Air freight Time Series.Rmd

---
title: "Times Series Project"
author: "Alex Navarro"
date: "11/26/2021"
output: html_document
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```
```{r, cache=TRUE}
# Read Data Into System:
Airfreight <- read.csv("Airfreight.csv")
# Load TSA Library:
library(TSA)
# Plot ACF:
acf(Airfreight$Ton.miles,lag.max = 36,ci.type='ma', col = c("red"))
# Plot Time Series Plot:
plot(Airfreight$Ton.miles,type = 'o', main = "Time Series Plot", col = c("green"))
# Plot First Difference of Plot:
plot(diff(Airfreight$Ton.miles),type='o', col = c("green"), main = "Time Series Plot of 1st Difference")
# Plot First Difference of ACF:
acf(diff(Airfreight$Ton.miles),lag.max = 36,ci.type='ma', col = c("red"))
# Plot the 12th Difference of Time Series Plot:
plot(diff(Airfreight$Ton.miles,lag=12),type = 'o', main = " Time Series Plot of 12th Difference", col = "red")
# 12th difference of ACF Plot:
acf(diff(Airfreight$Ton.miles,lag=12),lag.max=36,ci.type='ma')
# Taking A Additional 1st Difference For The Time Series Plot:
plot(diff(diff(Airfreight$Ton.miles),lag=12),type='o', main = "Taking Additional 1st Difference Plot", col = c("blue"))
# Taking 1st Difference Again for ACF Plot:
acf(diff(diff(Airfreight$Ton.miles,lag=12)),lag.max = 36,ci.type='ma')
# Plot PACF:
pacf(diff(diff(Airfreight$Ton.miles,lag=12)),lag.max=36,ci.type='ma')
# Fit Model:
fit <- arima(Airfreight$Ton.miles, order = c(0,1,1), seasonal = list(order=c(0,1,1),period = 12))
fit
# Perform diagnostics:
plot(rstandard(fit),ylab='Standardized Residuals',type='o', col = c("blue"))
hist(rstandard(fit), col = c("red","blue","green"))
qqnorm(residuals(fit))
qqline(residuals(fit))
acf(rstandard(fit),lag.max=36)
Box.test(residuals(fit),lag=36,type="Ljung",fitdf=1)
```