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R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Wed, 25 Nov 2015 11:29:50 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Nov/25/t1448451009zjp9ioy9dgc19vl.htm/, Retrieved Tue, 21 May 2024 11:52:23 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284114, Retrieved Tue, 21 May 2024 11:52:23 +0000

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Estimated Impact

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

-       [Exponential Smoothing] [] [2015-11-25 11:29:50] [4b96c7bb02a36edde4d8c72e28fc1c90] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284114&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284114&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284114&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	1 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.0295263390496258
gamma	0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0295263390496258 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284114&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]0.0295263390496258[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284114&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284114&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	1
beta	0.0295263390496258
gamma	0

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	103.2	103.539716880342	-0.339716880341911
14	103.21	103.181207749198	0.0287922508015157
15	103	102.972057878958	0.0279421210423436
16	102.46	102.440382907497	0.0196170925026848
17	102.52	102.505962128422	0.0140378715782816
18	102.55	102.536376615377	0.0136233846225338
19	102.78	102.583028864051	0.196971135949198
20	102.81	102.766761367261	0.0432386327394738
21	102.81	102.820954712458	-0.0109547124575045
22	102.68	102.852714593237	-0.172714593236634
23	102.72	102.700948296931	0.0190517030687545
24	102.73	102.790677490642	-0.0606774906421919
25	102.87	102.746385906481	0.12361409351918
26	102.93	102.858369111451	0.0716308885493078
27	103.2	102.700484109352	0.499515890647558
28	102.62	102.6627329849	-0.0427329849003542
29	102.18	102.6864712363	-0.506471236299603
30	101.19	102.201516994858	-1.01151699485773
31	100.91	101.197900601113	-0.287900601113066
32	100.72	100.857316617019	-0.137316617018712
33	100.86	100.686178826694	0.173821173305868
34	100.89	100.863394462925	0.026605537075497
35	100.47	100.877513360366	-0.407513360366124
36	100.45	100.494647649387	-0.0446476493873718
37	100.64	100.420829367754	0.219170632246204
38	100.63	100.585634007485	0.044365992515452
39	100.66	100.356943972822	0.303056027178158
40	100.38	100.073392107831	0.306607892168685
41	99.68	100.407445116411	-0.727445116410792
42	99.71	99.6559663252636	0.0540336747363455
43	99.63	99.703811741864	-0.0738117418639774
44	99.63	99.5695490180146	0.06045098198544
45	99.71	99.5942505808712	0.11574941912879
46	99.77	99.7097515707985	0.0602484292014651
47	99.76	99.7548638196797	0.00513618032033492
48	99.79	99.7941821389479	-0.00418213894791108
49	98.13	99.7715586556954	-1.64155865569539
50	98.13	98.0314227715908	0.0985772284091979
51	97.87	97.8143333962594	0.0556666037406188
52	97.72	97.2334770272752	0.486522972724828
53	97.72	97.7028422695233	0.0171577304767112
54	97.6	97.6733488744906	-0.0733488744906481
55	97.31	97.5674331507535	-0.257433150753485
56	97.31	97.2177487589284	0.0922512410715655
