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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Tue, 22 May 2012 07:36:20 -0400

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/2012/May/22/t13376866089vzw0msonrt9yvs.htm/, Retrieved Fri, 03 May 2024 16:48:42 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167043, Retrieved Fri, 03 May 2024 16:48:42 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

105

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

-       [Exponential Smoothing] [Triple exponentia...] [2012-05-22 11:36:20] [76c30f62b7052b57088120e90a652e05] [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	2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167043&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167043&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167043&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	2 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.747001106156908
beta	0
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.747001106156908 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167043&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]0.747001106156908[/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=167043&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167043&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	0.747001106156908
beta	0
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	407.77	406.584706196581	1.18529380341886
14	408.06	407.880162771397	0.179837228603276
15	403.74	404.088292172632	-0.348292172632341
16	403.44	403.968574993618	-0.52857499361761
17	404.3	404.883353014573	-0.583353014572651
18	403.29	403.853878459948	-0.56387845994783
19	403.29	401.652701419169	1.63729858083053
20	400.66	406.2245560627	-5.56455606269986
21	400.84	401.887033987798	-1.04703398779844
22	401.31	402.25243923327	-0.942439233270022
23	402	401.218893542739	0.781106457260876
24	402	401.63117172288	0.368828277119974
25	402	402.057022334222	-0.057022334222097
26	403.33	402.170087978788	1.15991202121222
27	403.79	398.9767181799	4.81328182009986
28	403.04	402.667091128679	0.372908871321101
29	402.91	404.241419815217	-1.3314198152172
30	406.55	402.65806557381	3.89193442619018
31	406.55	404.342281044275	2.20771895572551
32	404.69	407.518179080394	-2.82817908039397
33	404.74	406.367661725999	-1.62766172599913
34	404.2	406.325799765967	-2.12579976596697
35	404.18	404.844337601721	-0.6643376017214
36	404.18	404.072561547383	0.107438452616634
37	404.18	404.195413937071	-0.0154139370713438
38	404.82	404.647444146139	0.172555853861411
39	406.46	401.640816715987	4.81918328401258
40	407.25	404.212188620545	3.03781137945492
41	407.34	407.34600915602	-0.00600915602046825
42	404.3	408.074240988372	-3.77424098837184
43	404.3	403.605710293145	0.694289706855216
44	404.7	404.376998373623	0.323001626376879
45	406.82	405.884146055588	0.935853944412258
46	406.82	407.63120476391	-0.811204763910382
47	406.76	407.501494831297	-0.741494831297075
48	406.76	406.86734072916	-0.107340729160114
49	406.76	406.798671313784	-0.0386713137843344
50	407.67	407.280884385903	0.389115614097477
51	406.03	405.611618936126	0.418381063873937
52	401.97	404.444901592886	-2.47490159288606
53	401.84	402.690636211565	-0.850636211565075
54	402.24	401.834572213805	0.40542778619465
55	402.24	401.618792039545	0.62120796045474
