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What do the letters in ARIMA stand for?
Auto-Regressive Integrated Moving Average
The acronym ARIMA stands for “Auto-Regressive Integrated Moving Average.” Lags of the differenced series appearing in the forecasting equation are called “auto-regressive” terms, lags of the forecast errors are called “moving average” terms, and a time series which needs to be differenced to be made stationary is said …
What is ARIMA equation?
The ARIMA forecasting equation for a stationary time series is a linear (i.e., regression-type) equation in which the predictors consist of lags of the dependent variable and/or lags of the forecast errors.
Which is the correct equation for the ARIMA model?
ARIMA(1,1,0) = differenced first-order autoregressive model: If the errors of the random walk model are autocorrelated, perhaps the problem can be fixed by adding one lag of the dependent variable to the prediction equation–i.e., by regressing DIFF(Y) on itself lagged by one period. This would yield the following prediction equation:
What’s the difference between Arima and ETS models?
On the other hand, there are also many ARIMA models that have no exponential smoothing counterparts. In particular, all ETS models are non-stationary, while some ARIMA models are stationary. Figure 9.27 shows the overlap between the two model classes.
Which is an example of an ARIMA process?
An autoregressive integrated moving average (ARIMA) process (aka a Box-Jenkins process) adds differencing to an ARMA process. An ARMA (p,q) process with d-order differencing is called an ARIMA (p.d,q) process. Thus, for example, an ARIMA (2,1,0) process is an AR (2) process with first-order differencing.
ARIMA(0,1,1) without constant = simple exponential smoothing: Another strategy for correcting autocorrelated errors in a random walk model is suggested by the simple exponential smoothing model.