Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sun, 19 Dec 2010 17:21:19 +0000

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/2010/Dec/19/t129277913633funkupnq6hxzy.htm/, Retrieved Sun, 05 May 2024 06:38:37 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112644, Retrieved Sun, 05 May 2024 06:38:37 +0000

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

201

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

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Exponential Smoothing] [Unemployment] [2010-11-30 13:37:23] [b98453cac15ba1066b407e146608df68]
-    D      [Exponential Smoothing] [] [2010-12-19 17:21:19] [7674ee8f347756742f81ca2ada5c384c] [Current]

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

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 Ronald Aylmer Fisher' @ 193.190.124.24

\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 Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112644&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 Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112644&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112644&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 Ronald Aylmer Fisher' @ 193.190.124.24

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.000564574695315228
gamma	0.192386515790093

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.000564574695315228 \tabularnewline
gamma & 0.192386515790093 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112644&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]0.000564574695315228[/C][/ROW]
[ROW][C]gamma[/C][C]0.192386515790093[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112644&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112644&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	0.000564574695315228
gamma	0.192386515790093

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	41.33	41.6101522435898	-0.280152243589754
14	41.29	41.2865186979343	0.00348130206570829
15	41.29	41.2915206633893	-0.00152066338934986
16	41.27	41.275686471528	-0.00568647152795876
17	41.04	41.06568326109	-0.0256832610900091
18	40.9	40.9473354276374	-0.0473354276373854
19	40.89	40.7627253699194	0.127274630080592
20	40.72	40.8282138926216	-0.108213892621571
21	40.72	40.7056527977961	0.0143472022038793
22	40.58	40.6664942311968	-0.0864942311967667
23	40.24	40.6097787320759	-0.369778732075865
24	40.07	40.2091532976942	-0.139153297694222
25	40.12	40.0586580685969	0.0613419314030992
26	40.1	40.0761927006991	0.0238072993008842
27	40.1	40.1012061416979	-0.00120614169787814
28	40.08	40.0853721274075	-0.00537212740748316
29	40.06	39.8753690944403	0.184630905559743
30	39.99	39.9671399990442	0.0228600009558022
31	40.05	39.8525695718889	0.197430428111069
32	39.66	39.9880977027794	-0.328097702779388
33	39.66	39.6454124671188	0.0145875328811869
34	39.67	39.6062540362041	0.0637459637959239
35	39.56	39.6996233588955	-0.139623358895491
36	39.64	39.5291278644135	0.110872135586462
37	39.73	39.628773793349	0.101226206650971
38	39.7	39.6863309431038	0.0136690568962123
39	39.7	39.7013386603074	-0.00133866030743945
40	39.68	39.6855045712004	-0.00550457120038317
41	39.76	39.4755014634587	0.28449853654125
42	40	39.6673287508	0.332671249199983
43	39.96	39.8629332352358	0.0970667647641648
44	40.01	39.8984047033416	0.111595296658358
45	40.01	39.9959677072222	0.0140322927777490
46	40.01	39.956808962833	0.0531910371669895
47	40	40.0401723264799	-0.040172326479933
48	39.91	39.9697329795343	-0.0597329795343029
49	39.86	39.8992825891389	-0.0392825891388995
50	39.79	39.8167604111831	-0.0267604111831048
51	39.79	39.7917453029321	-0.00174530293212172
52	39.8	39.7759109842449	0.0240890157550666
53	39.64	39.5959245842936	0.0440754157063665
54	39.55	39.5476161348247	0.00238386517528255
55	39.36	39.4130341473613	-0.0530341473613234
56	39.28	39.2984208722904	-0.0184208722903989

