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4. 1,,,,, 2 3.

,..,,, [WallisK.F., M.J.Andrews, D.N.F.Bell, P.G.Fisher, J.D.Whitley (1984)], [WallisK.F., M.J.Andrews, P.G.Fisher, J.Longbottom, J.D.Whitley (1986)], [WallisK.F. (1989)], [WallisK.F., J.D.Whitley (1991)],, [KleinL.R.

(1991)] [KleinL.R., E.Burmeister [eds] (1976)].

,, [Clements M.P., D.F.Hendry (1998b)], [Clements M.P., D.F.Hendry (2001)].

4.1. ,., ,,, (, ).

: (.., ),,., 127,.

.

Xt, T-1 XT. () ,,,, T-1,.

:,,,.

, :

, Xt T-1.

:

;

;

, ;

,.

,,,,,.

-. ( ),, .

,,,, (, data generating 128 process DGP),,.,,,,, (statistical model SM),,,, ().

.,,, :.

,.

, ( ) (),,,.

Clements Hendry ( ), DGP,,,.,, ( ) DGP.

129 4.2. .

,,.

, (31, 30, 28 29).

M0:

08.200002.2001 08.200011.2001 RMSE 20762.60 19773.54 24404.03 23987.22 MAE 19084.87 17246.75 21787.85 21443.12 MAPE 5.247909 4.757094 5.128878 5.00533,, (P-=0.2248),,,.

M1:

08.200002.2001 08.200011. RMSE 30788.31 30803.10 35259.73 35139.MAE 25004.23 25015.30 30334.93 30190.MAPE 3.119278 3.119104 3.362247 3., P- (0.8588)..

M2:

08.200002.2001 08.200011. RMSE 41472.50 41062.65 37951.93 38869.MAE 30513.84 30165.17 31062.16 31184.MAPE 2.847573 2.806430 2.598554 2. P- 0.83788..

4.3. back-on-track back-on-average ( 4.3.2) back-on-track back-on-average.

4.3.1. M.

08.200011.2001 (16 ):

DS TS. DS. TS.

.

Root Mean Squared Error 17422.22 21420.81 24404.03 54664.Mean Absolute Error 13679.97 18606.90 21787.85 44497.Mean Absolute Percent Error 3.309110 4.320607 5.128878 9. TS,.

S-:

:

00:10 01:01 01:04 01:07 01:X XF :

-00:10 01:01 01:04 01:07 01:DELTA_TS,, DS-:

DS-:

:

00:10 01:01 01:04 01:07 01:X XF 00:09 00:11 01:01 01:03 01:05 01:07 01:09 01:DELTA_DS, back-on-track back-on-ave.

TSBack-on-ave:

---64 66 68 70 72 74 76 DELTA_BACK_ON_AV :

Back-on-ave Root Mean Squared Error 38846.Mean Absolute Error 32756.Mean Absolute Percent Error 7. TS-, TS-.

Back-on-track:

64 66 68 70 72 74 76 DELTA_BACK_ON_TR Back-on-track Root Mean Squared Error 26312.Mean Absolute Error 20334.Mean Absolute Percent Error 4. TS-,, backon-ave,, TS-.

DSBack-on-ave:

64 66 68 70 72 74 76 DELTA_BACK_ON_AV Back-on-ave Root Mean Squared Error 24368.Mean Absolute Error 20210.Mean Absolute Percent Error 4., DS-,, DS-.

Back-on-track:

64 66 68 70 72 74 76 DELTA_BACK_ON_TR Back-on-track Root Mean Squared Error 30762.Mean Absolute Error 25194.Mean Absolute Percent Error 6., back-ontrack,, DS,, back-on-ave.

4.3.2. M (TS-) 2 TS-:

00:08 00:09 00:10 00:11 00:12 01:01 01:02 00:08 00:09 00:10 00:11 00:12 01:01 01:X XF_FIX DELTA_TS, :., back-on-track, [Clements P., D.F.Hendry (1998a)] [Clements P., D.F.Hendry (1998b)]. back-ontrack,,,.

