Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 10 Jan 2011 10:17:54 +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/2011/Jan/10/t1294654537f4qyv2it0gwff2f.htm/, Retrieved Fri, 17 May 2024 18:22:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=117298, Retrieved Fri, 17 May 2024 18:22:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact237
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponential smoot...] [2011-01-10 10:17:54] [6828a15931dcaf58ef367cb5857a54a7] [Current]
Feedback Forum

Post a new message
Dataseries X:
96,92
99,06
99,65
99,82
99,99
100,33
99,31
101,1
101,1
100,93
100,85
100,93
99,6
101,88
101,81
102,38
102,74
102,82
101,72
103,47
102,98
102,68
102,9
103,03
101,29
103,69
103,68
104,2
104,08
104,16
103,05
104,66
104,46
104,95
105,85
106,23
104,86
107,44
108,23
108,45
109,39
110,15
109,13
110,28
110,17
109,99
109,26
109,11
107,06
109,53
108,92
109,24
109,12
109
107,23
109,49
109,04
109,02
109,23
109,46




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ www.wessa.org

\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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ www.wessa.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117298&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ www.wessa.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117298&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117298&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 time1 seconds
R Server'Gwilym Jenkins' @ www.wessa.org







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117298&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]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117298&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117298&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
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1399.698.3284668803421.27153311965806
14101.88101.8760868298370.00391317016317316
15101.81101.82817016317-0.0181701631701685
16102.38102.424003496504-0.0440034965035068
17102.74102.77692016317-0.0369201631701515
18102.82102.842336829837-0.0223368298368314
19101.72101.6410868298370.0789131701631618
20103.47103.476086829837-0.00608682983683195
21102.98103.457753496503-0.477753496503482
22102.68102.808586829837-0.128586829836834
23102.9102.5740034965030.325996503496526
24103.03102.956920163170.0730798368297911
25101.29101.691086829837-0.4010868298368
26103.69103.5660868298370.123913170163163
27103.68103.638170163170.0418298368298338
28104.2104.294003496504-0.094003496503504
29104.08104.59692016317-0.516920163170155
30104.16104.182336829837-0.0223368298368314
31103.05102.9810868298370.0689131701631567
32104.66104.806086829837-0.146086829836833
33104.46104.647753496503-0.18775349650349
34104.95104.2885868298370.661413170163172
35105.85104.8440034965031.00599650349652
36106.23105.906920163170.323079836829805
37104.86104.891086829837-0.0310868298368092
38107.44107.1360868298370.30391317016317
39108.23107.388170163170.841829836829831
40108.45108.844003496504-0.394003496503501
41109.39108.846920163170.543079836829847
42110.15109.4923368298370.657663170163175
43109.13108.9710868298370.158913170163146
44110.28110.886086829837-0.606086829836826
45110.17110.267753496503-0.0977534965034863
46109.99109.998586829837-0.00858682983684389
47109.26109.884003496503-0.624003496503462
48109.11109.31692016317-0.20692016317021
49107.06107.771086829837-0.711086829836802
