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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sun, 01 Jun 2008 08:54:09 -0600

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Jun/01/t1212332219dijia74dopd58g4.htm/, Retrieved Sat, 18 May 2024 15:30:17 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13696, Retrieved Sat, 18 May 2024 15:30:17 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

209

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [Classical Decomposition] [Aardappelprijs - ...] [2008-05-19 20:16:09] [095b45ba9bd4a1bbcf9a642ea8ead7f4]
- RMPD    [Exponential Smoothing] [Exponential smoot...] [2008-06-01 14:54:09] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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Dataseries X:

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Histogram

Boxplots

0,36
0,35
0,35
0,35
0,33
0,78
0,71
0,62
0,52
0,46
0,43
0,43
0,42
0,42
0,42
0,42
0,43
0,99
1,03
0,83
0,64
0,6
0,58
0,58
0,58
0,57
0,57
0,56
0,56
0,88
0,84
0,69
0,59
0,54
0,52
0,52
0,51
0,52
0,51
0,51
0,53
0,95
0,98
0,88
0,81
0,77
0,76
0,75
0,73
0,74
0,73
0,75
0,77
1,09
1,03
0,9
0,76
0,66
0,63
0,61
0,61
0,61
0,61
0,61
0,62
0,76
0,83
0,81
0,77
0,75
0,76
0,76

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	7 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\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 & 7 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13696&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]7 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13696&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13696&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 Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	7 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.427961762367385
beta	0
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.427961762367385 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13696&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]0.427961762367385[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13696&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13696&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
Parameter	Value
alpha	0.427961762367385
beta	0
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	0.42	0.381454930921276	0.0385450690787244
14	0.42	0.382199148727861	0.037800851272139
15	0.42	0.388794526379802	0.0312054736201978
16	0.42	0.3946701047839	0.0253298952160997
17	0.43	0.406728202033024	0.023271797966976
18	0.99	0.93959734412076	0.0504026558792394
19	1.03	0.979169422343925	0.0508305776560753
20	0.83	0.790108400298008	0.0398915997019921
21	0.64	0.610349914875342	0.0296500851246579
22	0.6	0.57336468524232	0.0266353147576803
23	0.58	0.5557622225549	0.0242377774450997
24	0.58	0.565430478240453	0.0145695217595465
25	0.58	0.54595681178643	0.0340431882135694
26	0.57	0.537764088426115	0.0322359115738852
27	0.57	0.533243385408397	0.0367566145916034
28	0.56	0.534298474616607	0.0257015253833931
29	0.56	0.544937297239602	0.0150627027603977
30	0.88	1.24097530413189	-0.360975304131893
31	0.84	1.10582300987989	-0.265823009879894
32	0.69	0.782519629802283	-0.0925196298022835
33	0.59	0.561190565266293	0.0288094347337066
34	0.54	0.527193919172221	0.0128060808277793
35	0.52	0.505484173907298	0.0145158260927024
36	0.52	0.506115283462974	0.0138847165370256
37	0.51	0.498748023053782	0.0112519769462185
38	0.52	0.482503228831789	0.0374967711682109
39	0.51	0.484264831525809	0.0257351684741908
40	0.51	0.476774346417104	0.0332256535828961
41	0.53	0.485253417113277	0.0447465828867230
42	0.95	0.905334876300396	0.0446651236996037
43	0.98	0.983619758460618	-0.00361975846061757
44	0.88	0.849694754143913	0.0303052458560866
45	0.81	0.721782893473176	0.0882171065268239
46	0.77	0.688016580973826	0.0819834190261745
47	0.76	0.687867141438742	0.0721328585612585
48	0.75	0.710396719944856	0.0396032800551437
49	0.73	0.706536383695711	0.0234636163042891
50	0.74	0.707111221938404	0.0328887780615956
51	0.73	0.691588547422003	0.0384114525779968
52	0.75	0.687522521436921	0.062477478563079
53	0.77	0.714090169714788	0.0559098302852118
54	1.09	1.29550847595839	-0.205508475958388
55	1.03	1.24765709399755	-0.217657093997551
56	0.9	1.02111522606375	-0.121115226063751
57	0.76	0.84783376002545	-0.08783376002545
58	0.66	0.732859642537123	-0.0728596425371233
59	0.63	0.662819764731786	-0.0328197647317865
60	0.61	0.625318763951989	-0.0153187639519892
61	0.61	0.593822964334313	0.0161770356656866
62	0.61	0.597090355896929	0.0129096441030709
63	0.61	0.580669583794658	0.0293304162053424
64	0.61	0.586659170947267	0.0233408290527328
65	0.62	0.592698997731945	0.0273010022680553
66	0.76	0.917867224012115	-0.157867224012115
67	0.83	0.868328871542498	-0.038328871542498
68	0.81	0.784208067147231	0.0257919328527693
69	0.77	0.702695754012859	0.0673042459871414
70	0.75	0.663478649584249	0.0865213504157514
71	0.76	0.683141511669046	0.0768584883309538
72	0.76	0.700648368700601	0.0593516312993986