57	97.44	97.2433892670167	0.196610732983274
58	96.94	97.4112777955129	-0.471277795512933
59	96.94	96.8806960208694	0.0593039791306182
60	96.94	96.9316137169309	0.00838628306914302

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 103.2 & 103.539716880342 & -0.339716880341911 \tabularnewline
14 & 103.21 & 103.181207749198 & 0.0287922508015157 \tabularnewline
15 & 103 & 102.972057878958 & 0.0279421210423436 \tabularnewline
16 & 102.46 & 102.440382907497 & 0.0196170925026848 \tabularnewline
17 & 102.52 & 102.505962128422 & 0.0140378715782816 \tabularnewline
18 & 102.55 & 102.536376615377 & 0.0136233846225338 \tabularnewline
19 & 102.78 & 102.583028864051 & 0.196971135949198 \tabularnewline
20 & 102.81 & 102.766761367261 & 0.0432386327394738 \tabularnewline
21 & 102.81 & 102.820954712458 & -0.0109547124575045 \tabularnewline
22 & 102.68 & 102.852714593237 & -0.172714593236634 \tabularnewline
23 & 102.72 & 102.700948296931 & 0.0190517030687545 \tabularnewline
24 & 102.73 & 102.790677490642 & -0.0606774906421919 \tabularnewline
25 & 102.87 & 102.746385906481 & 0.12361409351918 \tabularnewline
26 & 102.93 & 102.858369111451 & 0.0716308885493078 \tabularnewline
27 & 103.2 & 102.700484109352 & 0.499515890647558 \tabularnewline
28 & 102.62 & 102.6627329849 & -0.0427329849003542 \tabularnewline
29 & 102.18 & 102.6864712363 & -0.506471236299603 \tabularnewline
30 & 101.19 & 102.201516994858 & -1.01151699485773 \tabularnewline
31 & 100.91 & 101.197900601113 & -0.287900601113066 \tabularnewline
32 & 100.72 & 100.857316617019 & -0.137316617018712 \tabularnewline
33 & 100.86 & 100.686178826694 & 0.173821173305868 \tabularnewline
34 & 100.89 & 100.863394462925 & 0.026605537075497 \tabularnewline
35 & 100.47 & 100.877513360366 & -0.407513360366124 \tabularnewline
36 & 100.45 & 100.494647649387 & -0.0446476493873718 \tabularnewline
37 & 100.64 & 100.420829367754 & 0.219170632246204 \tabularnewline
38 & 100.63 & 100.585634007485 & 0.044365992515452 \tabularnewline
39 & 100.66 & 100.356943972822 & 0.303056027178158 \tabularnewline
40 & 100.38 & 100.073392107831 & 0.306607892168685 \tabularnewline
41 & 99.68 & 100.407445116411 & -0.727445116410792 \tabularnewline
42 & 99.71 & 99.6559663252636 & 0.0540336747363455 \tabularnewline
43 & 99.63 & 99.703811741864 & -0.0738117418639774 \tabularnewline
44 & 99.63 & 99.5695490180146 & 0.06045098198544 \tabularnewline
45 & 99.71 & 99.5942505808712 & 0.11574941912879 \tabularnewline
46 & 99.77 & 99.7097515707985 & 0.0602484292014651 \tabularnewline
47 & 99.76 & 99.7548638196797 & 0.00513618032033492 \tabularnewline
48 & 99.79 & 99.7941821389479 & -0.00418213894791108 \tabularnewline
49 & 98.13 & 99.7715586556954 & -1.64155865569539 \tabularnewline
50 & 98.13 & 98.0314227715908 & 0.0985772284091979 \tabularnewline
51 & 97.87 & 97.8143333962594 & 0.0556666037406188 \tabularnewline
52 & 97.72 & 97.2334770272752 & 0.486522972724828 \tabularnewline
53 & 97.72 & 97.7028422695233 & 0.0171577304767112 \tabularnewline
54 & 97.6 & 97.6733488744906 & -0.0733488744906481 \tabularnewline
55 & 97.31 & 97.5674331507535 & -0.257433150753485 \tabularnewline
56 & 97.31 & 97.2177487589284 & 0.0922512410715655 \tabularnewline
57 & 97.44 & 97.2433892670167 & 0.196610732983274 \tabularnewline
58 & 96.94 & 97.4112777955129 & -0.471277795512933 \tabularnewline
59 & 96.94 & 96.8806960208694 & 0.0593039791306182 \tabularnewline
