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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 03 Jan 2016 22:42:05 +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/2016/Jan/03/t1451861053zbw9omaf28c1up5.htm/, Retrieved Fri, 03 May 2024 10:42:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=287320, Retrieved Fri, 03 May 2024 10:42:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact119
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [] [2015-11-29 20:14:57] [a35a7564c14340793d25633850976e7b]
- R PD    [Exponential Smoothing] [] [2016-01-03 22:42:05] [5460c453892b15ffecb85c645e1cdda5] [Current]
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Dataseries X:
94.3
94.6
94.9
95.6
95.4
97.4
98.4
100.5
106.6
106.7
106.8
109
109.3
110.5
113.4
113
113.6
121.2
120.5
120.9
125.8
125.4
125.7
127.7
128.1
130
130.5
130.1
129.6
128.8
128.4
128.3
127.6
127.3
127.7
126.9
125.1
119
118.7
118.9
116.9
117
117
115.5
115.6
117.5
117.6
117.8
119.3
120
120.2
109.4
109
108.8
96.3
96.9
97
111.4
111.8
111.7




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287320&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 Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287320&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287320&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 Maurice George Kendall' @ kendall.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=287320&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=287320&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287320&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
394.994.91.4210854715202e-14
495.695.20.399999999999991
595.495.9-0.499999999999986
697.495.71.7
798.497.70.700000000000003
8100.598.71.8
9106.6100.85.8
10106.7106.9-0.199999999999989
11106.8107-0.200000000000003
12109107.11.90000000000001
13109.3109.30
14110.5109.60.900000000000006
15113.4110.82.60000000000001
16113113.7-0.700000000000003
17113.6113.30.299999999999997
18121.2113.97.30000000000001
19120.5121.5-1
20120.9120.80.100000000000009
21125.8121.24.59999999999999
22125.4126.1-0.699999999999989
23125.7125.70
24127.71261.7
25128.11280.0999999999999943
26130128.41.60000000000002
27130.5130.30.199999999999989
28130.1130.8-0.700000000000017
29129.6130.4-0.799999999999983
30128.8129.9-1.09999999999997
31128.4129.1-0.700000000000017
32128.3128.7-0.399999999999977
33127.6128.6-1.00000000000003
34127.3127.9-0.599999999999994
35127.7127.60.100000000000009
36126.9128-1.09999999999999
37125.1127.2-2.10000000000001
38119125.4-6.39999999999999
39118.7119.3-0.599999999999994
40118.9119-0.0999999999999943
41116.9119.2-2.3
42117117.2-0.200000000000003
43117117.3-0.299999999999997
44115.5117.3-1.8
45115.6115.8-0.200000000000003
46117.5115.91.60000000000001
47117.6117.8-0.200000000000003
48117.8117.9-0.0999999999999943
49119.3118.11.2
50120119.60.400000000000006
51120.2120.3-0.0999999999999943
52109.4120.5-11.1
53109109.7-0.700000000000003
54108.8109.3-0.5