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 0.42 & 0.381454930921276 & 0.0385450690787244 \tabularnewline
14 & 0.42 & 0.382199148727861 & 0.037800851272139 \tabularnewline
15 & 0.42 & 0.388794526379802 & 0.0312054736201978 \tabularnewline
16 & 0.42 & 0.3946701047839 & 0.0253298952160997 \tabularnewline
17 & 0.43 & 0.406728202033024 & 0.023271797966976 \tabularnewline
18 & 0.99 & 0.93959734412076 & 0.0504026558792394 \tabularnewline
19 & 1.03 & 0.979169422343925 & 0.0508305776560753 \tabularnewline
20 & 0.83 & 0.790108400298008 & 0.0398915997019921 \tabularnewline
21 & 0.64 & 0.610349914875342 & 0.0296500851246579 \tabularnewline
22 & 0.6 & 0.57336468524232 & 0.0266353147576803 \tabularnewline
23 & 0.58 & 0.5557622225549 & 0.0242377774450997 \tabularnewline
24 & 0.58 & 0.565430478240453 & 0.0145695217595465 \tabularnewline
25 & 0.58 & 0.54595681178643 & 0.0340431882135694 \tabularnewline
26 & 0.57 & 0.537764088426115 & 0.0322359115738852 \tabularnewline
27 & 0.57 & 0.533243385408397 & 0.0367566145916034 \tabularnewline
28 & 0.56 & 0.534298474616607 & 0.0257015253833931 \tabularnewline
29 & 0.56 & 0.544937297239602 & 0.0150627027603977 \tabularnewline
30 & 0.88 & 1.24097530413189 & -0.360975304131893 \tabularnewline
31 & 0.84 & 1.10582300987989 & -0.265823009879894 \tabularnewline
32 & 0.69 & 0.782519629802283 & -0.0925196298022835 \tabularnewline
33 & 0.59 & 0.561190565266293 & 0.0288094347337066 \tabularnewline
34 & 0.54 & 0.527193919172221 & 0.0128060808277793 \tabularnewline
35 & 0.52 & 0.505484173907298 & 0.0145158260927024 \tabularnewline
36 & 0.52 & 0.506115283462974 & 0.0138847165370256 \tabularnewline
37 & 0.51 & 0.498748023053782 & 0.0112519769462185 \tabularnewline
38 & 0.52 & 0.482503228831789 & 0.0374967711682109 \tabularnewline
39 & 0.51 & 0.484264831525809 & 0.0257351684741908 \tabularnewline
40 & 0.51 & 0.476774346417104 & 0.0332256535828961 \tabularnewline
41 & 0.53 & 0.485253417113277 & 0.0447465828867230 \tabularnewline
42 & 0.95 & 0.905334876300396 & 0.0446651236996037 \tabularnewline
43 & 0.98 & 0.983619758460618 & -0.00361975846061757 \tabularnewline
44 & 0.88 & 0.849694754143913 & 0.0303052458560866 \tabularnewline
45 & 0.81 & 0.721782893473176 & 0.0882171065268239 \tabularnewline
46 & 0.77 & 0.688016580973826 & 0.0819834190261745 \tabularnewline
47 & 0.76 & 0.687867141438742 & 0.0721328585612585 \tabularnewline
48 & 0.75 & 0.710396719944856 & 0.0396032800551437 \tabularnewline
49 & 0.73 & 0.706536383695711 & 0.0234636163042891 \tabularnewline
50 & 0.74 & 0.707111221938404 & 0.0328887780615956 \tabularnewline
51 & 0.73 & 0.691588547422003 & 0.0384114525779968 \tabularnewline
52 & 0.75 & 0.687522521436921 & 0.062477478563079 \tabularnewline
53 & 0.77 & 0.714090169714788 & 0.0559098302852118 \tabularnewline
54 & 1.09 & 1.29550847595839 & -0.205508475958388 \tabularnewline
55 & 1.03 & 1.24765709399755 & -0.217657093997551 \tabularnewline
56 & 0.9 & 1.02111522606375 & -0.121115226063751 \tabularnewline