56	401.57	402.241552500964	-0.671552500964424
57	401.63	403.160818108224	-1.53081810822431
58	402.06	402.623266144017	-0.563266144016552
59	402.11	402.696403170564	-0.586403170563983
60	402.43	402.338542996917	0.0914570030828941

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 407.77 & 406.584706196581 & 1.18529380341886 \tabularnewline
14 & 408.06 & 407.880162771397 & 0.179837228603276 \tabularnewline
15 & 403.74 & 404.088292172632 & -0.348292172632341 \tabularnewline
16 & 403.44 & 403.968574993618 & -0.52857499361761 \tabularnewline
17 & 404.3 & 404.883353014573 & -0.583353014572651 \tabularnewline
18 & 403.29 & 403.853878459948 & -0.56387845994783 \tabularnewline
19 & 403.29 & 401.652701419169 & 1.63729858083053 \tabularnewline
20 & 400.66 & 406.2245560627 & -5.56455606269986 \tabularnewline
21 & 400.84 & 401.887033987798 & -1.04703398779844 \tabularnewline
22 & 401.31 & 402.25243923327 & -0.942439233270022 \tabularnewline
23 & 402 & 401.218893542739 & 0.781106457260876 \tabularnewline
24 & 402 & 401.63117172288 & 0.368828277119974 \tabularnewline
25 & 402 & 402.057022334222 & -0.057022334222097 \tabularnewline
26 & 403.33 & 402.170087978788 & 1.15991202121222 \tabularnewline
27 & 403.79 & 398.9767181799 & 4.81328182009986 \tabularnewline
28 & 403.04 & 402.667091128679 & 0.372908871321101 \tabularnewline
29 & 402.91 & 404.241419815217 & -1.3314198152172 \tabularnewline
30 & 406.55 & 402.65806557381 & 3.89193442619018 \tabularnewline
31 & 406.55 & 404.342281044275 & 2.20771895572551 \tabularnewline
32 & 404.69 & 407.518179080394 & -2.82817908039397 \tabularnewline
33 & 404.74 & 406.367661725999 & -1.62766172599913 \tabularnewline
34 & 404.2 & 406.325799765967 & -2.12579976596697 \tabularnewline
35 & 404.18 & 404.844337601721 & -0.6643376017214 \tabularnewline
36 & 404.18 & 404.072561547383 & 0.107438452616634 \tabularnewline
37 & 404.18 & 404.195413937071 & -0.0154139370713438 \tabularnewline
38 & 404.82 & 404.647444146139 & 0.172555853861411 \tabularnewline
39 & 406.46 & 401.640816715987 & 4.81918328401258 \tabularnewline
40 & 407.25 & 404.212188620545 & 3.03781137945492 \tabularnewline
41 & 407.34 & 407.34600915602 & -0.00600915602046825 \tabularnewline
42 & 404.3 & 408.074240988372 & -3.77424098837184 \tabularnewline
43 & 404.3 & 403.605710293145 & 0.694289706855216 \tabularnewline
44 & 404.7 & 404.376998373623 & 0.323001626376879 \tabularnewline
45 & 406.82 & 405.884146055588 & 0.935853944412258 \tabularnewline
46 & 406.82 & 407.63120476391 & -0.811204763910382 \tabularnewline
47 & 406.76 & 407.501494831297 & -0.741494831297075 \tabularnewline
48 & 406.76 & 406.86734072916 & -0.107340729160114 \tabularnewline
49 & 406.76 & 406.798671313784 & -0.0386713137843344 \tabularnewline
50 & 407.67 & 407.280884385903 & 0.389115614097477 \tabularnewline
51 & 406.03 & 405.611618936126 & 0.418381063873937 \tabularnewline
52 & 401.97 & 404.444901592886 & -2.47490159288606 \tabularnewline
53 & 401.84 & 402.690636211565 & -0.850636211565075 \tabularnewline
54 & 402.24 & 401.834572213805 & 0.40542778619465 \tabularnewline
55 & 402.24 & 401.618792039545 & 0.62120796045474 \tabularnewline
56 & 401.57 & 402.241552500964 & -0.671552500964424 \tabularnewline
57 & 401.63 & 403.160818108224 & -1.53081810822431 \tabularnewline
58 & 402.06 & 402.623266144017 & -0.563266144016552 \tabularnewline