5596.3109.1-12.8
5696.996.60.300000000000011
579797.2-0.200000000000003
58111.497.314.1
59111.8111.70.0999999999999943
60111.7112.1-0.399999999999991

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 94.9 & 94.9 & 1.4210854715202e-14 \tabularnewline
4 & 95.6 & 95.2 & 0.399999999999991 \tabularnewline
5 & 95.4 & 95.9 & -0.499999999999986 \tabularnewline
6 & 97.4 & 95.7 & 1.7 \tabularnewline
7 & 98.4 & 97.7 & 0.700000000000003 \tabularnewline
8 & 100.5 & 98.7 & 1.8 \tabularnewline
9 & 106.6 & 100.8 & 5.8 \tabularnewline
10 & 106.7 & 106.9 & -0.199999999999989 \tabularnewline
11 & 106.8 & 107 & -0.200000000000003 \tabularnewline
12 & 109 & 107.1 & 1.90000000000001 \tabularnewline
13 & 109.3 & 109.3 & 0 \tabularnewline
14 & 110.5 & 109.6 & 0.900000000000006 \tabularnewline
15 & 113.4 & 110.8 & 2.60000000000001 \tabularnewline
16 & 113 & 113.7 & -0.700000000000003 \tabularnewline
17 & 113.6 & 113.3 & 0.299999999999997 \tabularnewline
18 & 121.2 & 113.9 & 7.30000000000001 \tabularnewline
19 & 120.5 & 121.5 & -1 \tabularnewline
20 & 120.9 & 120.8 & 0.100000000000009 \tabularnewline
21 & 125.8 & 121.2 & 4.59999999999999 \tabularnewline
22 & 125.4 & 126.1 & -0.699999999999989 \tabularnewline
23 & 125.7 & 125.7 & 0 \tabularnewline
24 & 127.7 & 126 & 1.7 \tabularnewline
25 & 128.1 & 128 & 0.0999999999999943 \tabularnewline
26 & 130 & 128.4 & 1.60000000000002 \tabularnewline
27 & 130.5 & 130.3 & 0.199999999999989 \tabularnewline
28 & 130.1 & 130.8 & -0.700000000000017 \tabularnewline
29 & 129.6 & 130.4 & -0.799999999999983 \tabularnewline
30 & 128.8 & 129.9 & -1.09999999999997 \tabularnewline
31 & 128.4 & 129.1 & -0.700000000000017 \tabularnewline
32 & 128.3 & 128.7 & -0.399999999999977 \tabularnewline
33 & 127.6 & 128.6 & -1.00000000000003 \tabularnewline
34 & 127.3 & 127.9 & -0.599999999999994 \tabularnewline
35 & 127.7 & 127.6 & 0.100000000000009 \tabularnewline
36 & 126.9 & 128 & -1.09999999999999 \tabularnewline
37 & 125.1 & 127.2 & -2.10000000000001 \tabularnewline
38 & 119 & 125.4 & -6.39999999999999 \tabularnewline
39 & 118.7 & 119.3 & -0.599999999999994 \tabularnewline
40 & 118.9 & 119 & -0.0999999999999943 \tabularnewline
41 & 116.9 & 119.2 & -2.3 \tabularnewline
42 & 117 & 117.2 & -0.200000000000003 \tabularnewline
43 & 117 & 117.3 & -0.299999999999997 \tabularnewline
44 & 115.5 & 117.3 & -1.8 \tabularnewline
45 & 115.6 & 115.8 & -0.200000000000003 \tabularnewline
46 & 117.5 & 115.9 & 1.60000000000001 \tabularnewline
47 & 117.6 & 117.8 & -0.200000000000003 \tabularnewline
48 & 117.8 & 117.9 & -0.0999999999999943 \tabularnewline
49 & 119.3 & 118.1 & 1.2 \tabularnewline
50 & 120 & 119.6 & 0.400000000000006 \tabularnewline
51 & 120.2 & 120.3 & -0.0999999999999943 \tabularnewline
52 & 109.4 & 120.5 & -11.1 \tabularnewline
53 & 109 & 109.7 & -0.700000000000003 \tabularnewline
54 & 108.8 & 109.3 & -0.5 \tabularnewline
55 & 96.3 & 109.1 & -12.8 \tabularnewline
56 & 96.9 & 96.6 & 0.300000000000011 \tabularnewline
