ARIMA model
Topic of Forecasting, part of Time series
ARIMA model
| Type | Topic |
| Taught in | Forecasting |
| Part | Time series |
| Questions using it | 1 |
An autoregressive integrated moving-average model: an ARMA model fitted to a series after differencing it d times. A seasonal ARIMA also differences, and models, at a seasonal lag such as 12 for monthly data. Concept check C47 asks about unit roots and ARIMA.
In Forecasting
From Forecasting
auto.arima, with the seasonal option left on, finds this without being told that the data are monthly.
need <- function(pkg) {
if (!requireNamespace(pkg, quietly = TRUE)) {
install.packages(pkg, repos = "https://cloud.r-project.org")
}
suppressPackageStartupMessages(library(pkg, character.only = TRUE))
}
need("forecast")
fit <- auto.arima(USAccDeaths, seasonal = TRUE)
fit
fc <- forecast(fit, h = 12)
fc$mean[1]
sum(fc$mean)The selected model differences once at lag 12, keeps a seasonal MA(1) on that yearly lag, differences once more at lag 1, and keeps an ordinary MA(1). There is no AR term. Both MA coefficients are negative. They are read as behaviour rather than as algebra. If last month was worse than the month before, this month is more careful, and the coefficient on that surprise is negative. If last year was worse than the year before, this year is more careful, and the seasonal coefficient is negative too. A good year, by the same arithmetic, is followed by a slack one. The AIC is what the function used to choose the orders. BIC is available and was not the default.
Used in
- Taught in Forecasting
- Questions that use it (1) — C47
- All 2 questions on Forecasting
See also
Autoregression and moving averages · Unit root · Accidental-deaths data · Traffic data · Partial autocorrelation · Seasonality · Trend · Cycle