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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 30 Nov 2010 13:07:26 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Nov/30/t12911223401zepsh7lbwrv6ii.htm/, Retrieved Mon, 29 Apr 2024 11:55:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=103373, Retrieved Mon, 29 Apr 2024 11:55:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact167
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [HPC Retail Sales] [2008-03-10 17:43:04] [74be16979710d4c4e7c6647856088456]
F  MPD  [Exponential Smoothing] [] [2010-11-26 12:44:04] [8a9a6f7c332640af31ddca253a8ded58]
F    D      [Exponential Smoothing] [ws 8] [2010-11-30 13:07:26] [86130087148d9c8eb48f66f03eaf10c2] [Current]
Feedback Forum
2010-12-05 10:35:42 [00c625c7d009d84797af914265b614f9] [reply
Slecht model want de verdeling van de resisu's is niet normaal

Post a new message
Dataseries X:
101.76
102.37
102.38
102.86
102.87
102.92
102.95
103.02
104.08
104.16
104.24
104.33
104.73
104.86
105.03
105.62
105.63
105.63
105.94
106.61
107.69
107.78
107.93
108.48
108.14
108.48
108.48
108.89
108.93
109.21
109.47
109.80
111.73
111.85
112.12
112.15
112.17
112.67
112.80
113.44
113.53
114.53
114.51
115.05
116.67
117.07
116.92
117.00
117.02
117.35
117.36
117.82
117.88
118.24
118.50
118.80
119.76
120.09




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=103373&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=103373&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=103373&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.800423354394571
beta0.0331010306156857
gamma0.155500317120044

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.800423354394571 \tabularnewline
beta & 0.0331010306156857 \tabularnewline
gamma & 0.155500317120044 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=103373&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]0.800423354394571[/C][/ROW]
[ROW][C]beta[/C][C]0.0331010306156857[/C][/ROW]
[ROW][C]gamma[/C][C]0.155500317120044[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=103373&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=103373&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
alpha0.800423354394571
beta0.0331010306156857
gamma0.155500317120044







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13104.73103.3681490384621.36185096153842
14104.86104.6080718819910.251928118009161
15105.03104.9804280213140.0495719786860462
16105.62105.6108769823600.00912301763962375
17105.63105.6258580298650.0041419701350236
18105.63105.6048785381120.0251214618882756
19105.94106.117190443916-0.177190443916487
20106.61106.1162058766770.49379412332317
21107.69107.6687093561100.0212906438897846
22107.78107.852324107732-0.0723241077323422
23107.93107.954507876992-0.0245078769920042
24108.48108.1063988751590.373601124840917
25108.14108.929524782175-0.789524782174595
26108.48108.4173629503480.0626370496522384
27108.48108.631283210951-0.151283210950908
28108.89109.093743139711-0.203743139710568
29108.93108.9265821609620.00341783903807880
30109.21108.8940505548710.315949445129021
31109.47109.628951231003-0.158951231002746
32109.8109.6599543462360.14004565376365
33111.73110.9018380982000.828161901800428
34111.85111.7369567015820.113043298417523
35112.12112.0024786060700.117521393930190
36112.15112.297652993425-0.147652993425410
37112.17112.670892505072-0.500892505071604
38112.67112.4272864351390.242713564860921