50109.53109.3360868298370.193913170163171
51108.92109.47817016317-0.558170163170175
52109.24109.534003496504-0.294003496503507
53109.12109.63692016317-0.516920163170141
54109109.222336829837-0.222336829836834
55107.23107.821086829837-0.59108682983684
56109.49108.9860868298370.503913170163159
57109.04109.477753496503-0.437753496503476
58109.02108.8685868298370.151413170163153
59109.23108.9140034965030.315996503496535
60109.46109.286920163170.173079836829785

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 99.6 & 98.328466880342 & 1.27153311965806 \tabularnewline
14 & 101.88 & 101.876086829837 & 0.00391317016317316 \tabularnewline
15 & 101.81 & 101.82817016317 & -0.0181701631701685 \tabularnewline
16 & 102.38 & 102.424003496504 & -0.0440034965035068 \tabularnewline
17 & 102.74 & 102.77692016317 & -0.0369201631701515 \tabularnewline
18 & 102.82 & 102.842336829837 & -0.0223368298368314 \tabularnewline
19 & 101.72 & 101.641086829837 & 0.0789131701631618 \tabularnewline
20 & 103.47 & 103.476086829837 & -0.00608682983683195 \tabularnewline
21 & 102.98 & 103.457753496503 & -0.477753496503482 \tabularnewline
22 & 102.68 & 102.808586829837 & -0.128586829836834 \tabularnewline
23 & 102.9 & 102.574003496503 & 0.325996503496526 \tabularnewline
24 & 103.03 & 102.95692016317 & 0.0730798368297911 \tabularnewline
25 & 101.29 & 101.691086829837 & -0.4010868298368 \tabularnewline
26 & 103.69 & 103.566086829837 & 0.123913170163163 \tabularnewline
27 & 103.68 & 103.63817016317 & 0.0418298368298338 \tabularnewline
28 & 104.2 & 104.294003496504 & -0.094003496503504 \tabularnewline
29 & 104.08 & 104.59692016317 & -0.516920163170155 \tabularnewline
30 & 104.16 & 104.182336829837 & -0.0223368298368314 \tabularnewline
31 & 103.05 & 102.981086829837 & 0.0689131701631567 \tabularnewline
32 & 104.66 & 104.806086829837 & -0.146086829836833 \tabularnewline
33 & 104.46 & 104.647753496503 & -0.18775349650349 \tabularnewline
34 & 104.95 & 104.288586829837 & 0.661413170163172 \tabularnewline
35 & 105.85 & 104.844003496503 & 1.00599650349652 \tabularnewline
36 & 106.23 & 105.90692016317 & 0.323079836829805 \tabularnewline
37 & 104.86 & 104.891086829837 & -0.0310868298368092 \tabularnewline
38 & 107.44 & 107.136086829837 & 0.30391317016317 \tabularnewline
39 & 108.23 & 107.38817016317 & 0.841829836829831 \tabularnewline
40 & 108.45 & 108.844003496504 & -0.394003496503501 \tabularnewline
41 & 109.39 & 108.84692016317 & 0.543079836829847 \tabularnewline
42 & 110.15 & 109.492336829837 & 0.657663170163175 \tabularnewline
43 & 109.13 & 108.971086829837 & 0.158913170163146 \tabularnewline
44 & 110.28 & 110.886086829837 & -0.606086829836826 \tabularnewline
45 & 110.17 & 110.267753496503 & -0.0977534965034863 \tabularnewline
46 & 109.99 & 109.998586829837 & -0.00858682983684389 \tabularnewline
47 & 109.26 & 109.884003496503 & -0.624003496503462 \tabularnewline
48 & 109.11 & 109.31692016317 & -0.20692016317021 \tabularnewline
49 & 107.06 & 107.771086829837 & -0.711086829836802 \tabularnewline
50 & 109.53 & 109.336086829837 & 0.193913170163171 \tabularnewline
51 & 108.92 & 109.47817016317 & -0.558170163170175 \tabularnewline
52 & 109.24 & 109.534003496504 & -0.294003496503507 \tabularnewline
53 & 109.12 & 109.63692016317 & -0.516920163170141 \tabularnewline
54 & 109 & 109.222336829837 & -0.222336829836834 \tabularnewline
55 & 107.23 & 107.821086829837 & -0.59108682983684 \tabularnewline