57 & 0.76 & 0.84783376002545 & -0.08783376002545 \tabularnewline
58 & 0.66 & 0.732859642537123 & -0.0728596425371233 \tabularnewline
59 & 0.63 & 0.662819764731786 & -0.0328197647317865 \tabularnewline
60 & 0.61 & 0.625318763951989 & -0.0153187639519892 \tabularnewline
61 & 0.61 & 0.593822964334313 & 0.0161770356656866 \tabularnewline
62 & 0.61 & 0.597090355896929 & 0.0129096441030709 \tabularnewline
63 & 0.61 & 0.580669583794658 & 0.0293304162053424 \tabularnewline
64 & 0.61 & 0.586659170947267 & 0.0233408290527328 \tabularnewline
65 & 0.62 & 0.592698997731945 & 0.0273010022680553 \tabularnewline
66 & 0.76 & 0.917867224012115 & -0.157867224012115 \tabularnewline
67 & 0.83 & 0.868328871542498 & -0.038328871542498 \tabularnewline
68 & 0.81 & 0.784208067147231 & 0.0257919328527693 \tabularnewline
69 & 0.77 & 0.702695754012859 & 0.0673042459871414 \tabularnewline
70 & 0.75 & 0.663478649584249 & 0.0865213504157514 \tabularnewline
71 & 0.76 & 0.683141511669046 & 0.0768584883309538 \tabularnewline
72 & 0.76 & 0.700648368700601 & 0.0593516312993986 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13696&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]0.42[/C][C]0.381454930921276[/C][C]0.0385450690787244[/C][/ROW]
[ROW][C]14[/C][C]0.42[/C][C]0.382199148727861[/C][C]0.037800851272139[/C][/ROW]
[ROW][C]15[/C][C]0.42[/C][C]0.388794526379802[/C][C]0.0312054736201978[/C][/ROW]
[ROW][C]16[/C][C]0.42[/C][C]0.3946701047839[/C][C]0.0253298952160997[/C][/ROW]
[ROW][C]17[/C][C]0.43[/C][C]0.406728202033024[/C][C]0.023271797966976[/C][/ROW]
[ROW][C]18[/C][C]0.99[/C][C]0.93959734412076[/C][C]0.0504026558792394[/C][/ROW]
[ROW][C]19[/C][C]1.03[/C][C]0.979169422343925[/C][C]0.0508305776560753[/C][/ROW]
[ROW][C]20[/C][C]0.83[/C][C]0.790108400298008[/C][C]0.0398915997019921[/C][/ROW]
[ROW][C]21[/C][C]0.64[/C][C]0.610349914875342[/C][C]0.0296500851246579[/C][/ROW]
[ROW][C]22[/C][C]0.6[/C][C]0.57336468524232[/C][C]0.0266353147576803[/C][/ROW]
[ROW][C]23[/C][C]0.58[/C][C]0.5557622225549[/C][C]0.0242377774450997[/C][/ROW]
[ROW][C]24[/C][C]0.58[/C][C]0.565430478240453[/C][C]0.0145695217595465[/C][/ROW]
[ROW][C]25[/C][C]0.58[/C][C]0.54595681178643[/C][C]0.0340431882135694[/C][/ROW]
[ROW][C]26[/C][C]0.57[/C][C]0.537764088426115[/C][C]0.0322359115738852[/C][/ROW]
[ROW][C]27[/C][C]0.57[/C][C]0.533243385408397[/C][C]0.0367566145916034[/C][/ROW]
[ROW][C]28[/C][C]0.56[/C][C]0.534298474616607[/C][C]0.0257015253833931[/C][/ROW]
[ROW][C]29[/C][C]0.56[/C][C]0.544937297239602[/C][C]0.0150627027603977[/C][/ROW]
[ROW][C]30[/C][C]0.88[/C][C]1.24097530413189[/C][C]-0.360975304131893[/C][/ROW]
[ROW][C]31[/C][C]0.84[/C][C]1.10582300987989[/C][C]-0.265823009879894[/C][/ROW]
[ROW][C]32[/C][C]0.69[/C][C]0.782519629802283[/C][C]-0.0925196298022835[/C][/ROW]
[ROW][C]33[/C][C]0.59[/C][C]0.561190565266293[/C][C]0.0288094347337066[/C][/ROW]
[ROW][C]34[/C][C]0.54[/C][C]0.527193919172221[/C][C]0.0128060808277793[/C][/ROW]
