Multistep-Ahead Air Passengers Traffic Prediction with Hybrid ARIMA-SVMs Models

Table 3

Multiple comparison results with ranked strategies for hold-out sample.

Data preprocess

Measure

Prediction horizon (ℎ)

Rank of strategies

1

2

3

4

5

6

Non-deseasonalization-detrending

MAPEℎ

1

I-ARIMA-SVM

<

D-ARIMA-SVM

<^∗

I-SVM

<

D-SVM

<^∗

I-ARIMA

<

D-ARIMA

2

D-ARIMA-SVM

<

D-SVM

<

I-ARIMA-SVM

<

I-SVM

<^∗

D-ARIMA

<

I-ARIMA

4, 12

D-SVM

<

D-ARIMA-SVM

<^∗

I-ARIMA-SVM

<

I-SVM

<^∗

D-ARIMA

<

I-ARIMA

6, 18

D-ARIMA-SVM

<^∗

I-ARIMA-SVM

<

D-SVM

<

I-SVM

<^∗

D-ARIMA

<

I-ARIMA

8, 1–24

D-SVM

<

D-ARIMA-SVM

<

I-ARIMA-SVM

<

I-SVM

<^∗

I-ARIMA

<

D-ARIMA

24

D-ARIMA-SVM

<^∗

I-ARIMA-SVM

<

D-SVM

<

I-SVM

<^∗

I-ARIMA

<

D-ARIMA

SMAPEℎ

1

I-ARIMA-SVM

<

D-ARIMA-SVM

<^∗

I-SVM

<

D-SVM

<^∗

I-ARIMA

<

D-ARIMA

2

D-ARIMA-SVM

<

D-SVM

<

I-ARIMA-SVM

<

I-SVM

<^∗

I-ARIMA

<

D-ARIMA

4, 12

D-SVM

<

D-ARIMA-SVM

<

I-ARIMA-SVM

<^∗

I-SVM

<^∗

D-ARIMA

<

I-ARIMA

6

I-ARIMA-SVM

<

D-ARIMA-SVM

<

D-SVM

<

I-SVM

<^∗

D-ARIMA

<

I-ARIMA

8, 24, 1–24

D-SVM

<

D-ARIMA-SVM

<^∗

I-ARIMA-SVM

<^∗

I-SVM

<^∗

I-ARIMA

<

D-ARIMA

18

D-ARIMA-SVM

<^∗

I-ARIMA-SVM

<

D-SVM

<

I-SVM

<

D-ARIMA

<^∗

I-ARIMA

MASEℎ

1

I-ARIMA-SVM

<

D-ARIMA-SVM

<^∗

I-SVM

<

D-SVM

<^∗

I-ARIMA

<

D-ARIMA

2

I-ARIMA-SVM

<

D-ARIMA-SVM

<^∗

D-SVM

<

I-SVM

<^∗

I-ARIMA

<

D-ARIMA

4, 1–24

D-ARIMA-SVM

<

D-SVM

<

I-ARIMA-SVM

<^∗

I-SVM

<

I-ARIMA

<

D-ARIMA

6

D-SVM

<

I-ARIMA-SVM

<

D-ARIMA-SVM

<^∗

I-SVM

<^∗

D-ARIMA

<

I-ARIMA

8

D-SVM

<

D-ARIMA-SVM

<^∗

I-ARIMA-SVM

<

I-SVM

<^∗

I-ARIMA

<

D-ARIMA

12

I-SVM

<

D-ARIMA-SVM

<

D-SVM

<

I-ARIMA-SVM

<

D-ARIMA

<

I-ARIMA

18

D-ARIMA-SVM

<

D-SVM

<

I-SVM

<

I-ARIMA-SVM

<^∗

D-ARIMA

<

I-ARIMA

24

I-SVM

<

D-SVM

<

D-ARIMA-SVM

<

I-ARIMA-SVM

<^∗

I-ARIMA

<

D-ARIMA

Deseasonalization-detrending

MAPEℎ

1

I-ARIMA-SVM

<

D-ARIMA-SVM

<^∗

I-SVM

<

D-SVM

<^∗

I-ARIMA

<

D-ARIMA

2

D-ARIMA-SVM

<

I-ARIMA-SVM

<

D-SVM

<

I-SVM

<^∗

I-ARIMA

<

D-ARIMA

4

D-SVM

<

D-ARIMA-SVM

<^∗

I-ARIMA-SVM

<^∗

I-SVM

<^∗

D-ARIMA

<

I-ARIMA

6, 18, 24

D-ARIMA-SVM

<

I-ARIMA-SVM

<

D-SVM

<

I-SVM

<^∗

D-ARIMA

<

I-ARIMA

8, 1–24

D-SVM

<

D-ARIMA-SVM

<^∗

I-ARIMA-SVM

<

I-SVM

<^∗

I-ARIMA

<^∗

D-ARIMA

12

D-SVM

<

D-ARIMA-SVM

<^∗

I-ARIMA-SVM

<

I-SVM

<^∗

D-ARIMA

<

I-ARIMA

SMAPEℎ

1

I-ARIMA-SVM

<

D-ARIMA-SVM

<

D-SVM

<

I-SVM

<^∗

I-ARIMA

<

D-ARIMA

2

D-ARIMA-SVM

<

D-SVM

<

I-ARIMA-SVM

<

I-SVM

<^∗

I-ARIMA

<

D-ARIMA

4, 12

D-SVM

<

D-ARIMA-SVM

<^∗

I-ARIMA-SVM

<^∗

I-SVM

<^∗

D-ARIMA

<

I-ARIMA

6, 18

I-ARIMA-SVM

<

D-ARIMA-SVM

<^∗

I-SVM

<

D-SVM

<^∗

I-ARIMA

<

D-ARIMA

8, 24, 1–24

D-SVM

<

D-ARIMA-SVM

<

I-ARIMA-SVM

<^∗

I-SVM

<^∗

I-ARIMA

<

D-ARIMA

MASEℎ

1, 2

I-ARIMA-SVM

<

D-ARIMA-SVM

<

D-SVM

<

I-SVM

<^∗

I-ARIMA

<

D-ARIMA

4

D-ARIMA-SVM

<

I-ARIMA-SVM

<

D-SVM

<

I-SVM

<^∗

I-ARIMA

<

D-ARIMA

6

D-SVM

<

I-ARIMA-SVM

<

D-ARIMA-SVM

<^∗

I-SVM

<^∗

D-ARIMA

<

I-ARIMA

8

D-SVM

<

D-ARIMA-SVM

<

I-ARIMA-SVM

<

I-SVM

<^∗

I-ARIMA

<

D-ARIMA

12

I-SVM

<

D-ARIMA-SVM

<

D-SVM

<

I-ARIMA-SVM

<

D-ARIMA

<

I-ARIMA

18

D-ARIMA-SVM

<

D-SVM

<

I-ARIMA-SVM

<^∗

I-SVM

<

D-ARIMA

<

I-ARIMA

24

I-SVM

<

D-SVM

<

D-ARIMA-SVM

<

I-ARIMA-SVM

<

I-ARIMA

<

D-ARIMA

1–24

D-ARIMA-SVM

<

D-SVM

<

I-ARIMA-SVM

<

I-SVM

<^∗

I-ARIMA

<

D-ARIMA

Note: * The mean difference between the two adjacent strategies is significant at the 0.05 level.