57 & 97 & 97.2 & -0.200000000000003 \tabularnewline
58 & 111.4 & 97.3 & 14.1 \tabularnewline
59 & 111.8 & 111.7 & 0.0999999999999943 \tabularnewline
60 & 111.7 & 112.1 & -0.399999999999991 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287320&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]94.9[/C][C]94.9[/C][C]1.4210854715202e-14[/C][/ROW]
[ROW][C]4[/C][C]95.6[/C][C]95.2[/C][C]0.399999999999991[/C][/ROW]
[ROW][C]5[/C][C]95.4[/C][C]95.9[/C][C]-0.499999999999986[/C][/ROW]
[ROW][C]6[/C][C]97.4[/C][C]95.7[/C][C]1.7[/C][/ROW]
[ROW][C]7[/C][C]98.4[/C][C]97.7[/C][C]0.700000000000003[/C][/ROW]
[ROW][C]8[/C][C]100.5[/C][C]98.7[/C][C]1.8[/C][/ROW]
[ROW][C]9[/C][C]106.6[/C][C]100.8[/C][C]5.8[/C][/ROW]
[ROW][C]10[/C][C]106.7[/C][C]106.9[/C][C]-0.199999999999989[/C][/ROW]
[ROW][C]11[/C][C]106.8[/C][C]107[/C][C]-0.200000000000003[/C][/ROW]
[ROW][C]12[/C][C]109[/C][C]107.1[/C][C]1.90000000000001[/C][/ROW]
[ROW][C]13[/C][C]109.3[/C][C]109.3[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]110.5[/C][C]109.6[/C][C]0.900000000000006[/C][/ROW]
[ROW][C]15[/C][C]113.4[/C][C]110.8[/C][C]2.60000000000001[/C][/ROW]
[ROW][C]16[/C][C]113[/C][C]113.7[/C][C]-0.700000000000003[/C][/ROW]
[ROW][C]17[/C][C]113.6[/C][C]113.3[/C][C]0.299999999999997[/C][/ROW]
[ROW][C]18[/C][C]121.2[/C][C]113.9[/C][C]7.30000000000001[/C][/ROW]
[ROW][C]19[/C][C]120.5[/C][C]121.5[/C][C]-1[/C][/ROW]
[ROW][C]20[/C][C]120.9[/C][C]120.8[/C][C]0.100000000000009[/C][/ROW]
[ROW][C]21[/C][C]125.8[/C][C]121.2[/C][C]4.59999999999999[/C][/ROW]
[ROW][C]22[/C][C]125.4[/C][C]126.1[/C][C]-0.699999999999989[/C][/ROW]
[ROW][C]23[/C][C]125.7[/C][C]125.7[/C][C]0[/C][/ROW]
[ROW][C]24[/C][C]127.7[/C][C]126[/C][C]1.7[/C][/ROW]
[ROW][C]25[/C][C]128.1[/C][C]128[/C][C]0.0999999999999943[/C][/ROW]
[ROW][C]26[/C][C]130[/C][C]128.4[/C][C]1.60000000000002[/C][/ROW]
[ROW][C]27[/C][C]130.5[/C][C]130.3[/C][C]0.199999999999989[/C][/ROW]
[ROW][C]28[/C][C]130.1[/C][C]130.8[/C][C]-0.700000000000017[/C][/ROW]
[ROW][C]29[/C][C]129.6[/C][C]130.4[/C][C]-0.799999999999983[/C][/ROW]
[ROW][C]30[/C][C]128.8[/C][C]129.9[/C][C]-1.09999999999997[/C][/ROW]
[ROW][C]31[/C][C]128.4[/C][C]129.1[/C][C]-0.700000000000017[/C][/ROW]
[ROW][C]32[/C][C]128.3[/C][C]128.7[/C][C]-0.399999999999977[/C][/ROW]
[ROW][C]33[/C][C]127.6[/C][C]128.6[/C][C]-1.00000000000003[/C][/ROW]
[ROW][C]34[/C][C]127.3[/C][C]127.9[/C][C]-0.599999999999994[/C][/ROW]
[ROW][C]35[/C][C]127.7[/C][C]127.6[/C][C]0.100000000000009[/C][/ROW]
[ROW][C]36[/C][C]126.9[/C][C]128[/C][C]-1.09999999999999[/C][/ROW]
[ROW][C]37[/C][C]125.1[/C][C]127.2[/C][C]-2.10000000000001[/C][/ROW]
[ROW][C]38[/C][C]119[/C][C]125.4[/C][C]-6.39999999999999[/C][/ROW]
[ROW][C]39[/C][C]118.7[/C][C]119.3[/C][C]-0.599999999999994[/C][/ROW]
[ROW][C]40[/C][C]118.9[/C][C]119[/C][C]-0.0999999999999943[/C][/ROW]
[ROW][C]41[/C][C]116.9[/C][C]119.2[/C][C]-2.3[/C][/ROW]
[ROW][C]42[/C][C]117[/C][C]117.2[/C][C]-0.200000000000003[/C][/ROW]
[ROW][C]43[/C][C]117[/C][C]117.3[/C][C]-0.299999999999997[/C][/ROW]