,.

:

00:08 00:09 00:10 00:11 00:12 01:01 01:DELTA_TS_BACK. Back-on-track Root Mean Squared Error 40981.79 42890.Mean Absolute Error 32088.90 38012.Mean Absolute Percent Error 3.958528 4.,.

,, 32088.9 ( delta_ts ).

, 32088.9. :

00:08 00:09 00:10 00:11 00:12 01:01 01:DELTA_TS, back-on-track,,, :

Root Mean Squared Error 25491.Mean Absolute Error 19057.Mean Absolute Percent Error 2..

, back-on-track.,,,,.,,,.

back-on-track back-on-ave back-ontrack,,,,. back-on-average,, back-on-ave.

back-on-ave,.

(X), TS(XF), back-on-ave (BACK_ON_AVE):

00:08 00:09 00:10 00:11 00:12 01:01 01:X XF BACK_ON_AVE 00:08 00:09 00:10 00:11 00:12 01:01 01:DELTA_BACK_ON_AV Back-on-ave Root Mean Squared Error 30187.Mean Absolute Error 24423.Mean Absolute Percent Error 3. back-on-ave.

, ( 32088.9),.,, back-on-ave,,,.

DS - TS. DS. TS.

.

Root Mean Squared Error 33750.29 35153.12 30788.31 40981.Mean Absolute Error 28915.77 29026.71 25004.23 32088.Mean Absolute Percent Error 3.604901 3.621122 3.119278 3. 08.200011.2001, 3.

M1 ( ).

DS TS. DS. TS.

.

Root Mean Squared Error 37646.23 41033.29 35359.73 108578.Mean Absolute Error 30672.38 33871.66 30334.93 90923.Mean Absolute Percent Error 3.440899 3.775183 3.362247 9. TS-.

:., : back-on-track back-on-average (back-on-ave).

ack-on- ave:

00:09 00:11 01:01 01:03 01:05 01:07 01:09 01:X XF BACK_ON_AVE -00:10 01:01 01:04 01:07 01:DELTA_BACK_ON_AVE :

Back-on-ave Root Mean Squared Error 62716.Mean Absolute Error 53497.Mean Absolute Percent Error 5., back-on-ave, - TS-., DS- DS-.

TS- :,.,,,,.

00:10 01:01 01:04 01:07 01:DELTA_TS back-on-track c..

00:09 00:11 01:01 01:03 01:05 01:07 01:09 01:00:09 00:11 01:01 01:03 01:05 01:07 01:09 01:DELTA_TS_BACK X BACK_ON_TRACK_TS Back-on-track Root Mean Squared Error 35886.Mean Absolute Error 31706.Mean Absolute Percent Error 3., back-on-track,, TS-,, DS-.

(DS-) :

00:08 00:09 00:10 00:11 00:12 01:01 01:DELTA_DS Back-on-track:

--63 64 65 66 67 68 DELTA_BACK_ON_TR. Back-on-track Root Mean Squared Error 30788.31 47972.Mean Absolute Error 25004.23 40060.Mean Absolute Percent Error 3.119278 5., TS-,. ( back-on-track).

back-on-ave:

63 64 65 66 67 68 DELTA_BACK_ON_AV Back-on-ave Root Mean Squared Error 33987.Mean Absolute Error 28623.Mean Absolute Percent Error 3., back-on-ave,, DS-,, DS-,.

08.200011.2001.

DS00:09 00:11 01:01 01:03 01:05 01:07 01:09 01:DELTA_DS, back-on-track --64 66 68 70 72 74 76 DELTA_BACK_ON_TR. Back-on-track Root Mean Squared Error 35359.73 38409.Mean Absolute Error 30334.93 31134.Mean Absolute Percent Error 3.362247 3..

