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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Mon, 02 May 2016 11:12:25 +0100

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/2016/May/02/t1462184025divg6t0e6vsnkfq.htm/, Retrieved Sun, 05 May 2024 16:08:15 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=295112, Retrieved Sun, 05 May 2024 16:08:15 +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)

-     [Harrell-Davis Quantiles] [Harrel-Davis Quan...] [2016-02-27 10:54:55] [c654849ccc5a3f9604e59101648dee14]
- RMP     [Exponential Smoothing] [Exponential Smoot...] [2016-05-02 10:12:25] [fcb50c3fd850be3d4e9c7b78a2663ee0] [Current]

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Dataseries X:

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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	'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=295112&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=295112&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295112&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	'Sir Maurice George Kendall' @ kendall.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.665932641075839
beta	0.0480086184585807
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.665932641075839 \tabularnewline
beta & 0.0480086184585807 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295112&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]0.665932641075839[/C][/ROW]
[ROW][C]beta[/C][C]0.0480086184585807[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295112&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295112&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	0.665932641075839
beta	0.0480086184585807
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	94.59	91.922358440171	2.66764155982902
14	94.69	93.9701497194323	0.719850280567741
15	94.67	94.5459405189388	0.124059481061209
16	96.55	96.573107688862	-0.0231076888619981
17	97.14	97.2606993387979	-0.120699338797905
18	97.32	97.5173593712663	-0.197359371266273
19	97.97	99.7958259735348	-1.82582597353478
20	98.49	98.1931375967213	0.296862403278695
21	99.11	97.6751742047972	1.43482579520283
22	99.09	98.3963065533871	0.693693446612883
23	98.76	100.018155743583	-1.25815574358292
24	99.2	99.5862309717144	-0.386230971714355
25	99.61	100.47544000348	-0.865440003479563
26	99.54	99.4747440853501	0.0652559146498675
27	99.68	99.3496577855048	0.330342214495232
28	100.75	101.405699490959	-0.655699490959464
29	100.38	101.559869024421	-1.17986902442057
30	100.79	100.9721651831	-0.182165183100281
31	100.39	102.60379972708	-2.21379972707965
32	100.39	101.326531319285	-0.936531319285166
33	100.12	100.202598447113	-0.0825984471125167
34	100	99.4523587491188	0.547641250881227
35	99.17	100.106946961317	-0.936946961317361
36	99.17	99.9725254656344	-0.802525465634432
37	99.59	100.203431422089	-0.613431422088979
38	99.96	99.4685373254597	0.491462674540273
39	99.68	99.5165246987492	0.163475301250855
40	101.03	100.927397111764	0.102602888236362
41	100.99	101.231037510628	-0.241037510627976
42	101.38	101.451447915658	-0.0714479156583394
43	101.84	102.331265012211	-0.491265012211301
44	101.52	102.536007783305	-1.01600778330518
45	101.37	101.550104539315	-0.180104539315096
46	101.22	100.848042044569	0.371957955430631
47	101.45	100.786635050182	0.663364949818131
48	101.99	101.710932605249	0.279067394750612
49	104.05	102.707969049806	1.34203095019419
