04-03-Forecast-ARIMA.Rmd

## ARIMA Modeling {-}

```{r a1, comment=NA, warning=FALSE, message=FALSE, fig.width=9}

library(forecast)

# Generated Time Series
set.seed(1)
x  = 100 + arima.sim(n = 100,
  model = list(order = c(1, 1, 1), ar = .1, ma = .2))

# Plot the series
plot(x, main = "Simulated ARIMA(1,1,1)")

# Check if there is auto correlation, there is
Acf(x, main = "ACF"); Pacf(x, main = "PACF")

# How many differences does it take for the data to be stationary?
# 1
plot(diff(x), main = "First Order Difference")

# Check the Acf/Pacf with differences
Acf(diff(x), main = "ACF 1 diff")  # One significant spike, suggests MA(1)
Pacf(diff(x), main = "PACF 1 diff") # One significant spike, indicates AR(1)

# Suggested model ARIMA(1,1,1)
mdl1 = arima(x, c(1,1,1))

# How do the ARMA terms compare with the terms used in the sim?
# AR1: .18 vs .1 in the sim
# MA1: .14 vs .2 in the sim
summary(mdl1)

# What does the forecast package auto.arima function suggest?
(mdl2 = auto.arima(x)) # No AR term

# How does the manual model compare with the auto.arima model?
AIC(mdl1, mdl2)

```