56 & 109.49 & 108.986086829837 & 0.503913170163159 \tabularnewline
57 & 109.04 & 109.477753496503 & -0.437753496503476 \tabularnewline
58 & 109.02 & 108.868586829837 & 0.151413170163153 \tabularnewline
59 & 109.23 & 108.914003496503 & 0.315996503496535 \tabularnewline
60 & 109.46 & 109.28692016317 & 0.173079836829785 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117298&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]99.6[/C][C]98.328466880342[/C][C]1.27153311965806[/C][/ROW]
[ROW][C]14[/C][C]101.88[/C][C]101.876086829837[/C][C]0.00391317016317316[/C][/ROW]
[ROW][C]15[/C][C]101.81[/C][C]101.82817016317[/C][C]-0.0181701631701685[/C][/ROW]
[ROW][C]16[/C][C]102.38[/C][C]102.424003496504[/C][C]-0.0440034965035068[/C][/ROW]
[ROW][C]17[/C][C]102.74[/C][C]102.77692016317[/C][C]-0.0369201631701515[/C][/ROW]
[ROW][C]18[/C][C]102.82[/C][C]102.842336829837[/C][C]-0.0223368298368314[/C][/ROW]
[ROW][C]19[/C][C]101.72[/C][C]101.641086829837[/C][C]0.0789131701631618[/C][/ROW]
[ROW][C]20[/C][C]103.47[/C][C]103.476086829837[/C][C]-0.00608682983683195[/C][/ROW]
[ROW][C]21[/C][C]102.98[/C][C]103.457753496503[/C][C]-0.477753496503482[/C][/ROW]
[ROW][C]22[/C][C]102.68[/C][C]102.808586829837[/C][C]-0.128586829836834[/C][/ROW]
[ROW][C]23[/C][C]102.9[/C][C]102.574003496503[/C][C]0.325996503496526[/C][/ROW]
[ROW][C]24[/C][C]103.03[/C][C]102.95692016317[/C][C]0.0730798368297911[/C][/ROW]
[ROW][C]25[/C][C]101.29[/C][C]101.691086829837[/C][C]-0.4010868298368[/C][/ROW]
[ROW][C]26[/C][C]103.69[/C][C]103.566086829837[/C][C]0.123913170163163[/C][/ROW]
[ROW][C]27[/C][C]103.68[/C][C]103.63817016317[/C][C]0.0418298368298338[/C][/ROW]
[ROW][C]28[/C][C]104.2[/C][C]104.294003496504[/C][C]-0.094003496503504[/C][/ROW]
[ROW][C]29[/C][C]104.08[/C][C]104.59692016317[/C][C]-0.516920163170155[/C][/ROW]
[ROW][C]30[/C][C]104.16[/C][C]104.182336829837[/C][C]-0.0223368298368314[/C][/ROW]
[ROW][C]31[/C][C]103.05[/C][C]102.981086829837[/C][C]0.0689131701631567[/C][/ROW]
[ROW][C]32[/C][C]104.66[/C][C]104.806086829837[/C][C]-0.146086829836833[/C][/ROW]
[ROW][C]33[/C][C]104.46[/C][C]104.647753496503[/C][C]-0.18775349650349[/C][/ROW]
[ROW][C]34[/C][C]104.95[/C][C]104.288586829837[/C][C]0.661413170163172[/C][/ROW]
[ROW][C]35[/C][C]105.85[/C][C]104.844003496503[/C][C]1.00599650349652[/C][/ROW]
[ROW][C]36[/C][C]106.23[/C][C]105.90692016317[/C][C]0.323079836829805[/C][/ROW]
[ROW][C]37[/C][C]104.86[/C][C]104.891086829837[/C][C]-0.0310868298368092[/C][/ROW]
[ROW][C]38[/C][C]107.44[/C][C]107.136086829837[/C][C]0.30391317016317[/C][/ROW]
[ROW][C]39[/C][C]108.23[/C][C]107.38817016317[/C][C]0.841829836829831[/C][/ROW]
[ROW][C]40[/C][C]108.45[/C][C]108.844003496504[/C][C]-0.394003496503501[/C][/ROW]
[ROW][C]41[/C][C]109.39[/C][C]108.84692016317[/C][C]0.543079836829847[/C][/ROW]
[ROW][C]42[/C][C]110.15[/C][C]109.492336829837[/C][C]0.657663170163175[/C][/ROW]
[ROW][C]43[/C][C]109.13[/C][C]108.971086829837[/C][C]0.158913170163146[/C][/ROW]
[ROW][C]44[/C][C]110.28[/C][C]110.886086829837[/C][C]-0.606086829836826[/C][/ROW]
[ROW][C]45[/C][C]110.17[/C][C]110.267753496503[/C][C]-0.0977534965034863[/C][/ROW]
[ROW][C]46[/C][C]109.99[/C][C]109.998586829837[/C][C]-0.00858682983684389[/C][/ROW]
[ROW][C]47[/C][C]109.26[/C][C]109.884003496503[/C][C]-0.624003496503462[/C][/ROW]
[ROW][C]48[/C][C]109.11[/C][C]109.31692016317[/C][C]-0.20692016317021[/C][/ROW]
