「インサンプル」予測と「擬似アウトオブサンプル」予測の違い

サンプル内予測と擬似サンプル外予測の間に明確な違いはありますか？両方は、予測モデルの評価と比較のコンテキストでの意味です。

$\{Y_t,X_{t-h}\}_{t=h+1}^T$$h \in \{1,2,\ldots\},$$\hat f(X_{t-h})$$Y_t$$X_{t-h}$$T$

$T$

$Y_{T+1}$$e_{T+1} \equiv Y_{T+1} - \hat f(X_{T+1-h}),$$Y_{T+2}$, and so forth. At the end of this exercise, one would have a sample of forecast errors $\{e_{T+l}\}_{l=1}^L$ which would be truly out-of-sample and would give a very realistic picture of the model's performance.

Since this procedure is very time-consuming, people often resort to "pseudo", or "simulated", out-of-sample analysis, which means to mimic the procedure described in the last paragraph, using some historical date $T_0 < T$, rather than today's date $T$, as a starting point. The resulting forecasting errors $\{e_t\}_{t=T_0+1}^T$ are then used to get an estimate of the model's out-of-sample forecasting ability.

Note that pseudo-out-of-sample analysis is not the only way to estimate a model's out-of-sample performance. Alternatives include cross-validation and information criteria.

A very good discussion of all these issues is provided in Chapter 7 of

http://www.stanford.edu/~hastie/local.ftp/Springer/OLD/ESLII_print4.pdf