50	104.61	103.6895997	0.920400300000139
51	105.06	103.97258358845	1.08741641154954
52	105.4	106.066864748823	-0.666864748823301
53	104.71	105.807153911503	-1.09715391150311
54	104.8	105.550593754173	-0.750593754172868
55	104.83	105.852676589419	-1.02267658941901
56	104.81	105.526024425976	-0.716024425975775
57	104.49	105.026517312422	-0.536517312422504
58	104.59	104.267518713193	0.322481286806521
59	104.5	104.264916096294	0.235083903706212
60	104.61	104.756336633257	-0.146336633257462

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 94.59 & 91.922358440171 & 2.66764155982902 \tabularnewline
14 & 94.69 & 93.9701497194323 & 0.719850280567741 \tabularnewline
15 & 94.67 & 94.5459405189388 & 0.124059481061209 \tabularnewline
16 & 96.55 & 96.573107688862 & -0.0231076888619981 \tabularnewline
17 & 97.14 & 97.2606993387979 & -0.120699338797905 \tabularnewline
18 & 97.32 & 97.5173593712663 & -0.197359371266273 \tabularnewline
19 & 97.97 & 99.7958259735348 & -1.82582597353478 \tabularnewline
20 & 98.49 & 98.1931375967213 & 0.296862403278695 \tabularnewline
21 & 99.11 & 97.6751742047972 & 1.43482579520283 \tabularnewline
22 & 99.09 & 98.3963065533871 & 0.693693446612883 \tabularnewline
23 & 98.76 & 100.018155743583 & -1.25815574358292 \tabularnewline
24 & 99.2 & 99.5862309717144 & -0.386230971714355 \tabularnewline
25 & 99.61 & 100.47544000348 & -0.865440003479563 \tabularnewline
26 & 99.54 & 99.4747440853501 & 0.0652559146498675 \tabularnewline
27 & 99.68 & 99.3496577855048 & 0.330342214495232 \tabularnewline
28 & 100.75 & 101.405699490959 & -0.655699490959464 \tabularnewline
29 & 100.38 & 101.559869024421 & -1.17986902442057 \tabularnewline
30 & 100.79 & 100.9721651831 & -0.182165183100281 \tabularnewline
31 & 100.39 & 102.60379972708 & -2.21379972707965 \tabularnewline
32 & 100.39 & 101.326531319285 & -0.936531319285166 \tabularnewline
33 & 100.12 & 100.202598447113 & -0.0825984471125167 \tabularnewline
34 & 100 & 99.4523587491188 & 0.547641250881227 \tabularnewline
35 & 99.17 & 100.106946961317 & -0.936946961317361 \tabularnewline
36 & 99.17 & 99.9725254656344 & -0.802525465634432 \tabularnewline
37 & 99.59 & 100.203431422089 & -0.613431422088979 \tabularnewline
38 & 99.96 & 99.4685373254597 & 0.491462674540273 \tabularnewline
39 & 99.68 & 99.5165246987492 & 0.163475301250855 \tabularnewline
40 & 101.03 & 100.927397111764 & 0.102602888236362 \tabularnewline
41 & 100.99 & 101.231037510628 & -0.241037510627976 \tabularnewline
42 & 101.38 & 101.451447915658 & -0.0714479156583394 \tabularnewline
43 & 101.84 & 102.331265012211 & -0.491265012211301 \tabularnewline
44 & 101.52 & 102.536007783305 & -1.01600778330518 \tabularnewline
45 & 101.37 & 101.550104539315 & -0.180104539315096 \tabularnewline
46 & 101.22 & 100.848042044569 & 0.371957955430631 \tabularnewline
47 & 101.45 & 100.786635050182 & 0.663364949818131 \tabularnewline
48 & 101.99 & 101.710932605249 & 0.279067394750612 \tabularnewline
49 & 104.05 & 102.707969049806 & 1.34203095019419 \tabularnewline
50 & 104.61 & 103.6895997 & 0.920400300000139 \tabularnewline
51 & 105.06 & 103.97258358845 & 1.08741641154954 \tabularnewline
52 & 105.4 & 106.066864748823 & -0.666864748823301 \tabularnewline
53 & 104.71 & 105.807153911503 & -1.09715391150311 \tabularnewline
54 & 104.8 & 105.550593754173 & -0.750593754172868 \tabularnewline
55 & 104.83 & 105.852676589419 & -1.02267658941901 \tabularnewline