39112.8112.7945579500050.00544204999491171
40113.44113.4008414515000.0391585485001116
41113.53113.4609744467300.0690255532704072
42114.53113.5188349394701.01116506052988
43114.51114.842062851837-0.332062851836938
44115.05114.7857945560260.26420544397412
45116.67116.1937154909330.476284509067455
46117.07116.7609687484860.309031251513616
47116.92117.224674324740-0.304674324739665
48117117.203669270894-0.203669270894281
49117.02117.549610742311-0.529610742310979
50117.35117.3338354959330.0161645040668503
51117.36117.534146260088-0.174146260088264
52117.82118.014709234096-0.194709234095882
53117.88117.899359389291-0.0193593892907273
54118.24117.9241548362920.315845163708474
55118.5118.639165780956-0.139165780956333
56118.8118.7509316734670.0490683265329324
57119.76119.98266366231-0.222663662310097
58120.09119.9561835013870.133816498612504

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 104.73 & 103.368149038462 & 1.36185096153842 \tabularnewline
14 & 104.86 & 104.608071881991 & 0.251928118009161 \tabularnewline
15 & 105.03 & 104.980428021314 & 0.0495719786860462 \tabularnewline
16 & 105.62 & 105.610876982360 & 0.00912301763962375 \tabularnewline
17 & 105.63 & 105.625858029865 & 0.0041419701350236 \tabularnewline
18 & 105.63 & 105.604878538112 & 0.0251214618882756 \tabularnewline
19 & 105.94 & 106.117190443916 & -0.177190443916487 \tabularnewline
20 & 106.61 & 106.116205876677 & 0.49379412332317 \tabularnewline
21 & 107.69 & 107.668709356110 & 0.0212906438897846 \tabularnewline
22 & 107.78 & 107.852324107732 & -0.0723241077323422 \tabularnewline
23 & 107.93 & 107.954507876992 & -0.0245078769920042 \tabularnewline
24 & 108.48 & 108.106398875159 & 0.373601124840917 \tabularnewline
25 & 108.14 & 108.929524782175 & -0.789524782174595 \tabularnewline
26 & 108.48 & 108.417362950348 & 0.0626370496522384 \tabularnewline
27 & 108.48 & 108.631283210951 & -0.151283210950908 \tabularnewline
28 & 108.89 & 109.093743139711 & -0.203743139710568 \tabularnewline
29 & 108.93 & 108.926582160962 & 0.00341783903807880 \tabularnewline
30 & 109.21 & 108.894050554871 & 0.315949445129021 \tabularnewline
31 & 109.47 & 109.628951231003 & -0.158951231002746 \tabularnewline
32 & 109.8 & 109.659954346236 & 0.14004565376365 \tabularnewline
33 & 111.73 & 110.901838098200 & 0.828161901800428 \tabularnewline
34 & 111.85 & 111.736956701582 & 0.113043298417523 \tabularnewline
35 & 112.12 & 112.002478606070 & 0.117521393930190 \tabularnewline
36 & 112.15 & 112.297652993425 & -0.147652993425410 \tabularnewline
37 & 112.17 & 112.670892505072 & -0.500892505071604 \tabularnewline
38 & 112.67 & 112.427286435139 & 0.242713564860921 \tabularnewline
39 & 112.8 & 112.794557950005 & 0.00544204999491171 \tabularnewline
40 & 113.44 & 113.400841451500 & 0.0391585485001116 \tabularnewline
41 & 113.53 & 113.460974446730 & 0.0690255532704072 \tabularnewline
42 & 114.53 & 113.518834939470 & 1.01116506052988 \tabularnewline
43 & 114.51 & 114.842062851837 & -0.332062851836938 \tabularnewline
44 & 115.05 & 114.785794556026 & 0.26420544397412 \tabularnewline
45 & 116.67 & 116.193715490933 & 0.476284509067455 \tabularnewline
46 & 117.07 & 116.760968748486 & 0.309031251513616 \tabularnewline
47 & 116.92 & 117.224674324740 & -0.304674324739665 \tabularnewline
48 & 117 & 117.203669270894 & -0.203669270894281 \tabularnewline
49 & 117.02 & 117.549610742311 & -0.529610742310979 \tabularnewline
50 & 117.35 & 117.333835495933 & 0.0161645040668503 \tabularnewline