60 & 96.94 & 96.9316137169309 & 0.00838628306914302 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284114&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]103.2[/C][C]103.539716880342[/C][C]-0.339716880341911[/C][/ROW]
[ROW][C]14[/C][C]103.21[/C][C]103.181207749198[/C][C]0.0287922508015157[/C][/ROW]
[ROW][C]15[/C][C]103[/C][C]102.972057878958[/C][C]0.0279421210423436[/C][/ROW]
[ROW][C]16[/C][C]102.46[/C][C]102.440382907497[/C][C]0.0196170925026848[/C][/ROW]
[ROW][C]17[/C][C]102.52[/C][C]102.505962128422[/C][C]0.0140378715782816[/C][/ROW]
[ROW][C]18[/C][C]102.55[/C][C]102.536376615377[/C][C]0.0136233846225338[/C][/ROW]
[ROW][C]19[/C][C]102.78[/C][C]102.583028864051[/C][C]0.196971135949198[/C][/ROW]
[ROW][C]20[/C][C]102.81[/C][C]102.766761367261[/C][C]0.0432386327394738[/C][/ROW]
[ROW][C]21[/C][C]102.81[/C][C]102.820954712458[/C][C]-0.0109547124575045[/C][/ROW]
[ROW][C]22[/C][C]102.68[/C][C]102.852714593237[/C][C]-0.172714593236634[/C][/ROW]
[ROW][C]23[/C][C]102.72[/C][C]102.700948296931[/C][C]0.0190517030687545[/C][/ROW]
[ROW][C]24[/C][C]102.73[/C][C]102.790677490642[/C][C]-0.0606774906421919[/C][/ROW]
[ROW][C]25[/C][C]102.87[/C][C]102.746385906481[/C][C]0.12361409351918[/C][/ROW]
[ROW][C]26[/C][C]102.93[/C][C]102.858369111451[/C][C]0.0716308885493078[/C][/ROW]
[ROW][C]27[/C][C]103.2[/C][C]102.700484109352[/C][C]0.499515890647558[/C][/ROW]
[ROW][C]28[/C][C]102.62[/C][C]102.6627329849[/C][C]-0.0427329849003542[/C][/ROW]
[ROW][C]29[/C][C]102.18[/C][C]102.6864712363[/C][C]-0.506471236299603[/C][/ROW]
[ROW][C]30[/C][C]101.19[/C][C]102.201516994858[/C][C]-1.01151699485773[/C][/ROW]
[ROW][C]31[/C][C]100.91[/C][C]101.197900601113[/C][C]-0.287900601113066[/C][/ROW]
[ROW][C]32[/C][C]100.72[/C][C]100.857316617019[/C][C]-0.137316617018712[/C][/ROW]
[ROW][C]33[/C][C]100.86[/C][C]100.686178826694[/C][C]0.173821173305868[/C][/ROW]
[ROW][C]34[/C][C]100.89[/C][C]100.863394462925[/C][C]0.026605537075497[/C][/ROW]
[ROW][C]35[/C][C]100.47[/C][C]100.877513360366[/C][C]-0.407513360366124[/C][/ROW]
[ROW][C]36[/C][C]100.45[/C][C]100.494647649387[/C][C]-0.0446476493873718[/C][/ROW]
[ROW][C]37[/C][C]100.64[/C][C]100.420829367754[/C][C]0.219170632246204[/C][/ROW]
[ROW][C]38[/C][C]100.63[/C][C]100.585634007485[/C][C]0.044365992515452[/C][/ROW]
[ROW][C]39[/C][C]100.66[/C][C]100.356943972822[/C][C]0.303056027178158[/C][/ROW]
[ROW][C]40[/C][C]100.38[/C][C]100.073392107831[/C][C]0.306607892168685[/C][/ROW]
[ROW][C]41[/C][C]99.68[/C][C]100.407445116411[/C][C]-0.727445116410792[/C][/ROW]
[ROW][C]42[/C][C]99.71[/C][C]99.6559663252636[/C][C]0.0540336747363455[/C][/ROW]
[ROW][C]43[/C][C]99.63[/C][C]99.703811741864[/C][C]-0.0738117418639774[/C][/ROW]
[ROW][C]44[/C][C]99.63[/C][C]99.5695490180146[/C][C]0.06045098198544[/C][/ROW]
[ROW][C]45[/C][C]99.71[/C][C]99.5942505808712[/C][C]0.11574941912879[/C][/ROW]
[ROW][C]46[/C][C]99.77[/C][C]99.7097515707985[/C][C]0.0602484292014651[/C][/ROW]
[ROW][C]47[/C][C]99.76[/C][C]99.7548638196797[/C][C]0.00513618032033492[/C][/ROW]
[ROW][C]48[/C][C]99.79[/C][C]99.7941821389479[/C][C]-0.00418213894791108[/C][/ROW]
[ROW][C]49[/C][C]98.13[/C][C]99.7715586556954[/C][C]-1.64155865569539[/C][/ROW]
[ROW][C]50[/C][C]98.13[/C][C]98.0314227715908[/C][C]0.0985772284091979[/C][/ROW]
[ROW][C]51[/C][C]97.87[/C][C]97.8143333962594[/C][C]0.0556666037406188[/C][/ROW]
[ROW][C]52[/C][C]97.72[/C][C]97.2334770272752[/C][C]0.486522972724828[/C][/ROW]