56 & 104.81 & 105.526024425976 & -0.716024425975775 \tabularnewline
57 & 104.49 & 105.026517312422 & -0.536517312422504 \tabularnewline
58 & 104.59 & 104.267518713193 & 0.322481286806521 \tabularnewline
59 & 104.5 & 104.264916096294 & 0.235083903706212 \tabularnewline
60 & 104.61 & 104.756336633257 & -0.146336633257462 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295112&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]94.59[/C][C]91.922358440171[/C][C]2.66764155982902[/C][/ROW]
[ROW][C]14[/C][C]94.69[/C][C]93.9701497194323[/C][C]0.719850280567741[/C][/ROW]
[ROW][C]15[/C][C]94.67[/C][C]94.5459405189388[/C][C]0.124059481061209[/C][/ROW]
[ROW][C]16[/C][C]96.55[/C][C]96.573107688862[/C][C]-0.0231076888619981[/C][/ROW]
[ROW][C]17[/C][C]97.14[/C][C]97.2606993387979[/C][C]-0.120699338797905[/C][/ROW]
[ROW][C]18[/C][C]97.32[/C][C]97.5173593712663[/C][C]-0.197359371266273[/C][/ROW]
[ROW][C]19[/C][C]97.97[/C][C]99.7958259735348[/C][C]-1.82582597353478[/C][/ROW]
[ROW][C]20[/C][C]98.49[/C][C]98.1931375967213[/C][C]0.296862403278695[/C][/ROW]
[ROW][C]21[/C][C]99.11[/C][C]97.6751742047972[/C][C]1.43482579520283[/C][/ROW]
[ROW][C]22[/C][C]99.09[/C][C]98.3963065533871[/C][C]0.693693446612883[/C][/ROW]
[ROW][C]23[/C][C]98.76[/C][C]100.018155743583[/C][C]-1.25815574358292[/C][/ROW]
[ROW][C]24[/C][C]99.2[/C][C]99.5862309717144[/C][C]-0.386230971714355[/C][/ROW]
[ROW][C]25[/C][C]99.61[/C][C]100.47544000348[/C][C]-0.865440003479563[/C][/ROW]
[ROW][C]26[/C][C]99.54[/C][C]99.4747440853501[/C][C]0.0652559146498675[/C][/ROW]
[ROW][C]27[/C][C]99.68[/C][C]99.3496577855048[/C][C]0.330342214495232[/C][/ROW]
[ROW][C]28[/C][C]100.75[/C][C]101.405699490959[/C][C]-0.655699490959464[/C][/ROW]
[ROW][C]29[/C][C]100.38[/C][C]101.559869024421[/C][C]-1.17986902442057[/C][/ROW]
[ROW][C]30[/C][C]100.79[/C][C]100.9721651831[/C][C]-0.182165183100281[/C][/ROW]
[ROW][C]31[/C][C]100.39[/C][C]102.60379972708[/C][C]-2.21379972707965[/C][/ROW]
[ROW][C]32[/C][C]100.39[/C][C]101.326531319285[/C][C]-0.936531319285166[/C][/ROW]
[ROW][C]33[/C][C]100.12[/C][C]100.202598447113[/C][C]-0.0825984471125167[/C][/ROW]
[ROW][C]34[/C][C]100[/C][C]99.4523587491188[/C][C]0.547641250881227[/C][/ROW]
[ROW][C]35[/C][C]99.17[/C][C]100.106946961317[/C][C]-0.936946961317361[/C][/ROW]
[ROW][C]36[/C][C]99.17[/C][C]99.9725254656344[/C][C]-0.802525465634432[/C][/ROW]
[ROW][C]37[/C][C]99.59[/C][C]100.203431422089[/C][C]-0.613431422088979[/C][/ROW]
[ROW][C]38[/C][C]99.96[/C][C]99.4685373254597[/C][C]0.491462674540273[/C][/ROW]
[ROW][C]39[/C][C]99.68[/C][C]99.5165246987492[/C][C]0.163475301250855[/C][/ROW]
[ROW][C]40[/C][C]101.03[/C][C]100.927397111764[/C][C]0.102602888236362[/C][/ROW]
[ROW][C]41[/C][C]100.99[/C][C]101.231037510628[/C][C]-0.241037510627976[/C][/ROW]
[ROW][C]42[/C][C]101.38[/C][C]101.451447915658[/C][C]-0.0714479156583394[/C][/ROW]
[ROW][C]43[/C][C]101.84[/C][C]102.331265012211[/C][C]-0.491265012211301[/C][/ROW]
[ROW][C]44[/C][C]101.52[/C][C]102.536007783305[/C][C]-1.01600778330518[/C][/ROW]
[ROW][C]45[/C][C]101.37[/C][C]101.550104539315[/C][C]-0.180104539315096[/C][/ROW]
[ROW][C]46[/C][C]101.22[/C][C]100.848042044569[/C][C]0.371957955430631[/C][/ROW]
[ROW][C]47[/C][C]101.45[/C][C]100.786635050182[/C][C]0.663364949818131[/C][/ROW]
[ROW][C]48[/C][C]101.99[/C][C]101.710932605249[/C][C]0.279067394750612[/C][/ROW]
[ROW][C]49[/C][C]104.05[/C][C]102.707969049806[/C][C]1.34203095019419[/C][/ROW]