Back-on-ave:

64 66 68 70 72 74 76 DELTA_BACK_ON_AV :

Back-on-ave Root Mean Squared Error 33164.Mean Absolute Error 26333.Mean Absolute Percent Error 3. back-on-ave.

4.3.3. M.

08.200011.2001 (16 ):

DS TS. DS. TS.

.

Root Mean Squared Error 39133.66 41913.71 37951.93 41623.Mean Absolute Error 28768.55 31083.92 31062.16 32920.Mean Absolute Percent Error 2.457265 2.656437 2.598554 2. TS00:09 00:11 01:01 01:03 01:05 01:07 01:09 01:DELTA_TS DS----00:10 01:01 01:04 01:07 01:D L AD ET _ S DS-, TS-.

, back-on-track back-on-ave.

TS-:

ack-on-ave:

--64 66 68 70 72 74 76 DELTA_BACK_ON_AV Back-on-ave Root Mean Squared Error 41913.Mean Absolute Error 35127.Mean Absolute Percent Error 2. TS-.

Back-on-track:

-64 66 68 70 72 74 76 DELTA_BACK_ON_TR Back-on-track Root Mean Squared Error 52884.Mean Absolute Error 40505.Mean Absolute Percent Error 3., back-ontrack,, TS-.

DSBack-on-ave:

64 66 68 70 72 74 76 DELTA_BACK_ON_AV Back-on-ave Root Mean Squared Error 44569.Mean Absolute Error 38767.Mean Absolute Percent Error 3., back-onave,, DS-.

Back-on-track:

-64 66 68 70 72 74 76 DELTA_BACK_ON_TR Back-on-track Root Mean Squared Error 55119.Mean Absolute Error 45006.Mean Absolute Percent Error 3., back-ontrack,, DS-.

4.3.4..

06.200009.2001 (16 ):

DS - TS. DS. TS.

.

Root Mean Squared Error 6676.117 6983.570 8038.587 16075.Mean Absolute Error 5097.416 5367.743 7134.696 15428.Mean Absolute Percent Error 5.740951 6.044299 7.761660 15. TS (, DS-), :

54 56 58 60 62 64 66 X XF -00:07 00:09 00:11 01:01 01:03 01:05 01:07 01:DELTA_TS,,, DS-:

-00:07 00:09 00:11 01:01 01:03 01:05 01:07 01:DELTA_DS, back-on-track back-on-ave.

TS-:

Back-on-ave:

54 56 58 60 62 64 66 X BACK_ON_AVE -54 56 58 60 62 64 66 DELTA_BACK_ON_AV Back-on-ave Root Mean Squared Error 5437.Mean Absolute Error 4485.Mean Absolute Percent Error 4., back-onave,, DS-.

Back-on-track:

54 56 58 60 62 64 66 X BACK_ON_TRACK -54 56 58 60 62 64 66 DELTA_BACK_ON_TR Back-on-track Root Mean Squared Error 5887.Mean Absolute Error 4543.Mean Absolute Percent Error 4., back-ontrack,, TS-,, back-on-ave.

DSBack-on-ave:

54 56 58 60 62 64 66 X BACK_ON_AVE -54 56 58 60 62 64 66 DELTA_BACK_ON_AV Back-on-ave Root Mean Squared Error 5750.Mean Absolute Error 4359.Mean Absolute Percent Error 4., back-onave,, DS-.

Back-on-track:

54 56 58 60 62 64 66 X BACK_ON_TRACK -54 56 58 60 62 64 66 DELTA_BACK_ON_TR Back-on-track Root Mean Squared Error 6419.Mean Absolute Error 5136.Mean Absolute Percent Error 5., back-ontrack,, DS-,, back-on-ave.

4.3.5.

05.2000-08.2001 (16 ):

DS TS. DS. TS.

.

