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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 18 Dec 2012 06:11:02 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/18/t1355829126wqwyv1kixstk4wa.htm/, Retrieved Thu, 25 Apr 2024 20:24:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=201354, Retrieved Thu, 25 Apr 2024 20:24:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact74
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2012-12-18 11:11:02] [e1a2d6f766d96e9510928a1680b9f058] [Current]
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Dataseries X:
14544
14931
14886
16005
17064
15168
16050
15839
15137
14954
15648
15305
15579
16348
15928
16171
15937
15713
15594
15683
16438
17032
17696
17745
19394
20148
20108
18584
18441
18391
19178
18079
18483
19644
19195
19650
20830
23595
22937
21814
21928
21777
21383
21467
22052
22680
24320
24977
25204
25739
26434
27525
30695
32436
30160
30236
31293
31077
32226
33865
32810
32242
32700
32819
33947
34148
35261
39506
41591
39148
41216
40225




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201354&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=201354&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201354&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201354&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]1[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=201354&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201354&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
31488615318-432
41600515273732
51706416392672
61516817451-2283
71605015555495
81583916437-598
91513716226-1089
101495415524-570
111564815341307
121530516035-730
131557915692-113
141634815966382
151592816735-807
161617116315-144
171593716558-621
181571316324-611
191559416100-506
201568315981-298
211643816070368
221703216825207
231769617419277
241774518083-338
2519394181321262
262014819781367
272010820535-427
281858420495-1911
291844118971-530
301839118828-437
311917818778400
321807919565-1486
33184831846617
341964418870774
351919520031-836
36196501958268
372083020037793
3823595212172378
392293723982-1045
402181423324-1510
412192822201-273
422177722315-538
432138322164-781
442146721770-303
452205221854198
462268022439241
4724320230671253
482497724707270
492520425364-160
502573925591148
512643426126308
522752526821704
5330695279122783
5432436310821354
553016032823-2663
563023630547-311
573129330623670
583107731680-603
593222631464762
6033865326131252
613281034252-1442
623224233197-955
63327003262971
643281933087-268
653394733206741
663414834334-186
673526134535726
6839506356483858
6941591398931698
703914841978-2830
7141216395351681
724022541603-1378

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 14886 & 15318 & -432 \tabularnewline
4 & 16005 & 15273 & 732 \tabularnewline
5 & 17064 & 16392 & 672 \tabularnewline
6 & 15168 & 17451 & -2283 \tabularnewline
7 & 16050 & 15555 & 495 \tabularnewline
8 & 15839 & 16437 & -598 \tabularnewline
9 & 15137 & 16226 & -1089 \tabularnewline
10 & 14954 & 15524 & -570 \tabularnewline
11 & 15648 & 15341 & 307 \tabularnewline
12 & 15305 & 16035 & -730 \tabularnewline
13 & 15579 & 15692 & -113 \tabularnewline
14 & 16348 & 15966 & 382 \tabularnewline
15 & 15928 & 16735 & -807 \tabularnewline
16 & 16171 & 16315 & -144 \tabularnewline
17 & 15937 & 16558 & -621 \tabularnewline
18 & 15713 & 16324 & -611 \tabularnewline
19 & 15594 & 16100 & -506 \tabularnewline
20 & 15683 & 15981 & -298 \tabularnewline
21 & 16438 & 16070 & 368 \tabularnewline