51 & 117.36 & 117.534146260088 & -0.174146260088264 \tabularnewline
52 & 117.82 & 118.014709234096 & -0.194709234095882 \tabularnewline
53 & 117.88 & 117.899359389291 & -0.0193593892907273 \tabularnewline
54 & 118.24 & 117.924154836292 & 0.315845163708474 \tabularnewline
55 & 118.5 & 118.639165780956 & -0.139165780956333 \tabularnewline
56 & 118.8 & 118.750931673467 & 0.0490683265329324 \tabularnewline
57 & 119.76 & 119.98266366231 & -0.222663662310097 \tabularnewline
58 & 120.09 & 119.956183501387 & 0.133816498612504 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=103373&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]13[/C][C]104.73[/C][C]103.368149038462[/C][C]1.36185096153842[/C][/ROW]
[ROW][C]14[/C][C]104.86[/C][C]104.608071881991[/C][C]0.251928118009161[/C][/ROW]
[ROW][C]15[/C][C]105.03[/C][C]104.980428021314[/C][C]0.0495719786860462[/C][/ROW]
[ROW][C]16[/C][C]105.62[/C][C]105.610876982360[/C][C]0.00912301763962375[/C][/ROW]
[ROW][C]17[/C][C]105.63[/C][C]105.625858029865[/C][C]0.0041419701350236[/C][/ROW]
[ROW][C]18[/C][C]105.63[/C][C]105.604878538112[/C][C]0.0251214618882756[/C][/ROW]
[ROW][C]19[/C][C]105.94[/C][C]106.117190443916[/C][C]-0.177190443916487[/C][/ROW]
[ROW][C]20[/C][C]106.61[/C][C]106.116205876677[/C][C]0.49379412332317[/C][/ROW]
[ROW][C]21[/C][C]107.69[/C][C]107.668709356110[/C][C]0.0212906438897846[/C][/ROW]
[ROW][C]22[/C][C]107.78[/C][C]107.852324107732[/C][C]-0.0723241077323422[/C][/ROW]
[ROW][C]23[/C][C]107.93[/C][C]107.954507876992[/C][C]-0.0245078769920042[/C][/ROW]
[ROW][C]24[/C][C]108.48[/C][C]108.106398875159[/C][C]0.373601124840917[/C][/ROW]
[ROW][C]25[/C][C]108.14[/C][C]108.929524782175[/C][C]-0.789524782174595[/C][/ROW]
[ROW][C]26[/C][C]108.48[/C][C]108.417362950348[/C][C]0.0626370496522384[/C][/ROW]
[ROW][C]27[/C][C]108.48[/C][C]108.631283210951[/C][C]-0.151283210950908[/C][/ROW]
[ROW][C]28[/C][C]108.89[/C][C]109.093743139711[/C][C]-0.203743139710568[/C][/ROW]
[ROW][C]29[/C][C]108.93[/C][C]108.926582160962[/C][C]0.00341783903807880[/C][/ROW]
[ROW][C]30[/C][C]109.21[/C][C]108.894050554871[/C][C]0.315949445129021[/C][/ROW]
[ROW][C]31[/C][C]109.47[/C][C]109.628951231003[/C][C]-0.158951231002746[/C][/ROW]
[ROW][C]32[/C][C]109.8[/C][C]109.659954346236[/C][C]0.14004565376365[/C][/ROW]
[ROW][C]33[/C][C]111.73[/C][C]110.901838098200[/C][C]0.828161901800428[/C][/ROW]
[ROW][C]34[/C][C]111.85[/C][C]111.736956701582[/C][C]0.113043298417523[/C][/ROW]
[ROW][C]35[/C][C]112.12[/C][C]112.002478606070[/C][C]0.117521393930190[/C][/ROW]
[ROW][C]36[/C][C]112.15[/C][C]112.297652993425[/C][C]-0.147652993425410[/C][/ROW]
[ROW][C]37[/C][C]112.17[/C][C]112.670892505072[/C][C]-0.500892505071604[/C][/ROW]
[ROW][C]38[/C][C]112.67[/C][C]112.427286435139[/C][C]0.242713564860921[/C][/ROW]
[ROW][C]39[/C][C]112.8[/C][C]112.794557950005[/C][C]0.00544204999491171[/C][/ROW]
[ROW][C]40[/C][C]113.44[/C][C]113.400841451500[/C][C]0.0391585485001116[/C][/ROW]
[ROW][C]41[/C][C]113.53[/C][C]113.460974446730[/C][C]0.0690255532704072[/C][/ROW]
[ROW][C]42[/C][C]114.53[/C][C]113.518834939470[/C][C]1.01116506052988[/C][/ROW]
[ROW][C]43[/C][C]114.51[/C][C]114.842062851837[/C][C]-0.332062851836938[/C][/ROW]
[ROW][C]44[/C][C]115.05[/C][C]114.785794556026[/C][C]0.26420544397412[/C][/ROW]
[ROW][C]45[/C][C]116.67[/C][C]116.193715490933[/C][C]0.476284509067455[/C][/ROW]
[ROW][C]46[/C][C]117.07[/C][C]116.760968748486[/C][C]0.309031251513616[/C][/ROW]