59 & 402.11 & 402.696403170564 & -0.586403170563983 \tabularnewline
60 & 402.43 & 402.338542996917 & 0.0914570030828941 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167043&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]407.77[/C][C]406.584706196581[/C][C]1.18529380341886[/C][/ROW]
[ROW][C]14[/C][C]408.06[/C][C]407.880162771397[/C][C]0.179837228603276[/C][/ROW]
[ROW][C]15[/C][C]403.74[/C][C]404.088292172632[/C][C]-0.348292172632341[/C][/ROW]
[ROW][C]16[/C][C]403.44[/C][C]403.968574993618[/C][C]-0.52857499361761[/C][/ROW]
[ROW][C]17[/C][C]404.3[/C][C]404.883353014573[/C][C]-0.583353014572651[/C][/ROW]
[ROW][C]18[/C][C]403.29[/C][C]403.853878459948[/C][C]-0.56387845994783[/C][/ROW]
[ROW][C]19[/C][C]403.29[/C][C]401.652701419169[/C][C]1.63729858083053[/C][/ROW]
[ROW][C]20[/C][C]400.66[/C][C]406.2245560627[/C][C]-5.56455606269986[/C][/ROW]
[ROW][C]21[/C][C]400.84[/C][C]401.887033987798[/C][C]-1.04703398779844[/C][/ROW]
[ROW][C]22[/C][C]401.31[/C][C]402.25243923327[/C][C]-0.942439233270022[/C][/ROW]
[ROW][C]23[/C][C]402[/C][C]401.218893542739[/C][C]0.781106457260876[/C][/ROW]
[ROW][C]24[/C][C]402[/C][C]401.63117172288[/C][C]0.368828277119974[/C][/ROW]
[ROW][C]25[/C][C]402[/C][C]402.057022334222[/C][C]-0.057022334222097[/C][/ROW]
[ROW][C]26[/C][C]403.33[/C][C]402.170087978788[/C][C]1.15991202121222[/C][/ROW]
[ROW][C]27[/C][C]403.79[/C][C]398.9767181799[/C][C]4.81328182009986[/C][/ROW]
[ROW][C]28[/C][C]403.04[/C][C]402.667091128679[/C][C]0.372908871321101[/C][/ROW]
[ROW][C]29[/C][C]402.91[/C][C]404.241419815217[/C][C]-1.3314198152172[/C][/ROW]
[ROW][C]30[/C][C]406.55[/C][C]402.65806557381[/C][C]3.89193442619018[/C][/ROW]
[ROW][C]31[/C][C]406.55[/C][C]404.342281044275[/C][C]2.20771895572551[/C][/ROW]
[ROW][C]32[/C][C]404.69[/C][C]407.518179080394[/C][C]-2.82817908039397[/C][/ROW]
[ROW][C]33[/C][C]404.74[/C][C]406.367661725999[/C][C]-1.62766172599913[/C][/ROW]
[ROW][C]34[/C][C]404.2[/C][C]406.325799765967[/C][C]-2.12579976596697[/C][/ROW]
[ROW][C]35[/C][C]404.18[/C][C]404.844337601721[/C][C]-0.6643376017214[/C][/ROW]
[ROW][C]36[/C][C]404.18[/C][C]404.072561547383[/C][C]0.107438452616634[/C][/ROW]
[ROW][C]37[/C][C]404.18[/C][C]404.195413937071[/C][C]-0.0154139370713438[/C][/ROW]
[ROW][C]38[/C][C]404.82[/C][C]404.647444146139[/C][C]0.172555853861411[/C][/ROW]
[ROW][C]39[/C][C]406.46[/C][C]401.640816715987[/C][C]4.81918328401258[/C][/ROW]
[ROW][C]40[/C][C]407.25[/C][C]404.212188620545[/C][C]3.03781137945492[/C][/ROW]
[ROW][C]41[/C][C]407.34[/C][C]407.34600915602[/C][C]-0.00600915602046825[/C][/ROW]
[ROW][C]42[/C][C]404.3[/C][C]408.074240988372[/C][C]-3.77424098837184[/C][/ROW]
[ROW][C]43[/C][C]404.3[/C][C]403.605710293145[/C][C]0.694289706855216[/C][/ROW]
[ROW][C]44[/C][C]404.7[/C][C]404.376998373623[/C][C]0.323001626376879[/C][/ROW]
[ROW][C]45[/C][C]406.82[/C][C]405.884146055588[/C][C]0.935853944412258[/C][/ROW]
[ROW][C]46[/C][C]406.82[/C][C]407.63120476391[/C][C]-0.811204763910382[/C][/ROW]
[ROW][C]47[/C][C]406.76[/C][C]407.501494831297[/C][C]-0.741494831297075[/C][/ROW]
[ROW][C]48[/C][C]406.76[/C][C]406.86734072916[/C][C]-0.107340729160114[/C][/ROW]
[ROW][C]49[/C][C]406.76[/C][C]406.798671313784[/C][C]-0.0386713137843344[/C][/ROW]
[ROW][C]50[/C][C]407.67[/C][C]407.280884385903[/C][C]0.389115614097477[/C][/ROW]
[ROW][C]51[/C][C]406.03[/C][C]405.611618936126[/C][C]0.418381063873937[/C][/ROW]