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 41.33 & 41.6101522435898 & -0.280152243589754 \tabularnewline
14 & 41.29 & 41.2865186979343 & 0.00348130206570829 \tabularnewline
15 & 41.29 & 41.2915206633893 & -0.00152066338934986 \tabularnewline
16 & 41.27 & 41.275686471528 & -0.00568647152795876 \tabularnewline
17 & 41.04 & 41.06568326109 & -0.0256832610900091 \tabularnewline
18 & 40.9 & 40.9473354276374 & -0.0473354276373854 \tabularnewline
19 & 40.89 & 40.7627253699194 & 0.127274630080592 \tabularnewline
20 & 40.72 & 40.8282138926216 & -0.108213892621571 \tabularnewline
21 & 40.72 & 40.7056527977961 & 0.0143472022038793 \tabularnewline
22 & 40.58 & 40.6664942311968 & -0.0864942311967667 \tabularnewline
23 & 40.24 & 40.6097787320759 & -0.369778732075865 \tabularnewline
24 & 40.07 & 40.2091532976942 & -0.139153297694222 \tabularnewline
25 & 40.12 & 40.0586580685969 & 0.0613419314030992 \tabularnewline
26 & 40.1 & 40.0761927006991 & 0.0238072993008842 \tabularnewline
27 & 40.1 & 40.1012061416979 & -0.00120614169787814 \tabularnewline
28 & 40.08 & 40.0853721274075 & -0.00537212740748316 \tabularnewline
29 & 40.06 & 39.8753690944403 & 0.184630905559743 \tabularnewline
30 & 39.99 & 39.9671399990442 & 0.0228600009558022 \tabularnewline
31 & 40.05 & 39.8525695718889 & 0.197430428111069 \tabularnewline
32 & 39.66 & 39.9880977027794 & -0.328097702779388 \tabularnewline
33 & 39.66 & 39.6454124671188 & 0.0145875328811869 \tabularnewline
34 & 39.67 & 39.6062540362041 & 0.0637459637959239 \tabularnewline
35 & 39.56 & 39.6996233588955 & -0.139623358895491 \tabularnewline
36 & 39.64 & 39.5291278644135 & 0.110872135586462 \tabularnewline
37 & 39.73 & 39.628773793349 & 0.101226206650971 \tabularnewline
38 & 39.7 & 39.6863309431038 & 0.0136690568962123 \tabularnewline
39 & 39.7 & 39.7013386603074 & -0.00133866030743945 \tabularnewline
40 & 39.68 & 39.6855045712004 & -0.00550457120038317 \tabularnewline
41 & 39.76 & 39.4755014634587 & 0.28449853654125 \tabularnewline
42 & 40 & 39.6673287508 & 0.332671249199983 \tabularnewline
43 & 39.96 & 39.8629332352358 & 0.0970667647641648 \tabularnewline
44 & 40.01 & 39.8984047033416 & 0.111595296658358 \tabularnewline
45 & 40.01 & 39.9959677072222 & 0.0140322927777490 \tabularnewline
46 & 40.01 & 39.956808962833 & 0.0531910371669895 \tabularnewline
47 & 40 & 40.0401723264799 & -0.040172326479933 \tabularnewline
48 & 39.91 & 39.9697329795343 & -0.0597329795343029 \tabularnewline
49 & 39.86 & 39.8992825891389 & -0.0392825891388995 \tabularnewline
50 & 39.79 & 39.8167604111831 & -0.0267604111831048 \tabularnewline
51 & 39.79 & 39.7917453029321 & -0.00174530293212172 \tabularnewline
52 & 39.8 & 39.7759109842449 & 0.0240890157550666 \tabularnewline
53 & 39.64 & 39.5959245842936 & 0.0440754157063665 \tabularnewline
54 & 39.55 & 39.5476161348247 & 0.00238386517528255 \tabularnewline
55 & 39.36 & 39.4130341473613 & -0.0530341473613234 \tabularnewline