[ROW][C]44[/C][C]115.5[/C][C]117.3[/C][C]-1.8[/C][/ROW]
[ROW][C]45[/C][C]115.6[/C][C]115.8[/C][C]-0.200000000000003[/C][/ROW]
[ROW][C]46[/C][C]117.5[/C][C]115.9[/C][C]1.60000000000001[/C][/ROW]
[ROW][C]47[/C][C]117.6[/C][C]117.8[/C][C]-0.200000000000003[/C][/ROW]
[ROW][C]48[/C][C]117.8[/C][C]117.9[/C][C]-0.0999999999999943[/C][/ROW]
[ROW][C]49[/C][C]119.3[/C][C]118.1[/C][C]1.2[/C][/ROW]
[ROW][C]50[/C][C]120[/C][C]119.6[/C][C]0.400000000000006[/C][/ROW]
[ROW][C]51[/C][C]120.2[/C][C]120.3[/C][C]-0.0999999999999943[/C][/ROW]
[ROW][C]52[/C][C]109.4[/C][C]120.5[/C][C]-11.1[/C][/ROW]
[ROW][C]53[/C][C]109[/C][C]109.7[/C][C]-0.700000000000003[/C][/ROW]
[ROW][C]54[/C][C]108.8[/C][C]109.3[/C][C]-0.5[/C][/ROW]
[ROW][C]55[/C][C]96.3[/C][C]109.1[/C][C]-12.8[/C][/ROW]
[ROW][C]56[/C][C]96.9[/C][C]96.6[/C][C]0.300000000000011[/C][/ROW]
[ROW][C]57[/C][C]97[/C][C]97.2[/C][C]-0.200000000000003[/C][/ROW]
[ROW][C]58[/C][C]111.4[/C][C]97.3[/C][C]14.1[/C][/ROW]
[ROW][C]59[/C][C]111.8[/C][C]111.7[/C][C]0.0999999999999943[/C][/ROW]
[ROW][C]60[/C][C]111.7[/C][C]112.1[/C][C]-0.399999999999991[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287320&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287320&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
394.994.91.4210854715202e-14
495.695.20.399999999999991
595.495.9-0.499999999999986
697.495.71.7
798.497.70.700000000000003
8100.598.71.8
9106.6100.85.8
10106.7106.9-0.199999999999989
11106.8107-0.200000000000003
12109107.11.90000000000001
13109.3109.30
14110.5109.60.900000000000006
15113.4110.82.60000000000001
16113113.7-0.700000000000003
17113.6113.30.299999999999997
18121.2113.97.30000000000001
19120.5121.5-1
20120.9120.80.100000000000009
21125.8121.24.59999999999999
22125.4126.1-0.699999999999989
23125.7125.70
24127.71261.7
25128.11280.0999999999999943
26130128.41.60000000000002
27130.5130.30.199999999999989
28130.1130.8-0.700000000000017
29129.6130.4-0.799999999999983
30128.8129.9-1.09999999999997
31128.4129.1-0.700000000000017
32128.3128.7-0.399999999999977
33127.6128.6-1.00000000000003
34127.3127.9-0.599999999999994
35127.7127.60.100000000000009
36126.9128-1.09999999999999
37125.1127.2-2.10000000000001
38119125.4-6.39999999999999
39118.7119.3-0.599999999999994
40118.9119-0.0999999999999943
41116.9119.2-2.3
42117117.2-0.200000000000003
43117117.3-0.299999999999997
44115.5117.3-1.8
45115.6115.8-0.200000000000003
46117.5115.91.60000000000001
47117.6117.8-0.200000000000003
48117.8117.9-0.0999999999999943
49119.3118.11.2
50120119.60.400000000000006
51120.2120.3-0.0999999999999943
52109.4120.5-11.1
53109109.7-0.700000000000003
54108.8109.3-0.5
5596.3109.1-12.8
5696.996.60.300000000000011
579797.2-0.200000000000003
58111.497.314.1
59111.8111.70.0999999999999943
60111.7112.1-0.399999999999991







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
61112105.205085670363118.794914329637
62112.3102.690539999864121.909460000136
63112.6100.830863147991124.369136852009
