## Jun 2018 -0.068893260 -0.08659275
## Jul 2018 -0.012514994 -0.03021463
## Aug 2018 -0.045712448 -0.06341210
## Sep 2018 -0.101921188 -0.11962084
## Oct 2018 0.003995450 -0.01370420
## Nov 2018 -0.073892777 -0.09159240
## Dec 2018 -0.009112022 -0.02681147
## Jan 2019 -0.043885209 -0.06158323
## Feb 2019 -0.137271828 -0.15509168
## Mar 2019 0.046259503 0.02842958
## Apr 2019 -0.084200099 -0.10203128
## May 2019 -0.016516947 -0.03434829
## Jun 2019 -0.070646021 -0.08847738
## Jul 2019 -0.014383092 -0.03221446
## Aug 2019 -0.047621445 -0.06545281
## Sep 2019 -0.103844675 -0.12167604
## Oct 2019 0.002066832 -0.01576453
## Nov 2019 -0.075823213 -0.09365455
## Dec 2019 -0.011043103 -0.02887426
## Jan 2020 -0.045816538 -0.06364628
##
## $upper
## 80% 95%
## Feb 2018 -0.081162368 -0.0641428013
## Mar 2018 0.110869034 0.1284848615
## Apr 2018 -0.016845493 0.0008436717
## May 2018 0.051777368 0.0694757053
## Jun 2018 -0.002023005 0.0156764822
## Jul 2018 0.054355805 0.0720554364
## Aug 2018 0.021158420 0.0388580691
## Sep 2018 -0.035050314 -0.0173506624
## Oct 2018 0.070866315 0.0885659639
## Nov 2018 -0.007021997 0.0106776294
## Dec 2018 0.057758082 0.0754575296
## Jan 2019 0.022979500 0.0406775197
## Feb 2019 -0.069946838 -0.0521269890
## Mar 2019 0.113622548 0.1314524688
## Apr 2019 -0.016832285 0.0009988988
## May 2019 0.050851466 0.0686828072
## Jun 2019 -0.003277533 0.0145538286
## Jul 2019 0.052985405 0.0708167693
## Aug 2019 0.019747053 0.0375784173
## Sep 2019 -0.036476178 -0.0186448143
## Oct 2019 0.069435318 0.0872666793
## Nov 2019 -0.008454811 0.0093765281
## Dec 2019 0.056324627 0.0741557887
## Jan 2020 0.021545838 0.0393755814