56 & 39.28 & 39.2984208722904 & -0.0184208722903989 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112644&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]41.33[/C][C]41.6101522435898[/C][C]-0.280152243589754[/C][/ROW]
[ROW][C]14[/C][C]41.29[/C][C]41.2865186979343[/C][C]0.00348130206570829[/C][/ROW]
[ROW][C]15[/C][C]41.29[/C][C]41.2915206633893[/C][C]-0.00152066338934986[/C][/ROW]
[ROW][C]16[/C][C]41.27[/C][C]41.275686471528[/C][C]-0.00568647152795876[/C][/ROW]
[ROW][C]17[/C][C]41.04[/C][C]41.06568326109[/C][C]-0.0256832610900091[/C][/ROW]
[ROW][C]18[/C][C]40.9[/C][C]40.9473354276374[/C][C]-0.0473354276373854[/C][/ROW]
[ROW][C]19[/C][C]40.89[/C][C]40.7627253699194[/C][C]0.127274630080592[/C][/ROW]
[ROW][C]20[/C][C]40.72[/C][C]40.8282138926216[/C][C]-0.108213892621571[/C][/ROW]
[ROW][C]21[/C][C]40.72[/C][C]40.7056527977961[/C][C]0.0143472022038793[/C][/ROW]
[ROW][C]22[/C][C]40.58[/C][C]40.6664942311968[/C][C]-0.0864942311967667[/C][/ROW]
[ROW][C]23[/C][C]40.24[/C][C]40.6097787320759[/C][C]-0.369778732075865[/C][/ROW]
[ROW][C]24[/C][C]40.07[/C][C]40.2091532976942[/C][C]-0.139153297694222[/C][/ROW]
[ROW][C]25[/C][C]40.12[/C][C]40.0586580685969[/C][C]0.0613419314030992[/C][/ROW]
[ROW][C]26[/C][C]40.1[/C][C]40.0761927006991[/C][C]0.0238072993008842[/C][/ROW]
[ROW][C]27[/C][C]40.1[/C][C]40.1012061416979[/C][C]-0.00120614169787814[/C][/ROW]
[ROW][C]28[/C][C]40.08[/C][C]40.0853721274075[/C][C]-0.00537212740748316[/C][/ROW]
[ROW][C]29[/C][C]40.06[/C][C]39.8753690944403[/C][C]0.184630905559743[/C][/ROW]
[ROW][C]30[/C][C]39.99[/C][C]39.9671399990442[/C][C]0.0228600009558022[/C][/ROW]
[ROW][C]31[/C][C]40.05[/C][C]39.8525695718889[/C][C]0.197430428111069[/C][/ROW]
[ROW][C]32[/C][C]39.66[/C][C]39.9880977027794[/C][C]-0.328097702779388[/C][/ROW]
[ROW][C]33[/C][C]39.66[/C][C]39.6454124671188[/C][C]0.0145875328811869[/C][/ROW]
[ROW][C]34[/C][C]39.67[/C][C]39.6062540362041[/C][C]0.0637459637959239[/C][/ROW]
[ROW][C]35[/C][C]39.56[/C][C]39.6996233588955[/C][C]-0.139623358895491[/C][/ROW]
[ROW][C]36[/C][C]39.64[/C][C]39.5291278644135[/C][C]0.110872135586462[/C][/ROW]
[ROW][C]37[/C][C]39.73[/C][C]39.628773793349[/C][C]0.101226206650971[/C][/ROW]
[ROW][C]38[/C][C]39.7[/C][C]39.6863309431038[/C][C]0.0136690568962123[/C][/ROW]
[ROW][C]39[/C][C]39.7[/C][C]39.7013386603074[/C][C]-0.00133866030743945[/C][/ROW]
[ROW][C]40[/C][C]39.68[/C][C]39.6855045712004[/C][C]-0.00550457120038317[/C][/ROW]
[ROW][C]41[/C][C]39.76[/C][C]39.4755014634587[/C][C]0.28449853654125[/C][/ROW]
[ROW][C]42[/C][C]40[/C][C]39.6673287508[/C][C]0.332671249199983[/C][/ROW]
[ROW][C]43[/C][C]39.96[/C][C]39.8629332352358[/C][C]0.0970667647641648[/C][/ROW]
[ROW][C]44[/C][C]40.01[/C][C]39.8984047033416[/C][C]0.111595296658358[/C][/ROW]
[ROW][C]45[/C][C]40.01[/C][C]39.9959677072222[/C][C]0.0140322927777490[/C][/ROW]
[ROW][C]46[/C][C]40.01[/C][C]39.956808962833[/C][C]0.0531910371669895[/C][/ROW]