Root Mean Squared Error 0.710022 0.770122 0.734464 0.Mean Absolute Error 0.594670 0.673983 0.622717 0.Mean Absolute Percent Error 6.693006 7.542889 6.989588 8. :

TS- DS2.1.1.1.1.0.0.0.0.-0.-0.-1.-1.-1.00:05 00:07 00:09 00:11 01:01 01:03 01:05 01:00:05 00:07 00:09 00:11 01:01 01:03 01:05 01:DELTA_TS DELTA_DS. back-on-track back-on-ave.

TSBack-on-track:

---78 80 82 84 86 88 90 DELTA_BACK_ON_TR Back-on-track Root Mean Squared Error 1.Mean Absolute Error 1.Mean Absolute Percent Error 11., back-ontrack,, TS-.

Back-on-ave:

1.1.0.0.-0.-1.-1.78 80 82 84 86 88 90 DELTA_BACK_ON_AV Back-on-ave Root Mean Squared Error 0.Mean Absolute Error 0.Mean Absolute Percent Error 7., back-onave,, TS-,, back-on-track.

DSBack-on-track:

---78 80 82 84 86 88 90 DELTA_BACK_ON_TR Back-on-track Root Mean Squared Error 1.Mean Absolute Error 1.Mean Absolute Percent Error 12., back-ontrack,, DS-.

Back-on-ave:

1.1.0.0.-0.-1.-1.-2.78 80 82 84 86 88 90 DELTA_BACK_ON_AV Back-on-ave Root Mean Squared Error 0.Mean Absolute Error 0.Mean Absolute Percent Error 8., back-onave,, DS-,, back-on-track.

4.3.6. TS-:

101.0 0.100.5 0.100.0 0.99.0.99.0.98.0.98.0.97.-0.00:08 00:09 00:10 00:11 00:12 01:01 01:00:08 00:09 00:10 00:11 00:12 01:01 01:X_SA X_SAF_TS_FIX DELTA_TS_FIX TS Root Mean Squared Error 0.Mean Absolute Error 0.Mean Absolute Percent Error 0., :., back-on-track.

, :

101.0 0.100.0.100.0.99.0.99.-0.98.-0.98.97.5 -0.00:08 00:09 00:10 00:11 00:12 01:01 01:02 00:08 00:09 00:10 00:11 00:12 01:01 01:X_SA BACK_ON_TRACK_TS DELTA_BACK_TS_SA Back-on-track Root Mean Squared Error 0.Mean Absolute Error 0.Mean Absolute Percent Error 0. back-on-track. RMSE TS-, ( DS-, TS- DS).

Back-on-ave:

101.0 0.100.0.100.0.99.0.99.0.98.-0.98.97.-0.128 129 130 131 132 133 128 129 130 131 132 133 X BACK_ON_AVE DELTA_BACK_ON_AV Back-on-ave Root Mean Squared Error 0.Mean Absolute Error 0.Mean Absolute Percent Error 0., TS-,,, back-on-track.

DS-.

:

101.0 0.100.0.100.0.99.0.99.0.98.98.0 -0.97.-0.00:08 00:09 00:10 00:11 00:12 01:01 01:00:08 00:09 00:10 00:11 00:12 01:01 01:X_SA X_SAF_DS_FIX DELTA_DS_FIX DS Root Mean Squared Error 0.Mean Absolute Error 0.Mean Absolute Percent Error 0. back-on-track :

101.0 0.100.0.100.0.99.99.-0.98.-0.98.97.-0.00:08 00:09 00:10 00:11 00:12 01:01 01:00:08 00:09 00:10 00:11 00:12 01:01 01:X_SA BACK_ON_TRACK_DS DELTA_BACK_DS_SA Back-on-track Root Mean Squared Error 0.Mean Absolute Error 0.Mean Absolute Percent Error 0.,.

