Order Estimation

Abstract

The order estimation of time series is a problem of long-standing interest. Various criteria such as multiple decision rule [An3], AIC [A2], BIC [Ri1], [Sw] and ΦIC [HQ] have been proposed to solve this problem. Among them, the information based criteria usually choose the order to minimize the following quantity

$$\log \hat \sigma _n^2 + {a_n}/n$$

((7.1))

where n is the data size, σ ²_n is the residual variance and a _n is a non-negative random variable that reflects the complexity of the nominal model. For example, in the order estimation of a scalar autoregressive model, we have AIC, if a _n = 2p BIC, if a _n = p log n ΦIC, if a _n = pc log log n, c > 1.