[ROW][C]49[/C][C]107.06[/C][C]107.771086829837[/C][C]-0.711086829836802[/C][/ROW]
[ROW][C]50[/C][C]109.53[/C][C]109.336086829837[/C][C]0.193913170163171[/C][/ROW]
[ROW][C]51[/C][C]108.92[/C][C]109.47817016317[/C][C]-0.558170163170175[/C][/ROW]
[ROW][C]52[/C][C]109.24[/C][C]109.534003496504[/C][C]-0.294003496503507[/C][/ROW]
[ROW][C]53[/C][C]109.12[/C][C]109.63692016317[/C][C]-0.516920163170141[/C][/ROW]
[ROW][C]54[/C][C]109[/C][C]109.222336829837[/C][C]-0.222336829836834[/C][/ROW]
[ROW][C]55[/C][C]107.23[/C][C]107.821086829837[/C][C]-0.59108682983684[/C][/ROW]
[ROW][C]56[/C][C]109.49[/C][C]108.986086829837[/C][C]0.503913170163159[/C][/ROW]
[ROW][C]57[/C][C]109.04[/C][C]109.477753496503[/C][C]-0.437753496503476[/C][/ROW]
[ROW][C]58[/C][C]109.02[/C][C]108.868586829837[/C][C]0.151413170163153[/C][/ROW]
[ROW][C]59[/C][C]109.23[/C][C]108.914003496503[/C][C]0.315996503496535[/C][/ROW]
[ROW][C]60[/C][C]109.46[/C][C]109.28692016317[/C][C]0.173079836829785[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117298&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117298&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
1399.698.3284668803421.27153311965806
14101.88101.8760868298370.00391317016317316
15101.81101.82817016317-0.0181701631701685
16102.38102.424003496504-0.0440034965035068
17102.74102.77692016317-0.0369201631701515
18102.82102.842336829837-0.0223368298368314
19101.72101.6410868298370.0789131701631618
20103.47103.476086829837-0.00608682983683195
21102.98103.457753496503-0.477753496503482
22102.68102.808586829837-0.128586829836834
23102.9102.5740034965030.325996503496526
24103.03102.956920163170.0730798368297911
25101.29101.691086829837-0.4010868298368
26103.69103.5660868298370.123913170163163
27103.68103.638170163170.0418298368298338
28104.2104.294003496504-0.094003496503504
29104.08104.59692016317-0.516920163170155
30104.16104.182336829837-0.0223368298368314
31103.05102.9810868298370.0689131701631567
32104.66104.806086829837-0.146086829836833
33104.46104.647753496503-0.18775349650349
34104.95104.2885868298370.661413170163172
35105.85104.8440034965031.00599650349652
36106.23105.906920163170.323079836829805
37104.86104.891086829837-0.0310868298368092
38107.44107.1360868298370.30391317016317
39108.23107.388170163170.841829836829831
40108.45108.844003496504-0.394003496503501
41109.39108.846920163170.543079836829847
42110.15109.4923368298370.657663170163175
43109.13108.9710868298370.158913170163146
44110.28110.886086829837-0.606086829836826
45110.17110.267753496503-0.0977534965034863
46109.99109.998586829837-0.00858682983684389
47109.26109.884003496503-0.624003496503462
48109.11109.31692016317-0.20692016317021
49107.06107.771086829837-0.711086829836802
50109.53109.3360868298370.193913170163171
51108.92109.47817016317-0.558170163170175
52109.24109.534003496504-0.294003496503507
53109.12109.63692016317-0.516920163170141
54109109.222336829837-0.222336829836834
55107.23107.821086829837-0.59108682983684
56109.49108.9860868298370.503913170163159
57109.04109.477753496503-0.437753496503476
58109.02108.8685868298370.151413170163153
59109.23108.9140034965030.315996503496535
60109.46109.286920163170.173079836829785







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
61108.121086829837107.27423736311108.967936296564
62110.397173659674109.19954765854111.594799660807
63110.345343822844108.87855752011111.812130125578
64110.959347319347109.265648385893112.653046252801