Back-on-ave:

0.101.100.0.100.0.99.0.99.0.98.-0.98.97.-0.128 129 130 131 132 133 128 129 130 131 132 133 X BACK_ON_AVE DELTA_BACK_ON_AV Back-on-ave Root Mean Squared Error 0.Mean Absolute Error 0.Mean Absolute Percent Error 0.,, DS-,,, DS-,, back-on-track.

TS-:

102 ---00:08 00:09 00:10 00:11 00:12 01:01 01:00:08 00:09 00:10 00:11 00:12 01:01 01:X_NSA X_NSAF_FIX DELTA_TS_FIX TS Root Mean Squared Error 2.Mean Absolute Error 2.Mean Absolute Percent Error 2. back-on-track, :

---90 -00:08 00:09 00:10 00:11 00:12 01:01 01:00:08 00:09 00:10 00:11 00:12 01:01 01:X_NSA BACK_ON_TRACK_TS DELTA_BACK_TS_NS TS Root Mean Squared Error 3.Mean Absolute Error 2.Mean Absolute Percent Error 2. back-on-track, 2001.

,,, :

TS-. ack-on-track Root Mean Squared Error 1.973102 1.Mean Absolute Error 1.648535 1.Mean Absolute Percent Error 1.654562 1. back-on-track.

Back-on-ave:

----128 129 130 131 132 133 DELTA_BACK_ON_AV Back-on-ave Root Mean Squared Error 2.Mean Absolute Error 2.Mean Absolute Percent Error 2. back-on-ave TS-.

DS-:

104 ----00:08 00:09 00:10 00:11 00:12 01:01 01:00:08 00:09 00:10 00:11 00:12 01:01 01:X_NSA X_NSAF_DS_FIX DELTA_DS_FIX DS Root Mean Squared Error 2.Mean Absolute Error 2.Mean Absolute Percent Error 2..

Back-on-track:

104 ----128 129 130 131 132 133 128 129 130 131 132 133 X BACK_ON_TRACK DELTA_BACK_ON_TR Back-on-track Root Mean Squared Error 3.Mean Absolute Error 2.Mean Absolute Percent Error 2. back-on-track.

Back-on-ave:

104 ----128 129 130 131 132 133 128 129 130 131 132 133 DELTA_BACK_ON_AV X BACK_ON_AVE Back-on-ave Root Mean Squared Error 3.Mean Absolute Error 2.Mean Absolute Percent Error 2. back-on-ave,, back-on-track.

4.3.7. ( ) TS- DS-, 01.1994 01.1998.

TS-:

0.0.0.-0.-0.-0.-0.-0.98:02 98:03 98:04 98:05 98:06 98:07 98:98:02 98:03 98:04 98:05 98:06 98:07 98:DELTA_TS_FIX X XF_TS_FIX TS Root Mean Squared Error 0.Mean Absolute Error 0.Mean Absolute Percent Error 0. back-on-track :

42 0.0.0.-0.-0.98:02 98:03 98:04 98:05 98:06 98:07 98:98:02 98:03 98:04 98:05 98:06 98:07 98:DELTA_TS_BACK X BACK_ON_TRACK_TS TS Root Mean Squared Error 0.Mean Absolute Error 0.Mean Absolute Percent Error 0. :,,,.

back-on-ave :

42 0.41 0.40 0.39 -0.38 -0.37 -0.98 99 100 101 102 103 104 98 99 100 101 102 103 X BACK_ON_AVE DELTA_BACK_ON_AV Back-on-ave Root Mean Squared Error 0.Mean Absolute Error 0.Mean Absolute Percent Error 0. TS- back-on-ave.

DS-:

0.41 0.0.-0.-0.-0.98:02 98:03 98:04 98:05 98:06 98:07 98:98:02 98:03 98:04 98:05 98:06 98:07 98:DELTA_DS_FIX X XF_DS_FIX DS Root Mean Squared Error 0.Mean Absolute Error 0.Mean Absolute Percent Error 0. back-on-track :

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