[ROW][C]52[/C][C]401.97[/C][C]404.444901592886[/C][C]-2.47490159288606[/C][/ROW]
[ROW][C]53[/C][C]401.84[/C][C]402.690636211565[/C][C]-0.850636211565075[/C][/ROW]
[ROW][C]54[/C][C]402.24[/C][C]401.834572213805[/C][C]0.40542778619465[/C][/ROW]
[ROW][C]55[/C][C]402.24[/C][C]401.618792039545[/C][C]0.62120796045474[/C][/ROW]
[ROW][C]56[/C][C]401.57[/C][C]402.241552500964[/C][C]-0.671552500964424[/C][/ROW]
[ROW][C]57[/C][C]401.63[/C][C]403.160818108224[/C][C]-1.53081810822431[/C][/ROW]
[ROW][C]58[/C][C]402.06[/C][C]402.623266144017[/C][C]-0.563266144016552[/C][/ROW]
[ROW][C]59[/C][C]402.11[/C][C]402.696403170564[/C][C]-0.586403170563983[/C][/ROW]
[ROW][C]60[/C][C]402.43[/C][C]402.338542996917[/C][C]0.0914570030828941[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167043&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167043&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	407.77	406.584706196581	1.18529380341886
14	408.06	407.880162771397	0.179837228603276
15	403.74	404.088292172632	-0.348292172632341
16	403.44	403.968574993618	-0.52857499361761
17	404.3	404.883353014573	-0.583353014572651
18	403.29	403.853878459948	-0.56387845994783
19	403.29	401.652701419169	1.63729858083053
20	400.66	406.2245560627	-5.56455606269986
21	400.84	401.887033987798	-1.04703398779844
22	401.31	402.25243923327	-0.942439233270022
23	402	401.218893542739	0.781106457260876
24	402	401.63117172288	0.368828277119974
25	402	402.057022334222	-0.057022334222097
26	403.33	402.170087978788	1.15991202121222
27	403.79	398.9767181799	4.81328182009986
28	403.04	402.667091128679	0.372908871321101
29	402.91	404.241419815217	-1.3314198152172
30	406.55	402.65806557381	3.89193442619018
31	406.55	404.342281044275	2.20771895572551
32	404.69	407.518179080394	-2.82817908039397
33	404.74	406.367661725999	-1.62766172599913
34	404.2	406.325799765967	-2.12579976596697
35	404.18	404.844337601721	-0.6643376017214
36	404.18	404.072561547383	0.107438452616634
37	404.18	404.195413937071	-0.0154139370713438
38	404.82	404.647444146139	0.172555853861411
39	406.46	401.640816715987	4.81918328401258
40	407.25	404.212188620545	3.03781137945492
41	407.34	407.34600915602	-0.00600915602046825
42	404.3	408.074240988372	-3.77424098837184
43	404.3	403.605710293145	0.694289706855216
44	404.7	404.376998373623	0.323001626376879
45	406.82	405.884146055588	0.935853944412258
46	406.82	407.63120476391	-0.811204763910382
47	406.76	407.501494831297	-0.741494831297075
48	406.76	406.86734072916	-0.107340729160114
49	406.76	406.798671313784	-0.0386713137843344
50	407.67	407.280884385903	0.389115614097477
51	406.03	405.611618936126	0.418381063873937
52	401.97	404.444901592886	-2.47490159288606
53	401.84	402.690636211565	-0.850636211565075
54	402.24	401.834572213805	0.40542778619465
55	402.24	401.618792039545	0.62120796045474
56	401.57	402.241552500964	-0.671552500964424
57	401.63	403.160818108224	-1.53081810822431
58	402.06	402.623266144017	-0.563266144016552
59	402.11	402.696403170564	-0.586403170563983
60	402.43	402.338542996917	0.0914570030828941

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	402.435748993559	398.802853839769	406.06864414735
62	403.055079199405	398.520488681245	407.589669717566
63	401.102548081897	395.817938811917	406.387157351876
64	398.891302309412	392.950622288967	404.831982329857
65	399.396728500388	392.865552260669	405.927904740108