65111.356267482517109.462654508206113.249880456828
66111.458604312354109.384255229925113.532953394783
67110.279691142191108.039138055324112.520244229058
68112.035777972028109.640525969761114.431029974295
69112.023531468531109.48298306835114.564079868712
70111.852118298368109.174145148212114.530091448524
71111.746121794872108.937439859826114.554803729918
72111.803041958042108.869469352574114.736614563509

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 108.121086829837 & 107.27423736311 & 108.967936296564 \tabularnewline
62 & 110.397173659674 & 109.19954765854 & 111.594799660807 \tabularnewline
63 & 110.345343822844 & 108.87855752011 & 111.812130125578 \tabularnewline
64 & 110.959347319347 & 109.265648385893 & 112.653046252801 \tabularnewline
65 & 111.356267482517 & 109.462654508206 & 113.249880456828 \tabularnewline
66 & 111.458604312354 & 109.384255229925 & 113.532953394783 \tabularnewline
67 & 110.279691142191 & 108.039138055324 & 112.520244229058 \tabularnewline
68 & 112.035777972028 & 109.640525969761 & 114.431029974295 \tabularnewline
69 & 112.023531468531 & 109.48298306835 & 114.564079868712 \tabularnewline
70 & 111.852118298368 & 109.174145148212 & 114.530091448524 \tabularnewline
71 & 111.746121794872 & 108.937439859826 & 114.554803729918 \tabularnewline
72 & 111.803041958042 & 108.869469352574 & 114.736614563509 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117298&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]61[/C][C]108.121086829837[/C][C]107.27423736311[/C][C]108.967936296564[/C][/ROW]
[ROW][C]62[/C][C]110.397173659674[/C][C]109.19954765854[/C][C]111.594799660807[/C][/ROW]
[ROW][C]63[/C][C]110.345343822844[/C][C]108.87855752011[/C][C]111.812130125578[/C][/ROW]
[ROW][C]64[/C][C]110.959347319347[/C][C]109.265648385893[/C][C]112.653046252801[/C][/ROW]
[ROW][C]65[/C][C]111.356267482517[/C][C]109.462654508206[/C][C]113.249880456828[/C][/ROW]
[ROW][C]66[/C][C]111.458604312354[/C][C]109.384255229925[/C][C]113.532953394783[/C][/ROW]
[ROW][C]67[/C][C]110.279691142191[/C][C]108.039138055324[/C][C]112.520244229058[/C][/ROW]
[ROW][C]68[/C][C]112.035777972028[/C][C]109.640525969761[/C][C]114.431029974295[/C][/ROW]
[ROW][C]69[/C][C]112.023531468531[/C][C]109.48298306835[/C][C]114.564079868712[/C][/ROW]
[ROW][C]70[/C][C]111.852118298368[/C][C]109.174145148212[/C][C]114.530091448524[/C][/ROW]
[ROW][C]71[/C][C]111.746121794872[/C][C]108.937439859826[/C][C]114.554803729918[/C][/ROW]
[ROW][C]72[/C][C]111.803041958042[/C][C]108.869469352574[/C][C]114.736614563509[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117298&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117298&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
61108.121086829837107.27423736311108.967936296564
62110.397173659674109.19954765854111.594799660807
63110.345343822844108.87855752011111.812130125578
64110.959347319347109.265648385893112.653046252801
65111.356267482517109.462654508206113.249880456828
66111.458604312354109.384255229925113.532953394783
67110.279691142191108.039138055324112.520244229058
68112.035777972028109.640525969761114.431029974295
69112.023531468531109.48298306835114.564079868712
70111.852118298368109.174145148212114.530091448524
71111.746121794872108.937439859826114.554803729918
72111.803041958042108.869469352574114.736614563509



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=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')