[ROW][C]53[/C][C]97.72[/C][C]97.7028422695233[/C][C]0.0171577304767112[/C][/ROW]
[ROW][C]54[/C][C]97.6[/C][C]97.6733488744906[/C][C]-0.0733488744906481[/C][/ROW]
[ROW][C]55[/C][C]97.31[/C][C]97.5674331507535[/C][C]-0.257433150753485[/C][/ROW]
[ROW][C]56[/C][C]97.31[/C][C]97.2177487589284[/C][C]0.0922512410715655[/C][/ROW]
[ROW][C]57[/C][C]97.44[/C][C]97.2433892670167[/C][C]0.196610732983274[/C][/ROW]
[ROW][C]58[/C][C]96.94[/C][C]97.4112777955129[/C][C]-0.471277795512933[/C][/ROW]
[ROW][C]59[/C][C]96.94[/C][C]96.8806960208694[/C][C]0.0593039791306182[/C][/ROW]
[ROW][C]60[/C][C]96.94[/C][C]96.9316137169309[/C][C]0.00838628306914302[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284114&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284114&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	103.2	103.539716880342	-0.339716880341911
14	103.21	103.181207749198	0.0287922508015157
15	103	102.972057878958	0.0279421210423436
16	102.46	102.440382907497	0.0196170925026848
17	102.52	102.505962128422	0.0140378715782816
18	102.55	102.536376615377	0.0136233846225338
19	102.78	102.583028864051	0.196971135949198
20	102.81	102.766761367261	0.0432386327394738
21	102.81	102.820954712458	-0.0109547124575045
22	102.68	102.852714593237	-0.172714593236634
23	102.72	102.700948296931	0.0190517030687545
24	102.73	102.790677490642	-0.0606774906421919
25	102.87	102.746385906481	0.12361409351918
26	102.93	102.858369111451	0.0716308885493078
27	103.2	102.700484109352	0.499515890647558
28	102.62	102.6627329849	-0.0427329849003542
29	102.18	102.6864712363	-0.506471236299603
30	101.19	102.201516994858	-1.01151699485773
31	100.91	101.197900601113	-0.287900601113066
32	100.72	100.857316617019	-0.137316617018712
33	100.86	100.686178826694	0.173821173305868
34	100.89	100.863394462925	0.026605537075497
35	100.47	100.877513360366	-0.407513360366124
36	100.45	100.494647649387	-0.0446476493873718
37	100.64	100.420829367754	0.219170632246204
38	100.63	100.585634007485	0.044365992515452
39	100.66	100.356943972822	0.303056027178158
40	100.38	100.073392107831	0.306607892168685
41	99.68	100.407445116411	-0.727445116410792
42	99.71	99.6559663252636	0.0540336747363455
43	99.63	99.703811741864	-0.0738117418639774
44	99.63	99.5695490180146	0.06045098198544
45	99.71	99.5942505808712	0.11574941912879
46	99.77	99.7097515707985	0.0602484292014651
47	99.76	99.7548638196797	0.00513618032033492
48	99.79	99.7941821389479	-0.00418213894791108
49	98.13	99.7715586556954	-1.64155865569539
50	98.13	98.0314227715908	0.0985772284091979
51	97.87	97.8143333962594	0.0556666037406188
52	97.72	97.2334770272752	0.486522972724828
53	97.72	97.7028422695233	0.0171577304767112
54	97.6	97.6733488744906	-0.0733488744906481
55	97.31	97.5674331507535	-0.257433150753485
56	97.31	97.2177487589284	0.0922512410715655
57	97.44	97.2433892670167	0.196610732983274
58	96.94	97.4112777955129	-0.471277795512933
59	96.94	96.8806960208694	0.0593039791306182
60	96.94	96.9316137169309	0.00838628306914302

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	96.8793613331681	96.1813571838671	97.5773654824691
62	96.7870559996696	95.7852499407398	97.7888620585994
63	96.474750666171	95.2297340938425	97.7197672384996
64	95.8399453326725	94.3813803005241	97.2985103648209
65	95.8101399991739	94.1559024267015	97.4643775716464
66	95.7503346656754	93.9123505121895	97.5883188191613