22 & 17032 & 16825 & 207 \tabularnewline
23 & 17696 & 17419 & 277 \tabularnewline
24 & 17745 & 18083 & -338 \tabularnewline
25 & 19394 & 18132 & 1262 \tabularnewline
26 & 20148 & 19781 & 367 \tabularnewline
27 & 20108 & 20535 & -427 \tabularnewline
28 & 18584 & 20495 & -1911 \tabularnewline
29 & 18441 & 18971 & -530 \tabularnewline
30 & 18391 & 18828 & -437 \tabularnewline
31 & 19178 & 18778 & 400 \tabularnewline
32 & 18079 & 19565 & -1486 \tabularnewline
33 & 18483 & 18466 & 17 \tabularnewline
34 & 19644 & 18870 & 774 \tabularnewline
35 & 19195 & 20031 & -836 \tabularnewline
36 & 19650 & 19582 & 68 \tabularnewline
37 & 20830 & 20037 & 793 \tabularnewline
38 & 23595 & 21217 & 2378 \tabularnewline
39 & 22937 & 23982 & -1045 \tabularnewline
40 & 21814 & 23324 & -1510 \tabularnewline
41 & 21928 & 22201 & -273 \tabularnewline
42 & 21777 & 22315 & -538 \tabularnewline
43 & 21383 & 22164 & -781 \tabularnewline
44 & 21467 & 21770 & -303 \tabularnewline
45 & 22052 & 21854 & 198 \tabularnewline
46 & 22680 & 22439 & 241 \tabularnewline
47 & 24320 & 23067 & 1253 \tabularnewline
48 & 24977 & 24707 & 270 \tabularnewline
49 & 25204 & 25364 & -160 \tabularnewline
50 & 25739 & 25591 & 148 \tabularnewline
51 & 26434 & 26126 & 308 \tabularnewline
52 & 27525 & 26821 & 704 \tabularnewline
53 & 30695 & 27912 & 2783 \tabularnewline
54 & 32436 & 31082 & 1354 \tabularnewline
55 & 30160 & 32823 & -2663 \tabularnewline
56 & 30236 & 30547 & -311 \tabularnewline
57 & 31293 & 30623 & 670 \tabularnewline
58 & 31077 & 31680 & -603 \tabularnewline
59 & 32226 & 31464 & 762 \tabularnewline
60 & 33865 & 32613 & 1252 \tabularnewline
61 & 32810 & 34252 & -1442 \tabularnewline
62 & 32242 & 33197 & -955 \tabularnewline
63 & 32700 & 32629 & 71 \tabularnewline
64 & 32819 & 33087 & -268 \tabularnewline
65 & 33947 & 33206 & 741 \tabularnewline
66 & 34148 & 34334 & -186 \tabularnewline
67 & 35261 & 34535 & 726 \tabularnewline
68 & 39506 & 35648 & 3858 \tabularnewline
69 & 41591 & 39893 & 1698 \tabularnewline
70 & 39148 & 41978 & -2830 \tabularnewline
71 & 41216 & 39535 & 1681 \tabularnewline
72 & 40225 & 41603 & -1378 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201354&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]14886[/C][C]15318[/C][C]-432[/C][/ROW]
[ROW][C]4[/C][C]16005[/C][C]15273[/C][C]732[/C][/ROW]
[ROW][C]5[/C][C]17064[/C][C]16392[/C][C]672[/C][/ROW]
[ROW][C]6[/C][C]15168[/C][C]17451[/C][C]-2283[/C][/ROW]
[ROW][C]7[/C][C]16050[/C][C]15555[/C][C]495[/C][/ROW]
[ROW][C]8[/C][C]15839[/C][C]16437[/C][C]-598[/C][/ROW]
[ROW][C]9[/C][C]15137[/C][C]16226[/C][C]-1089[/C][/ROW]
[ROW][C]10[/C][C]14954[/C][C]15524[/C][C]-570[/C][/ROW]
[ROW][C]11[/C][C]15648[/C][C]15341[/C][C]307[/C][/ROW]
[ROW][C]12[/C][C]15305[/C][C]16035[/C][C]-730[/C][/ROW]
[ROW][C]13[/C][C]15579[/C][C]15692[/C][C]-113[/C][/ROW]
[ROW][C]14[/C][C]16348[/C][C]15966[/C][C]382[/C][/ROW]
[ROW][C]15[/C][C]15928[/C][C]16735[/C][C]-807[/C][/ROW]
[ROW][C]16[/C][C]16171[/C][C]16315[/C][C]-144[/C][/ROW]
[ROW][C]17[/C][C]15937[/C][C]16558[/C][C]-621[/C][/ROW]
[ROW][C]18[/C][C]15713[/C][C]16324[/C][C]-611[/C][/ROW]
[ROW][C]19[/C][C]15594[/C][C]16100[/C][C]-506[/C][/ROW]
[ROW][C]20[/C][C]15683[/C][C]15981[/C][C]-298[/C][/ROW]
[ROW][C]21[/C][C]16438[/C][C]16070[/C][C]368[/C][/ROW]
[ROW][C]22[/C][C]17032[/C][C]16825[/C][C]207[/C][/ROW]
[ROW][C]23[/C][C]17696[/C][C]17419[/C][C]277[/C][/ROW]
[ROW][C]24[/C][C]17745[/C][C]18083[/C][C]-338[/C][/ROW]
[ROW][C]25[/C][C]19394[/C][C]18132[/C][C]1262[/C][/ROW]
[ROW][C]26[/C][C]20148[/C][C]19781[/C][C]367[/C][/ROW]