[ROW][C]47[/C][C]40[/C][C]40.0401723264799[/C][C]-0.040172326479933[/C][/ROW]
[ROW][C]48[/C][C]39.91[/C][C]39.9697329795343[/C][C]-0.0597329795343029[/C][/ROW]
[ROW][C]49[/C][C]39.86[/C][C]39.8992825891389[/C][C]-0.0392825891388995[/C][/ROW]
[ROW][C]50[/C][C]39.79[/C][C]39.8167604111831[/C][C]-0.0267604111831048[/C][/ROW]
[ROW][C]51[/C][C]39.79[/C][C]39.7917453029321[/C][C]-0.00174530293212172[/C][/ROW]
[ROW][C]52[/C][C]39.8[/C][C]39.7759109842449[/C][C]0.0240890157550666[/C][/ROW]
[ROW][C]53[/C][C]39.64[/C][C]39.5959245842936[/C][C]0.0440754157063665[/C][/ROW]
[ROW][C]54[/C][C]39.55[/C][C]39.5476161348247[/C][C]0.00238386517528255[/C][/ROW]
[ROW][C]55[/C][C]39.36[/C][C]39.4130341473613[/C][C]-0.0530341473613234[/C][/ROW]
[ROW][C]56[/C][C]39.28[/C][C]39.2984208722904[/C][C]-0.0184208722903989[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112644&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112644&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	41.33	41.6101522435898	-0.280152243589754
14	41.29	41.2865186979343	0.00348130206570829
15	41.29	41.2915206633893	-0.00152066338934986
16	41.27	41.275686471528	-0.00568647152795876
17	41.04	41.06568326109	-0.0256832610900091
18	40.9	40.9473354276374	-0.0473354276373854
19	40.89	40.7627253699194	0.127274630080592
20	40.72	40.8282138926216	-0.108213892621571
21	40.72	40.7056527977961	0.0143472022038793
22	40.58	40.6664942311968	-0.0864942311967667
23	40.24	40.6097787320759	-0.369778732075865
24	40.07	40.2091532976942	-0.139153297694222
25	40.12	40.0586580685969	0.0613419314030992
26	40.1	40.0761927006991	0.0238072993008842
27	40.1	40.1012061416979	-0.00120614169787814
28	40.08	40.0853721274075	-0.00537212740748316
29	40.06	39.8753690944403	0.184630905559743
30	39.99	39.9671399990442	0.0228600009558022
31	40.05	39.8525695718889	0.197430428111069
32	39.66	39.9880977027794	-0.328097702779388
33	39.66	39.6454124671188	0.0145875328811869
34	39.67	39.6062540362041	0.0637459637959239
35	39.56	39.6996233588955	-0.139623358895491
36	39.64	39.5291278644135	0.110872135586462
37	39.73	39.628773793349	0.101226206650971
38	39.7	39.6863309431038	0.0136690568962123
39	39.7	39.7013386603074	-0.00133866030743945
40	39.68	39.6855045712004	-0.00550457120038317
41	39.76	39.4755014634587	0.28449853654125
42	40	39.6673287508	0.332671249199983
43	39.96	39.8629332352358	0.0970667647641648
44	40.01	39.8984047033416	0.111595296658358
45	40.01	39.9959677072222	0.0140322927777490
46	40.01	39.956808962833	0.0531910371669895
47	40	40.0401723264799	-0.040172326479933
48	39.91	39.9697329795343	-0.0597329795343029
49	39.86	39.8992825891389	-0.0392825891388995
50	39.79	39.8167604111831	-0.0267604111831048
51	39.79	39.7917453029321	-0.00174530293212172
52	39.8	39.7759109842449	0.0240890157550666
53	39.64	39.5959245842936	0.0440754157063665
54	39.55	39.5476161348247	0.00238386517528255
55	39.36	39.4130341473613	-0.0530341473613234
56	39.28	39.2984208722904	-0.0184208722903989