[ROW][C]47[/C][C]116.92[/C][C]117.224674324740[/C][C]-0.304674324739665[/C][/ROW]
[ROW][C]48[/C][C]117[/C][C]117.203669270894[/C][C]-0.203669270894281[/C][/ROW]
[ROW][C]49[/C][C]117.02[/C][C]117.549610742311[/C][C]-0.529610742310979[/C][/ROW]
[ROW][C]50[/C][C]117.35[/C][C]117.333835495933[/C][C]0.0161645040668503[/C][/ROW]
[ROW][C]51[/C][C]117.36[/C][C]117.534146260088[/C][C]-0.174146260088264[/C][/ROW]
[ROW][C]52[/C][C]117.82[/C][C]118.014709234096[/C][C]-0.194709234095882[/C][/ROW]
[ROW][C]53[/C][C]117.88[/C][C]117.899359389291[/C][C]-0.0193593892907273[/C][/ROW]
[ROW][C]54[/C][C]118.24[/C][C]117.924154836292[/C][C]0.315845163708474[/C][/ROW]
[ROW][C]55[/C][C]118.5[/C][C]118.639165780956[/C][C]-0.139165780956333[/C][/ROW]
[ROW][C]56[/C][C]118.8[/C][C]118.750931673467[/C][C]0.0490683265329324[/C][/ROW]
[ROW][C]57[/C][C]119.76[/C][C]119.98266366231[/C][C]-0.222663662310097[/C][/ROW]
[ROW][C]58[/C][C]120.09[/C][C]119.956183501387[/C][C]0.133816498612504[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=103373&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=103373&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
13104.73103.3681490384621.36185096153842
14104.86104.6080718819910.251928118009161
15105.03104.9804280213140.0495719786860462
16105.62105.6108769823600.00912301763962375
17105.63105.6258580298650.0041419701350236
18105.63105.6048785381120.0251214618882756
19105.94106.117190443916-0.177190443916487
20106.61106.1162058766770.49379412332317
21107.69107.6687093561100.0212906438897846
22107.78107.852324107732-0.0723241077323422
23107.93107.954507876992-0.0245078769920042
24108.48108.1063988751590.373601124840917
25108.14108.929524782175-0.789524782174595
26108.48108.4173629503480.0626370496522384
27108.48108.631283210951-0.151283210950908
28108.89109.093743139711-0.203743139710568
29108.93108.9265821609620.00341783903807880
30109.21108.8940505548710.315949445129021
31109.47109.628951231003-0.158951231002746
32109.8109.6599543462360.14004565376365
33111.73110.9018380982000.828161901800428
34111.85111.7369567015820.113043298417523
35112.12112.0024786060700.117521393930190
36112.15112.297652993425-0.147652993425410
37112.17112.670892505072-0.500892505071604
38112.67112.4272864351390.242713564860921
39112.8112.7945579500050.00544204999491171
40113.44113.4008414515000.0391585485001116
41113.53113.4609744467300.0690255532704072
42114.53113.5188349394701.01116506052988
43114.51114.842062851837-0.332062851836938
44115.05114.7857945560260.26420544397412
45116.67116.1937154909330.476284509067455
46117.07116.7609687484860.309031251513616
47116.92117.224674324740-0.304674324739665
48117117.203669270894-0.203669270894281
49117.02117.549610742311-0.529610742310979
50117.35117.3338354959330.0161645040668503
51117.36117.534146260088-0.174146260088264
52117.82118.014709234096-0.194709234095882
53117.88117.899359389291-0.0193593892907273
54118.24117.9241548362920.315845163708474
55118.5118.639165780956-0.139165780956333
56118.8118.7509316734670.0490683265329324
57119.76119.98266366231-0.222663662310097
58120.09119.9561835013870.133816498612504







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
59120.226866527610119.495761283632120.957971771589
60120.427206141141119.478516106375121.375896175907
61120.905791702873119.770314999450122.041268406296
62121.124636722078119.819589214388122.429684229769
63121.299444358661119.835788601420122.763100115901
