A New Strategy for Short-Term Load Forecasting

and Applied Analysis 3 is the order of regular differences and φ(B) and θ(B) are, respectively, defined as follows φ (B) = 1 − φ 1 B − φ 2 B 2 − ⋅ ⋅ ⋅ − φ p B p θ (B) = 1 − θ 1 B − θ 2 B 2 − ⋅ ⋅ ⋅ − θ q B q . (5) Random errors, ε t , are assumed to be independently and identically distributed with a mean of zero and a constant variance of σ, and the roots of φ(x) = 0 and θ(x) = 0 all lie outside the unit circle [21]. Equation (1) entails several important special cases of the ARIMA family of models. If q = 0, then (1) becomes an AR model for order p. When p = 0, the model reduces to an MA model of order q. One central task of ARIMAmodel building is to determine the appropriate model order (p, q). Similarly, a seasonal model (p, d, q)(P,D,Q) s can be written as follows (using the second expression): φ p (B)Φ p (B s ) (1 − B) d (1 − B s ) D