[ROW][C]50[/C][C]104.61[/C][C]103.6895997[/C][C]0.920400300000139[/C][/ROW]
[ROW][C]51[/C][C]105.06[/C][C]103.97258358845[/C][C]1.08741641154954[/C][/ROW]
[ROW][C]52[/C][C]105.4[/C][C]106.066864748823[/C][C]-0.666864748823301[/C][/ROW]
[ROW][C]53[/C][C]104.71[/C][C]105.807153911503[/C][C]-1.09715391150311[/C][/ROW]
[ROW][C]54[/C][C]104.8[/C][C]105.550593754173[/C][C]-0.750593754172868[/C][/ROW]
[ROW][C]55[/C][C]104.83[/C][C]105.852676589419[/C][C]-1.02267658941901[/C][/ROW]
[ROW][C]56[/C][C]104.81[/C][C]105.526024425976[/C][C]-0.716024425975775[/C][/ROW]
[ROW][C]57[/C][C]104.49[/C][C]105.026517312422[/C][C]-0.536517312422504[/C][/ROW]
[ROW][C]58[/C][C]104.59[/C][C]104.267518713193[/C][C]0.322481286806521[/C][/ROW]
[ROW][C]59[/C][C]104.5[/C][C]104.264916096294[/C][C]0.235083903706212[/C][/ROW]
[ROW][C]60[/C][C]104.61[/C][C]104.756336633257[/C][C]-0.146336633257462[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295112&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295112&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	94.59	91.922358440171	2.66764155982902
14	94.69	93.9701497194323	0.719850280567741
15	94.67	94.5459405189388	0.124059481061209
16	96.55	96.573107688862	-0.0231076888619981
17	97.14	97.2606993387979	-0.120699338797905
18	97.32	97.5173593712663	-0.197359371266273
19	97.97	99.7958259735348	-1.82582597353478
20	98.49	98.1931375967213	0.296862403278695
21	99.11	97.6751742047972	1.43482579520283
22	99.09	98.3963065533871	0.693693446612883
23	98.76	100.018155743583	-1.25815574358292
24	99.2	99.5862309717144	-0.386230971714355
25	99.61	100.47544000348	-0.865440003479563
26	99.54	99.4747440853501	0.0652559146498675
27	99.68	99.3496577855048	0.330342214495232
28	100.75	101.405699490959	-0.655699490959464
29	100.38	101.559869024421	-1.17986902442057
30	100.79	100.9721651831	-0.182165183100281
31	100.39	102.60379972708	-2.21379972707965
32	100.39	101.326531319285	-0.936531319285166
33	100.12	100.202598447113	-0.0825984471125167
34	100	99.4523587491188	0.547641250881227
35	99.17	100.106946961317	-0.936946961317361
36	99.17	99.9725254656344	-0.802525465634432
37	99.59	100.203431422089	-0.613431422088979
38	99.96	99.4685373254597	0.491462674540273
39	99.68	99.5165246987492	0.163475301250855
40	101.03	100.927397111764	0.102602888236362
41	100.99	101.231037510628	-0.241037510627976
42	101.38	101.451447915658	-0.0714479156583394
43	101.84	102.331265012211	-0.491265012211301
44	101.52	102.536007783305	-1.01600778330518
45	101.37	101.550104539315	-0.180104539315096
46	101.22	100.848042044569	0.371957955430631
47	101.45	100.786635050182	0.663364949818131
48	101.99	101.710932605249	0.279067394750612
49	104.05	102.707969049806	1.34203095019419
50	104.61	103.6895997	0.920400300000139
51	105.06	103.97258358845	1.08741641154954
52	105.4	106.066864748823	-0.666864748823301
53	104.71	105.807153911503	-1.09715391150311
54	104.8	105.550593754173	-0.750593754172868
55	104.83	105.852676589419	-1.02267658941901
56	104.81	105.526024425976	-0.716024425975775
57	104.49	105.026517312422	-0.536517312422504
58	104.59	104.267518713193	0.322481286806521
59	104.5	104.264916096294	0.235083903706212
60	104.61	104.756336633257	-0.146336633257462

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	105.792294274771	104.085782978754	107.498805570787
62	105.663574460739	103.582561913697	107.74458700778
63	105.284207503049	102.858928711142	107.709486294956
64	105.928308378674	103.176540591733	108.680076165615
