# Using ARIMA to explain time series data

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:

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?