64112.999.3101713407262126.489828659274
65113.298.0061096576445128.393890342355
66113.596.855927046464130.144072953536
67113.895.8223465037916131.777653496208
68114.194.8810799997285133.318920000272
69114.494.0152570110893134.784742988911
70114.793.2125942126313136.187405787369
7111592.4638186859852137.536181314015
72115.391.7617262959822138.838273704018

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 112 & 105.205085670363 & 118.794914329637 \tabularnewline
62 & 112.3 & 102.690539999864 & 121.909460000136 \tabularnewline
63 & 112.6 & 100.830863147991 & 124.369136852009 \tabularnewline
64 & 112.9 & 99.3101713407262 & 126.489828659274 \tabularnewline
65 & 113.2 & 98.0061096576445 & 128.393890342355 \tabularnewline
66 & 113.5 & 96.855927046464 & 130.144072953536 \tabularnewline
67 & 113.8 & 95.8223465037916 & 131.777653496208 \tabularnewline
68 & 114.1 & 94.8810799997285 & 133.318920000272 \tabularnewline
69 & 114.4 & 94.0152570110893 & 134.784742988911 \tabularnewline
70 & 114.7 & 93.2125942126313 & 136.187405787369 \tabularnewline
71 & 115 & 92.4638186859852 & 137.536181314015 \tabularnewline
72 & 115.3 & 91.7617262959822 & 138.838273704018 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287320&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]112[/C][C]105.205085670363[/C][C]118.794914329637[/C][/ROW]
[ROW][C]62[/C][C]112.3[/C][C]102.690539999864[/C][C]121.909460000136[/C][/ROW]
[ROW][C]63[/C][C]112.6[/C][C]100.830863147991[/C][C]124.369136852009[/C][/ROW]
[ROW][C]64[/C][C]112.9[/C][C]99.3101713407262[/C][C]126.489828659274[/C][/ROW]
[ROW][C]65[/C][C]113.2[/C][C]98.0061096576445[/C][C]128.393890342355[/C][/ROW]
[ROW][C]66[/C][C]113.5[/C][C]96.855927046464[/C][C]130.144072953536[/C][/ROW]
[ROW][C]67[/C][C]113.8[/C][C]95.8223465037916[/C][C]131.777653496208[/C][/ROW]
[ROW][C]68[/C][C]114.1[/C][C]94.8810799997285[/C][C]133.318920000272[/C][/ROW]
[ROW][C]69[/C][C]114.4[/C][C]94.0152570110893[/C][C]134.784742988911[/C][/ROW]
[ROW][C]70[/C][C]114.7[/C][C]93.2125942126313[/C][C]136.187405787369[/C][/ROW]
[ROW][C]71[/C][C]115[/C][C]92.4638186859852[/C][C]137.536181314015[/C][/ROW]
[ROW][C]72[/C][C]115.3[/C][C]91.7617262959822[/C][C]138.838273704018[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287320&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287320&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
61112105.205085670363118.794914329637
62112.3102.690539999864121.909460000136
63112.6100.830863147991124.369136852009
64112.999.3101713407262126.489828659274
65113.298.0061096576445128.393890342355
66113.596.855927046464130.144072953536
67113.895.8223465037916131.777653496208
68114.194.8810799997285133.318920000272
69114.494.0152570110893134.784742988911
70114.793.2125942126313136.187405787369
7111592.4638186859852137.536181314015
72115.391.7617262959822138.838273704018



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
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')