65	105.850272856338	102.783138594118	108.917407118559
66	106.356528178944	102.981148161314	109.731908196574
67	107.007969204801	103.328864401555	110.687074008046
68	107.437896033689	103.457804149164	111.417987918214
69	107.471174879624	103.191560272136	111.750789487112
70	107.369571249695	102.790960690958	111.948181808432
71	107.125858499976	102.248071609761	112.00364539019
72	107.328630384423	102.150943136319	112.506317632526

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 105.792294274771 & 104.085782978754 & 107.498805570787 \tabularnewline
62 & 105.663574460739 & 103.582561913697 & 107.74458700778 \tabularnewline
63 & 105.284207503049 & 102.858928711142 & 107.709486294956 \tabularnewline
64 & 105.928308378674 & 103.176540591733 & 108.680076165615 \tabularnewline
65 & 105.850272856338 & 102.783138594118 & 108.917407118559 \tabularnewline
66 & 106.356528178944 & 102.981148161314 & 109.731908196574 \tabularnewline
67 & 107.007969204801 & 103.328864401555 & 110.687074008046 \tabularnewline
68 & 107.437896033689 & 103.457804149164 & 111.417987918214 \tabularnewline
69 & 107.471174879624 & 103.191560272136 & 111.750789487112 \tabularnewline
70 & 107.369571249695 & 102.790960690958 & 111.948181808432 \tabularnewline
71 & 107.125858499976 & 102.248071609761 & 112.00364539019 \tabularnewline
72 & 107.328630384423 & 102.150943136319 & 112.506317632526 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295112&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]105.792294274771[/C][C]104.085782978754[/C][C]107.498805570787[/C][/ROW]
[ROW][C]62[/C][C]105.663574460739[/C][C]103.582561913697[/C][C]107.74458700778[/C][/ROW]
[ROW][C]63[/C][C]105.284207503049[/C][C]102.858928711142[/C][C]107.709486294956[/C][/ROW]
[ROW][C]64[/C][C]105.928308378674[/C][C]103.176540591733[/C][C]108.680076165615[/C][/ROW]
[ROW][C]65[/C][C]105.850272856338[/C][C]102.783138594118[/C][C]108.917407118559[/C][/ROW]
[ROW][C]66[/C][C]106.356528178944[/C][C]102.981148161314[/C][C]109.731908196574[/C][/ROW]
[ROW][C]67[/C][C]107.007969204801[/C][C]103.328864401555[/C][C]110.687074008046[/C][/ROW]
[ROW][C]68[/C][C]107.437896033689[/C][C]103.457804149164[/C][C]111.417987918214[/C][/ROW]
[ROW][C]69[/C][C]107.471174879624[/C][C]103.191560272136[/C][C]111.750789487112[/C][/ROW]
[ROW][C]70[/C][C]107.369571249695[/C][C]102.790960690958[/C][C]111.948181808432[/C][/ROW]
[ROW][C]71[/C][C]107.125858499976[/C][C]102.248071609761[/C][C]112.00364539019[/C][/ROW]
[ROW][C]72[/C][C]107.328630384423[/C][C]102.150943136319[/C][C]112.506317632526[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295112&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295112&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	105.792294274771	104.085782978754	107.498805570787
62	105.663574460739	103.582561913697	107.74458700778
63	105.284207503049	102.858928711142	107.709486294956
64	105.928308378674	103.176540591733	108.680076165615
65	105.850272856338	102.783138594118	108.917407118559
66	106.356528178944	102.981148161314	109.731908196574
67	107.007969204801	103.328864401555	110.687074008046
68	107.437896033689	103.457804149164	111.417987918214
69	107.471174879624	103.191560272136	111.750789487112
70	107.369571249695	102.790960690958	111.948181808432
71	107.125858499976	102.248071609761	112.00364539019
72	107.328630384423	102.150943136319	112.506317632526

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