64121.916715354507120.301947472475123.531483236539
65121.965771409587120.205242840537123.726299978637
66122.020092537433120.117726852765123.922458222101
67122.463431612958120.422150443244124.504712782672
68122.691376813736120.513370357589124.869383269883
69123.873046383359121.559954176059126.186138590659
70124.039399952275121.59243661849126.486363286060

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
59 & 120.226866527610 & 119.495761283632 & 120.957971771589 \tabularnewline
60 & 120.427206141141 & 119.478516106375 & 121.375896175907 \tabularnewline
61 & 120.905791702873 & 119.770314999450 & 122.041268406296 \tabularnewline
62 & 121.124636722078 & 119.819589214388 & 122.429684229769 \tabularnewline
63 & 121.299444358661 & 119.835788601420 & 122.763100115901 \tabularnewline
64 & 121.916715354507 & 120.301947472475 & 123.531483236539 \tabularnewline
65 & 121.965771409587 & 120.205242840537 & 123.726299978637 \tabularnewline
66 & 122.020092537433 & 120.117726852765 & 123.922458222101 \tabularnewline
67 & 122.463431612958 & 120.422150443244 & 124.504712782672 \tabularnewline
68 & 122.691376813736 & 120.513370357589 & 124.869383269883 \tabularnewline
69 & 123.873046383359 & 121.559954176059 & 126.186138590659 \tabularnewline
70 & 124.039399952275 & 121.59243661849 & 126.486363286060 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=103373&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]59[/C][C]120.226866527610[/C][C]119.495761283632[/C][C]120.957971771589[/C][/ROW]
[ROW][C]60[/C][C]120.427206141141[/C][C]119.478516106375[/C][C]121.375896175907[/C][/ROW]
[ROW][C]61[/C][C]120.905791702873[/C][C]119.770314999450[/C][C]122.041268406296[/C][/ROW]
[ROW][C]62[/C][C]121.124636722078[/C][C]119.819589214388[/C][C]122.429684229769[/C][/ROW]
[ROW][C]63[/C][C]121.299444358661[/C][C]119.835788601420[/C][C]122.763100115901[/C][/ROW]
[ROW][C]64[/C][C]121.916715354507[/C][C]120.301947472475[/C][C]123.531483236539[/C][/ROW]
[ROW][C]65[/C][C]121.965771409587[/C][C]120.205242840537[/C][C]123.726299978637[/C][/ROW]
[ROW][C]66[/C][C]122.020092537433[/C][C]120.117726852765[/C][C]123.922458222101[/C][/ROW]
[ROW][C]67[/C][C]122.463431612958[/C][C]120.422150443244[/C][C]124.504712782672[/C][/ROW]
[ROW][C]68[/C][C]122.691376813736[/C][C]120.513370357589[/C][C]124.869383269883[/C][/ROW]
[ROW][C]69[/C][C]123.873046383359[/C][C]121.559954176059[/C][C]126.186138590659[/C][/ROW]
[ROW][C]70[/C][C]124.039399952275[/C][C]121.59243661849[/C][C]126.486363286060[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=103373&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=103373&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
59120.226866527610119.495761283632120.957971771589
60120.427206141141119.478516106375121.375896175907
61120.905791702873119.770314999450122.041268406296
62121.124636722078119.819589214388122.429684229769
63121.299444358661119.835788601420122.763100115901
64121.916715354507120.301947472475123.531483236539
65121.965771409587120.205242840537123.726299978637
66122.020092537433120.117726852765123.922458222101
67122.463431612958120.422150443244124.504712782672
68122.691376813736120.513370357589124.869383269883
69123.873046383359121.559954176059126.186138590659
70124.039399952275121.59243661849126.486363286060



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; 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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')