[ROW][C]35[/C][C]0.52[/C][C]0.505484173907298[/C][C]0.0145158260927024[/C][/ROW]
[ROW][C]36[/C][C]0.52[/C][C]0.506115283462974[/C][C]0.0138847165370256[/C][/ROW]
[ROW][C]37[/C][C]0.51[/C][C]0.498748023053782[/C][C]0.0112519769462185[/C][/ROW]
[ROW][C]38[/C][C]0.52[/C][C]0.482503228831789[/C][C]0.0374967711682109[/C][/ROW]
[ROW][C]39[/C][C]0.51[/C][C]0.484264831525809[/C][C]0.0257351684741908[/C][/ROW]
[ROW][C]40[/C][C]0.51[/C][C]0.476774346417104[/C][C]0.0332256535828961[/C][/ROW]
[ROW][C]41[/C][C]0.53[/C][C]0.485253417113277[/C][C]0.0447465828867230[/C][/ROW]
[ROW][C]42[/C][C]0.95[/C][C]0.905334876300396[/C][C]0.0446651236996037[/C][/ROW]
[ROW][C]43[/C][C]0.98[/C][C]0.983619758460618[/C][C]-0.00361975846061757[/C][/ROW]
[ROW][C]44[/C][C]0.88[/C][C]0.849694754143913[/C][C]0.0303052458560866[/C][/ROW]
[ROW][C]45[/C][C]0.81[/C][C]0.721782893473176[/C][C]0.0882171065268239[/C][/ROW]
[ROW][C]46[/C][C]0.77[/C][C]0.688016580973826[/C][C]0.0819834190261745[/C][/ROW]
[ROW][C]47[/C][C]0.76[/C][C]0.687867141438742[/C][C]0.0721328585612585[/C][/ROW]
[ROW][C]48[/C][C]0.75[/C][C]0.710396719944856[/C][C]0.0396032800551437[/C][/ROW]
[ROW][C]49[/C][C]0.73[/C][C]0.706536383695711[/C][C]0.0234636163042891[/C][/ROW]
[ROW][C]50[/C][C]0.74[/C][C]0.707111221938404[/C][C]0.0328887780615956[/C][/ROW]
[ROW][C]51[/C][C]0.73[/C][C]0.691588547422003[/C][C]0.0384114525779968[/C][/ROW]
[ROW][C]52[/C][C]0.75[/C][C]0.687522521436921[/C][C]0.062477478563079[/C][/ROW]
[ROW][C]53[/C][C]0.77[/C][C]0.714090169714788[/C][C]0.0559098302852118[/C][/ROW]
[ROW][C]54[/C][C]1.09[/C][C]1.29550847595839[/C][C]-0.205508475958388[/C][/ROW]
[ROW][C]55[/C][C]1.03[/C][C]1.24765709399755[/C][C]-0.217657093997551[/C][/ROW]
[ROW][C]56[/C][C]0.9[/C][C]1.02111522606375[/C][C]-0.121115226063751[/C][/ROW]
[ROW][C]57[/C][C]0.76[/C][C]0.84783376002545[/C][C]-0.08783376002545[/C][/ROW]
[ROW][C]58[/C][C]0.66[/C][C]0.732859642537123[/C][C]-0.0728596425371233[/C][/ROW]
[ROW][C]59[/C][C]0.63[/C][C]0.662819764731786[/C][C]-0.0328197647317865[/C][/ROW]
[ROW][C]60[/C][C]0.61[/C][C]0.625318763951989[/C][C]-0.0153187639519892[/C][/ROW]
[ROW][C]61[/C][C]0.61[/C][C]0.593822964334313[/C][C]0.0161770356656866[/C][/ROW]
[ROW][C]62[/C][C]0.61[/C][C]0.597090355896929[/C][C]0.0129096441030709[/C][/ROW]
[ROW][C]63[/C][C]0.61[/C][C]0.580669583794658[/C][C]0.0293304162053424[/C][/ROW]
[ROW][C]64[/C][C]0.61[/C][C]0.586659170947267[/C][C]0.0233408290527328[/C][/ROW]
[ROW][C]65[/C][C]0.62[/C][C]0.592698997731945[/C][C]0.0273010022680553[/C][/ROW]
[ROW][C]66[/C][C]0.76[/C][C]0.917867224012115[/C][C]-0.157867224012115[/C][/ROW]
[ROW][C]67[/C][C]0.83[/C][C]0.868328871542498[/C][C]-0.038328871542498[/C][/ROW]
[ROW][C]68[/C][C]0.81[/C][C]0.784208067147231[/C][C]0.0257919328527693[/C][/ROW]
[ROW][C]69[/C][C]0.77[/C][C]0.702695754012859[/C][C]0.0673042459871414[/C][/ROW]
[ROW][C]70[/C][C]0.75[/C][C]0.663478649584249[/C][C]0.0865213504157514[/C][/ROW]
[ROW][C]71[/C][C]0.76[/C][C]0.683141511669046[/C][C]0.0768584883309538[/C][/ROW]