66	399.493873495634	392.421331728826	406.566415262441
67	399.029830462021	391.454513240135	406.605147683906
68	398.861480923084	390.814741522484	406.908220323683
69	400.065003743252	391.572972246012	408.557035240492
70	400.915764175893	392.000654366189	409.830873985597
71	401.403807992958	392.084807677043	410.722808308874
72	401.65548951049	391.949390868038	411.361588152941

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 402.435748993559 & 398.802853839769 & 406.06864414735 \tabularnewline
62 & 403.055079199405 & 398.520488681245 & 407.589669717566 \tabularnewline
63 & 401.102548081897 & 395.817938811917 & 406.387157351876 \tabularnewline
64 & 398.891302309412 & 392.950622288967 & 404.831982329857 \tabularnewline
65 & 399.396728500388 & 392.865552260669 & 405.927904740108 \tabularnewline
66 & 399.493873495634 & 392.421331728826 & 406.566415262441 \tabularnewline
67 & 399.029830462021 & 391.454513240135 & 406.605147683906 \tabularnewline
68 & 398.861480923084 & 390.814741522484 & 406.908220323683 \tabularnewline
69 & 400.065003743252 & 391.572972246012 & 408.557035240492 \tabularnewline
70 & 400.915764175893 & 392.000654366189 & 409.830873985597 \tabularnewline
71 & 401.403807992958 & 392.084807677043 & 410.722808308874 \tabularnewline
72 & 401.65548951049 & 391.949390868038 & 411.361588152941 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167043&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]402.435748993559[/C][C]398.802853839769[/C][C]406.06864414735[/C][/ROW]
[ROW][C]62[/C][C]403.055079199405[/C][C]398.520488681245[/C][C]407.589669717566[/C][/ROW]
[ROW][C]63[/C][C]401.102548081897[/C][C]395.817938811917[/C][C]406.387157351876[/C][/ROW]
[ROW][C]64[/C][C]398.891302309412[/C][C]392.950622288967[/C][C]404.831982329857[/C][/ROW]
[ROW][C]65[/C][C]399.396728500388[/C][C]392.865552260669[/C][C]405.927904740108[/C][/ROW]
[ROW][C]66[/C][C]399.493873495634[/C][C]392.421331728826[/C][C]406.566415262441[/C][/ROW]
[ROW][C]67[/C][C]399.029830462021[/C][C]391.454513240135[/C][C]406.605147683906[/C][/ROW]
[ROW][C]68[/C][C]398.861480923084[/C][C]390.814741522484[/C][C]406.908220323683[/C][/ROW]
[ROW][C]69[/C][C]400.065003743252[/C][C]391.572972246012[/C][C]408.557035240492[/C][/ROW]
[ROW][C]70[/C][C]400.915764175893[/C][C]392.000654366189[/C][C]409.830873985597[/C][/ROW]
[ROW][C]71[/C][C]401.403807992958[/C][C]392.084807677043[/C][C]410.722808308874[/C][/ROW]
[ROW][C]72[/C][C]401.65548951049[/C][C]391.949390868038[/C][C]411.361588152941[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167043&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167043&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	402.435748993559	398.802853839769	406.06864414735
62	403.055079199405	398.520488681245	407.589669717566
63	401.102548081897	395.817938811917	406.387157351876
64	398.891302309412	392.950622288967	404.831982329857
65	399.396728500388	392.865552260669	405.927904740108
66	399.493873495634	392.421331728826	406.566415262441
67	399.029830462021	391.454513240135	406.605147683906
68	398.861480923084	390.814741522484	406.908220323683
69	400.065003743252	391.572972246012	408.557035240492
70	400.915764175893	392.000654366189	409.830873985597
71	401.403807992958	392.084807677043	410.722808308874
72	401.65548951049	391.949390868038	411.361588152941

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