[ROW][C]27[/C][C]20108[/C][C]20535[/C][C]-427[/C][/ROW]
[ROW][C]28[/C][C]18584[/C][C]20495[/C][C]-1911[/C][/ROW]
[ROW][C]29[/C][C]18441[/C][C]18971[/C][C]-530[/C][/ROW]
[ROW][C]30[/C][C]18391[/C][C]18828[/C][C]-437[/C][/ROW]
[ROW][C]31[/C][C]19178[/C][C]18778[/C][C]400[/C][/ROW]
[ROW][C]32[/C][C]18079[/C][C]19565[/C][C]-1486[/C][/ROW]
[ROW][C]33[/C][C]18483[/C][C]18466[/C][C]17[/C][/ROW]
[ROW][C]34[/C][C]19644[/C][C]18870[/C][C]774[/C][/ROW]
[ROW][C]35[/C][C]19195[/C][C]20031[/C][C]-836[/C][/ROW]
[ROW][C]36[/C][C]19650[/C][C]19582[/C][C]68[/C][/ROW]
[ROW][C]37[/C][C]20830[/C][C]20037[/C][C]793[/C][/ROW]
[ROW][C]38[/C][C]23595[/C][C]21217[/C][C]2378[/C][/ROW]
[ROW][C]39[/C][C]22937[/C][C]23982[/C][C]-1045[/C][/ROW]
[ROW][C]40[/C][C]21814[/C][C]23324[/C][C]-1510[/C][/ROW]
[ROW][C]41[/C][C]21928[/C][C]22201[/C][C]-273[/C][/ROW]
[ROW][C]42[/C][C]21777[/C][C]22315[/C][C]-538[/C][/ROW]
[ROW][C]43[/C][C]21383[/C][C]22164[/C][C]-781[/C][/ROW]
[ROW][C]44[/C][C]21467[/C][C]21770[/C][C]-303[/C][/ROW]
[ROW][C]45[/C][C]22052[/C][C]21854[/C][C]198[/C][/ROW]
[ROW][C]46[/C][C]22680[/C][C]22439[/C][C]241[/C][/ROW]
[ROW][C]47[/C][C]24320[/C][C]23067[/C][C]1253[/C][/ROW]
[ROW][C]48[/C][C]24977[/C][C]24707[/C][C]270[/C][/ROW]
[ROW][C]49[/C][C]25204[/C][C]25364[/C][C]-160[/C][/ROW]
[ROW][C]50[/C][C]25739[/C][C]25591[/C][C]148[/C][/ROW]
[ROW][C]51[/C][C]26434[/C][C]26126[/C][C]308[/C][/ROW]
[ROW][C]52[/C][C]27525[/C][C]26821[/C][C]704[/C][/ROW]
[ROW][C]53[/C][C]30695[/C][C]27912[/C][C]2783[/C][/ROW]
[ROW][C]54[/C][C]32436[/C][C]31082[/C][C]1354[/C][/ROW]
[ROW][C]55[/C][C]30160[/C][C]32823[/C][C]-2663[/C][/ROW]
[ROW][C]56[/C][C]30236[/C][C]30547[/C][C]-311[/C][/ROW]
[ROW][C]57[/C][C]31293[/C][C]30623[/C][C]670[/C][/ROW]
[ROW][C]58[/C][C]31077[/C][C]31680[/C][C]-603[/C][/ROW]
[ROW][C]59[/C][C]32226[/C][C]31464[/C][C]762[/C][/ROW]
[ROW][C]60[/C][C]33865[/C][C]32613[/C][C]1252[/C][/ROW]
[ROW][C]61[/C][C]32810[/C][C]34252[/C][C]-1442[/C][/ROW]
[ROW][C]62[/C][C]32242[/C][C]33197[/C][C]-955[/C][/ROW]
[ROW][C]63[/C][C]32700[/C][C]32629[/C][C]71[/C][/ROW]
[ROW][C]64[/C][C]32819[/C][C]33087[/C][C]-268[/C][/ROW]
[ROW][C]65[/C][C]33947[/C][C]33206[/C][C]741[/C][/ROW]
[ROW][C]66[/C][C]34148[/C][C]34334[/C][C]-186[/C][/ROW]
[ROW][C]67[/C][C]35261[/C][C]34535[/C][C]726[/C][/ROW]
[ROW][C]68[/C][C]39506[/C][C]35648[/C][C]3858[/C][/ROW]
[ROW][C]69[/C][C]41591[/C][C]39893[/C][C]1698[/C][/ROW]
[ROW][C]70[/C][C]39148[/C][C]41978[/C][C]-2830[/C][/ROW]
[ROW][C]71[/C][C]41216[/C][C]39535[/C][C]1681[/C][/ROW]
[ROW][C]72[/C][C]40225[/C][C]41603[/C][C]-1378[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=201354&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201354&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
31488615318-432
41600515273732
51706416392672
61516817451-2283
71605015555495
81583916437-598
91513716226-1089
101495415524-570
111564815341307
121530516035-730
131557915692-113
141634815966382
151592816735-807
161617116315-144
171593716558-621
181571316324-611
191559416100-506
201568315981-298
211643816070368
221703216825207
231769617419277
241774518083-338
2519394181321262
262014819781367
272010820535-427
281858420495-1911
291844118971-530
301839118828-437
311917818778400
321807919565-1486
33184831846617
341964418870774
351919520031-836
36196501958268
372083020037793
3823595212172378
392293723982-1045
402181423324-1510
412192822201-273
422177722315-538
432138322164-781
442146721770-303
452205221854198
462268022439241
4724320230671253
482497724707270