[ROW][C]72[/C][C]0.76[/C][C]0.700648368700601[/C][C]0.0593516312993986[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13696&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13696&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
t	Observed	Fitted	Residuals
13	0.42	0.381454930921276	0.0385450690787244
14	0.42	0.382199148727861	0.037800851272139
15	0.42	0.388794526379802	0.0312054736201978
16	0.42	0.3946701047839	0.0253298952160997
17	0.43	0.406728202033024	0.023271797966976
18	0.99	0.93959734412076	0.0504026558792394
19	1.03	0.979169422343925	0.0508305776560753
20	0.83	0.790108400298008	0.0398915997019921
21	0.64	0.610349914875342	0.0296500851246579
22	0.6	0.57336468524232	0.0266353147576803
23	0.58	0.5557622225549	0.0242377774450997
24	0.58	0.565430478240453	0.0145695217595465
25	0.58	0.54595681178643	0.0340431882135694
26	0.57	0.537764088426115	0.0322359115738852
27	0.57	0.533243385408397	0.0367566145916034
28	0.56	0.534298474616607	0.0257015253833931
29	0.56	0.544937297239602	0.0150627027603977
30	0.88	1.24097530413189	-0.360975304131893
31	0.84	1.10582300987989	-0.265823009879894
32	0.69	0.782519629802283	-0.0925196298022835
33	0.59	0.561190565266293	0.0288094347337066
34	0.54	0.527193919172221	0.0128060808277793
35	0.52	0.505484173907298	0.0145158260927024
36	0.52	0.506115283462974	0.0138847165370256
37	0.51	0.498748023053782	0.0112519769462185
38	0.52	0.482503228831789	0.0374967711682109
39	0.51	0.484264831525809	0.0257351684741908
40	0.51	0.476774346417104	0.0332256535828961
41	0.53	0.485253417113277	0.0447465828867230
42	0.95	0.905334876300396	0.0446651236996037
43	0.98	0.983619758460618	-0.00361975846061757
44	0.88	0.849694754143913	0.0303052458560866
45	0.81	0.721782893473176	0.0882171065268239
46	0.77	0.688016580973826	0.0819834190261745
47	0.76	0.687867141438742	0.0721328585612585
48	0.75	0.710396719944856	0.0396032800551437
49	0.73	0.706536383695711	0.0234636163042891
50	0.74	0.707111221938404	0.0328887780615956
51	0.73	0.691588547422003	0.0384114525779968
52	0.75	0.687522521436921	0.062477478563079
53	0.77	0.714090169714788	0.0559098302852118
54	1.09	1.29550847595839	-0.205508475958388
55	1.03	1.24765709399755	-0.217657093997551
56	0.9	1.02111522606375	-0.121115226063751
57	0.76	0.84783376002545	-0.08783376002545
58	0.66	0.732859642537123	-0.0728596425371233
59	0.63	0.662819764731786	-0.0328197647317865
60	0.61	0.625318763951989	-0.0153187639519892
61	0.61	0.593822964334313	0.0161770356656866
62	0.61	0.597090355896929	0.0129096441030709
63	0.61	0.580669583794658	0.0293304162053424
64	0.61	0.586659170947267	0.0233408290527328
65	0.62	0.592698997731945	0.0273010022680553
66	0.76	0.917867224012115	-0.157867224012115
67	0.83	0.868328871542498	-0.038328871542498
68	0.81	0.784208067147231	0.0257919328527693
69	0.77	0.702695754012859	0.0673042459871414
70	0.75	0.663478649584249	0.0865213504157514
71	0.76	0.683141511669046	0.0768584883309538
72	0.76	0.700648368700601	0.0593516312993986