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
57	39.2659104723320	39.0097388057074	39.5220821389567
58	39.2126542779974	38.8502705508625	39.5750380051323
59	39.2427314169961	38.7987785247121	39.6866843092801
60	39.2123918893282	38.6996145699768	39.7251692086796
61	39.2016356949936	38.6281714558744	39.7750999341127
62	39.1583795006589	38.5300036773465	39.7867553239714
63	39.1601233063243	38.4812084026721	39.8390382099765
64	39.1460337786564	38.4200385385787	39.8720290187341
65	38.9419442509884	38.1716928999339	39.712195602043
66	38.8495213899871	38.0373762959348	39.6616664840395
67	38.7125151956525	37.8604901605592	39.5645402307458
68	38.6509256679846	37.760763769489	39.5410875664801

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
57 & 39.2659104723320 & 39.0097388057074 & 39.5220821389567 \tabularnewline
58 & 39.2126542779974 & 38.8502705508625 & 39.5750380051323 \tabularnewline
59 & 39.2427314169961 & 38.7987785247121 & 39.6866843092801 \tabularnewline
60 & 39.2123918893282 & 38.6996145699768 & 39.7251692086796 \tabularnewline
61 & 39.2016356949936 & 38.6281714558744 & 39.7750999341127 \tabularnewline
62 & 39.1583795006589 & 38.5300036773465 & 39.7867553239714 \tabularnewline
63 & 39.1601233063243 & 38.4812084026721 & 39.8390382099765 \tabularnewline
64 & 39.1460337786564 & 38.4200385385787 & 39.8720290187341 \tabularnewline
65 & 38.9419442509884 & 38.1716928999339 & 39.712195602043 \tabularnewline
66 & 38.8495213899871 & 38.0373762959348 & 39.6616664840395 \tabularnewline
67 & 38.7125151956525 & 37.8604901605592 & 39.5645402307458 \tabularnewline
68 & 38.6509256679846 & 37.760763769489 & 39.5410875664801 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112644&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]57[/C][C]39.2659104723320[/C][C]39.0097388057074[/C][C]39.5220821389567[/C][/ROW]
[ROW][C]58[/C][C]39.2126542779974[/C][C]38.8502705508625[/C][C]39.5750380051323[/C][/ROW]
[ROW][C]59[/C][C]39.2427314169961[/C][C]38.7987785247121[/C][C]39.6866843092801[/C][/ROW]
[ROW][C]60[/C][C]39.2123918893282[/C][C]38.6996145699768[/C][C]39.7251692086796[/C][/ROW]
[ROW][C]61[/C][C]39.2016356949936[/C][C]38.6281714558744[/C][C]39.7750999341127[/C][/ROW]
[ROW][C]62[/C][C]39.1583795006589[/C][C]38.5300036773465[/C][C]39.7867553239714[/C][/ROW]
[ROW][C]63[/C][C]39.1601233063243[/C][C]38.4812084026721[/C][C]39.8390382099765[/C][/ROW]
[ROW][C]64[/C][C]39.1460337786564[/C][C]38.4200385385787[/C][C]39.8720290187341[/C][/ROW]
[ROW][C]65[/C][C]38.9419442509884[/C][C]38.1716928999339[/C][C]39.712195602043[/C][/ROW]
[ROW][C]66[/C][C]38.8495213899871[/C][C]38.0373762959348[/C][C]39.6616664840395[/C][/ROW]
[ROW][C]67[/C][C]38.7125151956525[/C][C]37.8604901605592[/C][C]39.5645402307458[/C][/ROW]
[ROW][C]68[/C][C]38.6509256679846[/C][C]37.760763769489[/C][C]39.5410875664801[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112644&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112644&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
57	39.2659104723320	39.0097388057074	39.5220821389567
58	39.2126542779974	38.8502705508625	39.5750380051323
59	39.2427314169961	38.7987785247121	39.6866843092801
60	39.2123918893282	38.6996145699768	39.7251692086796
61	39.2016356949936	38.6281714558744	39.7750999341127
62	39.1583795006589	38.5300036773465	39.7867553239714
63	39.1601233063243	38.4812084026721	39.8390382099765
64	39.1460337786564	38.4200385385787	39.8720290187341
65	38.9419442509884	38.1716928999339	39.712195602043
66	38.8495213899871	38.0373762959348	39.6616664840395
67	38.7125151956525	37.8604901605592	39.5645402307458
68	38.6509256679846	37.760763769489	39.5410875664801

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