In a nonseasonal ARIMA model, ARIMA(p, d, q):
- p is the order of the autoregressive part
- d is the degree of first differencing
- q is the order of the moving average part
To calculate the coefficients of the input parameters, the Arima function uses this formula:
AR(p) * d_differences = MA(q) + c
- AR(p) = 1 - φ 1 B - … - φ p B p
- d_differences = (1 - B) d y t
- MA(q) = (1 + θ 1 B + … + θ q B q )e t
The φ values are nonseasonal autoregressive parameters and the θ values are nonseasonal moving average parameters.
The value B is the backshift operator, which is defined as follows:
By t = y t-1
B n y t = y t-n
e t is the residual error, the difference between the actual and predicted values of y t .