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	0.717681426740382	0.548662980728098	0.886699872752667
74	0.71110165436842	0.52785241316225	0.89435089557459
75	0.696055077058173	0.499911671762975	0.892198482353371
76	0.684401840838947	0.47558141217863	0.893222269499264
77	0.682173951961466	0.429075549849497	0.935272354073435
78	0.902654617799094	0.62153801447683	1.18377122112136
79	1.00477469986815	0.72167591638452	1.28787348335178
80	0.966953109627418	0.69137845589209	1.24252776336275
81	0.883007672372452	0.612195159617789	1.15382018512711
82	0.814610138319783	0.540192928127893	1.08902734851167
83	0.787551871519812	0.510127467963302	1.06497627507632
84	0.76	NA	NA

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 0.717681426740382 & 0.548662980728098 & 0.886699872752667 \tabularnewline
74 & 0.71110165436842 & 0.52785241316225 & 0.89435089557459 \tabularnewline
75 & 0.696055077058173 & 0.499911671762975 & 0.892198482353371 \tabularnewline
76 & 0.684401840838947 & 0.47558141217863 & 0.893222269499264 \tabularnewline
77 & 0.682173951961466 & 0.429075549849497 & 0.935272354073435 \tabularnewline
78 & 0.902654617799094 & 0.62153801447683 & 1.18377122112136 \tabularnewline
79 & 1.00477469986815 & 0.72167591638452 & 1.28787348335178 \tabularnewline
80 & 0.966953109627418 & 0.69137845589209 & 1.24252776336275 \tabularnewline
81 & 0.883007672372452 & 0.612195159617789 & 1.15382018512711 \tabularnewline
82 & 0.814610138319783 & 0.540192928127893 & 1.08902734851167 \tabularnewline
83 & 0.787551871519812 & 0.510127467963302 & 1.06497627507632 \tabularnewline
84 & 0.76 & NA & NA \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13696&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]0.717681426740382[/C][C]0.548662980728098[/C][C]0.886699872752667[/C][/ROW]
[ROW][C]74[/C][C]0.71110165436842[/C][C]0.52785241316225[/C][C]0.89435089557459[/C][/ROW]
[ROW][C]75[/C][C]0.696055077058173[/C][C]0.499911671762975[/C][C]0.892198482353371[/C][/ROW]
[ROW][C]76[/C][C]0.684401840838947[/C][C]0.47558141217863[/C][C]0.893222269499264[/C][/ROW]
[ROW][C]77[/C][C]0.682173951961466[/C][C]0.429075549849497[/C][C]0.935272354073435[/C][/ROW]
[ROW][C]78[/C][C]0.902654617799094[/C][C]0.62153801447683[/C][C]1.18377122112136[/C][/ROW]
[ROW][C]79[/C][C]1.00477469986815[/C][C]0.72167591638452[/C][C]1.28787348335178[/C][/ROW]
[ROW][C]80[/C][C]0.966953109627418[/C][C]0.69137845589209[/C][C]1.24252776336275[/C][/ROW]
[ROW][C]81[/C][C]0.883007672372452[/C][C]0.612195159617789[/C][C]1.15382018512711[/C][/ROW]
[ROW][C]82[/C][C]0.814610138319783[/C][C]0.540192928127893[/C][C]1.08902734851167[/C][/ROW]
[ROW][C]83[/C][C]0.787551871519812[/C][C]0.510127467963302[/C][C]1.06497627507632[/C][/ROW]
[ROW][C]84[/C][C]0.76[/C][C]NA[/C][C]NA[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13696&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13696&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
t	Forecast	95% Lower Bound	95% Upper Bound
73	0.717681426740382	0.548662980728098	0.886699872752667
74	0.71110165436842	0.52785241316225	0.89435089557459
75	0.696055077058173	0.499911671762975	0.892198482353371
76	0.684401840838947	0.47558141217863	0.893222269499264
77	0.682173951961466	0.429075549849497	0.935272354073435
78	0.902654617799094	0.62153801447683	1.18377122112136
79	1.00477469986815	0.72167591638452	1.28787348335178
80	0.966953109627418	0.69137845589209	1.24252776336275
81	0.883007672372452	0.612195159617789	1.15382018512711
82	0.814610138319783	0.540192928127893	1.08902734851167
83	0.787551871519812	0.510127467963302	1.06497627507632
84	0.76	NA	NA

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code