492520425364-160
502573925591148
512643426126308
522752526821704
5330695279122783
5432436310821354
553016032823-2663
563023630547-311
573129330623670
583107731680-603
593222631464762
6033865326131252
613281034252-1442
623224233197-955
63327003262971
643281933087-268
653394733206741
663414834334-186
673526134535726
6839506356483858
6941591398931698
703914841978-2830
7141216395351681
724022541603-1378







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
734061238391.092453662242832.9075463378
744099937858.162427192444139.8375728076
754138637539.275290829845232.7247091702
764177337331.184907324446214.8150926756
774216037193.899754646547126.1002453535
784254737106.909745575847987.0902544242
794293437058.030947523648809.9690524764
804332137039.324854384749602.6751456153
814370837045.277360986650370.7226390134
824409537071.873680916751118.1263190833
834448237116.082974728751847.9170252713
844486937175.550581659752562.4494183403

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 40612 & 38391.0924536622 & 42832.9075463378 \tabularnewline
74 & 40999 & 37858.1624271924 & 44139.8375728076 \tabularnewline
75 & 41386 & 37539.2752908298 & 45232.7247091702 \tabularnewline
76 & 41773 & 37331.1849073244 & 46214.8150926756 \tabularnewline
77 & 42160 & 37193.8997546465 & 47126.1002453535 \tabularnewline
78 & 42547 & 37106.9097455758 & 47987.0902544242 \tabularnewline
79 & 42934 & 37058.0309475236 & 48809.9690524764 \tabularnewline
80 & 43321 & 37039.3248543847 & 49602.6751456153 \tabularnewline
81 & 43708 & 37045.2773609866 & 50370.7226390134 \tabularnewline
82 & 44095 & 37071.8736809167 & 51118.1263190833 \tabularnewline
83 & 44482 & 37116.0829747287 & 51847.9170252713 \tabularnewline
84 & 44869 & 37175.5505816597 & 52562.4494183403 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201354&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]73[/C][C]40612[/C][C]38391.0924536622[/C][C]42832.9075463378[/C][/ROW]
[ROW][C]74[/C][C]40999[/C][C]37858.1624271924[/C][C]44139.8375728076[/C][/ROW]
[ROW][C]75[/C][C]41386[/C][C]37539.2752908298[/C][C]45232.7247091702[/C][/ROW]
[ROW][C]76[/C][C]41773[/C][C]37331.1849073244[/C][C]46214.8150926756[/C][/ROW]
[ROW][C]77[/C][C]42160[/C][C]37193.8997546465[/C][C]47126.1002453535[/C][/ROW]
[ROW][C]78[/C][C]42547[/C][C]37106.9097455758[/C][C]47987.0902544242[/C][/ROW]
[ROW][C]79[/C][C]42934[/C][C]37058.0309475236[/C][C]48809.9690524764[/C][/ROW]
[ROW][C]80[/C][C]43321[/C][C]37039.3248543847[/C][C]49602.6751456153[/C][/ROW]
[ROW][C]81[/C][C]43708[/C][C]37045.2773609866[/C][C]50370.7226390134[/C][/ROW]
[ROW][C]82[/C][C]44095[/C][C]37071.8736809167[/C][C]51118.1263190833[/C][/ROW]
[ROW][C]83[/C][C]44482[/C][C]37116.0829747287[/C][C]51847.9170252713[/C][/ROW]
[ROW][C]84[/C][C]44869[/C][C]37175.5505816597[/C][C]52562.4494183403[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=201354&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201354&T=3

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
734061238391.092453662242832.9075463378
744099937858.162427192444139.8375728076
754138637539.275290829845232.7247091702
764177337331.184907324446214.8150926756
774216037193.899754646547126.1002453535
784254737106.909745575847987.0902544242
794293437058.030947523648809.9690524764
804332137039.324854384749602.6751456153
814370837045.277360986650370.7226390134
824409537071.873680916751118.1263190833
834448237116.082974728751847.9170252713
844486937175.550581659752562.4494183403



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')