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I am creating models to analyze energy use in four U.S. states. The goal is to create a model to explain historical data (1960-2009) as well as to create a forecast for 2025 and 2050. I am using R and settled on using the auto.arima function. After running auto.arima for one state my output is as follows:

image

The code I am using is

CAP <- ts(ca_prod$Data,frequency = 1,start = c(1960))
plot(CAP)
autoarimaCAP <- auto.arima(CAP)
forecastCAP <- forecast(autoarimaCAP, h=45)
forecastCAP
plot(forecastCAP, main = "CA Forecast Total Production")
plot(forecastCAP$residuals)
qqnorm(forecastCAP$residuals)
acf(forecastCAP$residuals)
pacf(forecastCAP$residuals)
summary(autoarimaCAP)

How would I use the coefficients to create an equation to explain the historical data?

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