Forecasting Air Travel Demand

Appendices

A.1 Notations and assumptions

Let ${\hat{\theta }}_{(s)}={\left({\hat{\beta }}_{(s)}^T,{\hat{\mu }}_{(s)},{\hat{\sigma }}_{u,(s)},{\hat{\sigma }}_{v,(s)}\right)}^T$ .

Assumption C.1

For any candidate model s, there exists a constant vector ${\theta }_{(s)}^{\ast }$ such that as n → ∞, ${\hat{\theta }}_{(s)}-{\theta }_{(s)}^{\ast }\text{=}{O}_p\left(n^{-1/2}\right)$ .

From White (1982), we know that even for a misspecified model, Assumption C.1 is satisfied under some regularity conditions. Let $\hat{\theta }\text{=}{\left({\theta }_{(1)}^T,\dots ,{\theta }_{(S)}^T\right)}^T$ and ${\hat{\theta }}^{(-i)}$ be a cross-validation version $\hat{\theta }$ , i.e., without using the $i^{th}$ observation $\left\{C_i,x_{(1),i},\dots ,x_{(S),i}\right\}.$ We can rewrite ...