67	95.7067793321768	93.6934952331399	97.7200634312137
68	95.6111406653449	93.4287720450932	97.7935092855967
69	95.5384186651797	93.1916559916844	97.885181338675
70	95.4977799983478	92.9902216001922	98.0053383965035
71	95.4404746648493	92.7749082106821	98.1060411190164
72	95.4323359980174	92.6109301864506	98.2537418095842

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 96.8793613331681 & 96.1813571838671 & 97.5773654824691 \tabularnewline
62 & 96.7870559996696 & 95.7852499407398 & 97.7888620585994 \tabularnewline
63 & 96.474750666171 & 95.2297340938425 & 97.7197672384996 \tabularnewline
64 & 95.8399453326725 & 94.3813803005241 & 97.2985103648209 \tabularnewline
65 & 95.8101399991739 & 94.1559024267015 & 97.4643775716464 \tabularnewline
66 & 95.7503346656754 & 93.9123505121895 & 97.5883188191613 \tabularnewline
67 & 95.7067793321768 & 93.6934952331399 & 97.7200634312137 \tabularnewline
68 & 95.6111406653449 & 93.4287720450932 & 97.7935092855967 \tabularnewline
69 & 95.5384186651797 & 93.1916559916844 & 97.885181338675 \tabularnewline
70 & 95.4977799983478 & 92.9902216001922 & 98.0053383965035 \tabularnewline
71 & 95.4404746648493 & 92.7749082106821 & 98.1060411190164 \tabularnewline
72 & 95.4323359980174 & 92.6109301864506 & 98.2537418095842 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284114&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]96.8793613331681[/C][C]96.1813571838671[/C][C]97.5773654824691[/C][/ROW]
[ROW][C]62[/C][C]96.7870559996696[/C][C]95.7852499407398[/C][C]97.7888620585994[/C][/ROW]
[ROW][C]63[/C][C]96.474750666171[/C][C]95.2297340938425[/C][C]97.7197672384996[/C][/ROW]
[ROW][C]64[/C][C]95.8399453326725[/C][C]94.3813803005241[/C][C]97.2985103648209[/C][/ROW]
[ROW][C]65[/C][C]95.8101399991739[/C][C]94.1559024267015[/C][C]97.4643775716464[/C][/ROW]
[ROW][C]66[/C][C]95.7503346656754[/C][C]93.9123505121895[/C][C]97.5883188191613[/C][/ROW]
[ROW][C]67[/C][C]95.7067793321768[/C][C]93.6934952331399[/C][C]97.7200634312137[/C][/ROW]
[ROW][C]68[/C][C]95.6111406653449[/C][C]93.4287720450932[/C][C]97.7935092855967[/C][/ROW]
[ROW][C]69[/C][C]95.5384186651797[/C][C]93.1916559916844[/C][C]97.885181338675[/C][/ROW]
[ROW][C]70[/C][C]95.4977799983478[/C][C]92.9902216001922[/C][C]98.0053383965035[/C][/ROW]
[ROW][C]71[/C][C]95.4404746648493[/C][C]92.7749082106821[/C][C]98.1060411190164[/C][/ROW]
[ROW][C]72[/C][C]95.4323359980174[/C][C]92.6109301864506[/C][C]98.2537418095842[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284114&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284114&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
61	96.8793613331681	96.1813571838671	97.5773654824691
62	96.7870559996696	95.7852499407398	97.7888620585994
63	96.474750666171	95.2297340938425	97.7197672384996
64	95.8399453326725	94.3813803005241	97.2985103648209
65	95.8101399991739	94.1559024267015	97.4643775716464
66	95.7503346656754	93.9123505121895	97.5883188191613
67	95.7067793321768	93.6934952331399	97.7200634312137
68	95.6111406653449	93.4287720450932	97.7935092855967
69	95.5384186651797	93.1916559916844	97.885181338675
70	95.4977799983478	92.9902216001922	98.0053383965035
71	95.4404746648493	92.7749082106821	98.1060411190164
72	95.4323359980174	92.6109301864506	98.2537418095842

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 = 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code