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Table 4 The results of Diebold-Mariano and PT statistics

From: Analysis and forecasting of crude oil price based on the variable selection-LSTM integrated model

Types

Models

In-sample

Out-of-sample

DM

PT

DM

PT

Time series

RW

–

1.025

–

0.984

ARMA

−2.053 *

2.178 *

−1.784 *

1.946

Without variables selection

MLP

−7.107 **

3.372 **

−6.543 **

2.521 *

RBFNN

−7.314 **

3.451 **

−6.745 **

2.873 **

GRNN

−7.943 **

3.233 **

−7.153 **

3.084 **

Elman

−8.017 **

5.484 **

−7.491 **

4.141 **

WNN

−7.462 **

4.177 **

−6.897 **

3.052 **

ELM

−7.516 **

4.635 **

−6.983 **

3.314 **

LSTM

−8.214 **

4.464 **

−7.635 **

3.633 **

GLNET

MLP

−8.425 **

3.951 **

−7.849 **

4.687 **

RBFNN

−7.566 **

4.130 **

−6.951 **

3.892 **

GRNN

−7.847 **

4.478 **

−7.283 **

4.174 **

Elman

−8.362 **

5.632 **

−7.719 **

3.952 **

WNN

−8.891 **

4.655 **

−8.206 **

5.613 **

ELM

−7.195 **

4.553 **

−6.618 **

2.370 **

LSTM

−7.219 **

4.468 **

−6.806 **

2.855 **

Spike-slab Lasso

MLP

−7.873 **

4.021 **

−7.194 **

3.324 **

RBFNN

−8.129 **

5.566 **

−7.506 **

4.068 **

GRNN

−7.502 **

5.171 **

−6.904 **

3.281 **

Elman

−7.604 **

5.044 **

−6.816 **

3.693 **

WNN

−8.138 **

4.936 **

−7.728 **

3.586 **

ELM

−8.608 **

6.052 **

−7.893 **

5.024 **

LSTM

−7.672 **

6.843 **

−7.015 **

4.338 **

Bayesian model averaging

MLP

−7.748 **

5.167 **

−7.296 **

4.844 **

RBFNN

−8.424 **

5.023 **

−7.693 **

4.463 **

GRNN

−8.795 **

6.431 **

−8.334 **

5.572 **

Elman

−7.796 **

6.082 **

−7.258 **

5.185 **

WNN

−8.013 **

7.690 **

−7.374 **

5.641 **

ELM

−8.507 **

7.724 **

−7.867 **

6.030 **

LSTM

−9.304 **

8.035 **

−8.746 **

6.544 **

  1. Note: The values in the table are the calculated DM statistics. * denotes a rejection of null hypothesis at the 5% significance level. ** denotes a rejection of null hypothesis at the 1% significance level