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

Mon, 13 Dec 2010 14:25:18 +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/13/t1292250232rjek651fq4mkmev.htm/, Retrieved Mon, 06 May 2024 12:54:55 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=108946, Retrieved Mon, 06 May 2024 12:54:55 +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

177

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

-     [Exponential Smoothing] [HPC Retail Sales] [2008-03-10 17:56:43] [74be16979710d4c4e7c6647856088456]
-  M D  [Exponential Smoothing] [Exponential Smoot...] [2010-12-08 17:32:26] [6a528ed37664d761abf4790b0717b23b]
- R PD      [Exponential Smoothing] [Paper ES] [2010-12-13 14:25:18] [fd751bc40fbbb4c72222c10190589d42] [Current]

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

2
1
-8
-1
1
-1
2
2
1
-1
-2
-2
-1
-8
-4
-6
-3
-3
-7
-9
-11
-13
-11
-9
-17
-22
-25
-20
-24
-24
-22
-19
-18
-17
-11
-11
-12
-10
-15
-15
-15
-13
-8
-13
-9
-7
-4
-4
-2
0

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	'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108946&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108946&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108946&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	'George Udny Yule' @ 72.249.76.132

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.842236341974113
beta	FALSE
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.842236341974113 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108946&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]0.842236341974113[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108946&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108946&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	0.842236341974113
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	1	2	-1
3	-8	1.15776365802589	-9.15776365802589
4	-1	-6.5552377059733	5.5552377059733
5	1	-1.87641462169769	2.87641462169769
6	-1	0.546206307281824	-1.54620630728182
7	2	-0.75606483690052	2.75606483690052
8	2	1.56519312957405	0.434806870425947
9	1	1.93140327758681	-0.931403277586815
10	-1	1.14694158816940	-2.14694158816940
11	-2	-0.661290641482488	-1.33870935851751
12	-2	-1.78880031456679	-0.211199685433212
13	-1	-1.96668036505214	0.96668036505214
14	-8	-1.15250703053243	-6.84749296946757
15	-4	-6.91971446083025	2.91971446083025
16	-6	-4.46062483373166	-1.53937516626834
17	-3	-5.7571425426953	2.7571425426953
18	-3	-3.43497689323441	0.434976893234406
19	-7	-3.06862354583340	-3.9313764541666
20	-9	-6.37977166951383	-2.62022833048617
21	-11	-8.58662319371944	-2.41337680628056
22	-13	-10.6192568468463	-2.38074315315366
23	-11	-12.6244052513384	1.62440525133839
24	-9	-11.2562721145676	2.25627211456760
25	-17	-9.35595774229599	-7.64404225770401
26	-22	-15.7940479313202	-6.20595206867985
27	-25	-21.0209263001117	-3.97907369988826
28	-20	-24.372246777551	4.37224677755103
29	-24	-20.6897816454183	-3.31021835458165
30	-24	-23.4777678435168	-0.522232156483238
31	-22	-23.9176107446545	1.91761074465446
32	-19	-22.3025292857464	3.30252928574643
33	-18	-19.5210191008570	1.52101910085698
34	-17	-18.2399615372784	1.23996153727844
35	-11	-17.1956208679325	6.19562086793245
36	-11	-11.9774438118665	0.977443811866546
37	-12	-11.1542051112748	-0.845794888725166
38	-10	-11.8665643044151	1.86656430441512
39	-15	-10.2944760126051	-4.70552398739493
40	-15	-14.2576393228200	-0.742360677179983
41	-15	-14.8828824639935	-0.117117536006489
42	-13	-14.9815231091006	1.98152310910064
43	-8	-13.3126123341545	5.31261233415455
44	-13	-8.83813715550967	-4.16186284449033
45	-9	-12.3434092934512	3.34340929345118
46	-7	-9.5274684804126	2.52746848041261
47	-4	-7.39874267301502	3.39874267301502
48	-4	-4.53619807678353	0.536198076783532
49	-2	-4.08459257001982	2.08459257001982
50	0	-2.32887294933991	2.32887294933991

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 1 & 2 & -1 \tabularnewline
3 & -8 & 1.15776365802589 & -9.15776365802589 \tabularnewline
4 & -1 & -6.5552377059733 & 5.5552377059733 \tabularnewline
5 & 1 & -1.87641462169769 & 2.87641462169769 \tabularnewline
6 & -1 & 0.546206307281824 & -1.54620630728182 \tabularnewline
7 & 2 & -0.75606483690052 & 2.75606483690052 \tabularnewline
8 & 2 & 1.56519312957405 & 0.434806870425947 \tabularnewline
9 & 1 & 1.93140327758681 & -0.931403277586815 \tabularnewline
10 & -1 & 1.14694158816940 & -2.14694158816940 \tabularnewline
11 & -2 & -0.661290641482488 & -1.33870935851751 \tabularnewline
12 & -2 & -1.78880031456679 & -0.211199685433212 \tabularnewline
13 & -1 & -1.96668036505214 & 0.96668036505214 \tabularnewline
14 & -8 & -1.15250703053243 & -6.84749296946757 \tabularnewline
15 & -4 & -6.91971446083025 & 2.91971446083025 \tabularnewline
16 & -6 & -4.46062483373166 & -1.53937516626834 \tabularnewline
17 & -3 & -5.7571425426953 & 2.7571425426953 \tabularnewline
18 & -3 & -3.43497689323441 & 0.434976893234406 \tabularnewline
19 & -7 & -3.06862354583340 & -3.9313764541666 \tabularnewline
20 & -9 & -6.37977166951383 & -2.62022833048617 \tabularnewline
21 & -11 & -8.58662319371944 & -2.41337680628056 \tabularnewline
22 & -13 & -10.6192568468463 & -2.38074315315366 \tabularnewline
23 & -11 & -12.6244052513384 & 1.62440525133839 \tabularnewline
24 & -9 & -11.2562721145676 & 2.25627211456760 \tabularnewline
25 & -17 & -9.35595774229599 & -7.64404225770401 \tabularnewline
26 & -22 & -15.7940479313202 & -6.20595206867985 \tabularnewline
27 & -25 & -21.0209263001117 & -3.97907369988826 \tabularnewline
28 & -20 & -24.372246777551 & 4.37224677755103 \tabularnewline
29 & -24 & -20.6897816454183 & -3.31021835458165 \tabularnewline
30 & -24 & -23.4777678435168 & -0.522232156483238 \tabularnewline
31 & -22 & -23.9176107446545 & 1.91761074465446 \tabularnewline
32 & -19 & -22.3025292857464 & 3.30252928574643 \tabularnewline
33 & -18 & -19.5210191008570 & 1.52101910085698 \tabularnewline
34 & -17 & -18.2399615372784 & 1.23996153727844 \tabularnewline
35 & -11 & -17.1956208679325 & 6.19562086793245 \tabularnewline
36 & -11 & -11.9774438118665 & 0.977443811866546 \tabularnewline
37 & -12 & -11.1542051112748 & -0.845794888725166 \tabularnewline
38 & -10 & -11.8665643044151 & 1.86656430441512 \tabularnewline
39 & -15 & -10.2944760126051 & -4.70552398739493 \tabularnewline
40 & -15 & -14.2576393228200 & -0.742360677179983 \tabularnewline
41 & -15 & -14.8828824639935 & -0.117117536006489 \tabularnewline
42 & -13 & -14.9815231091006 & 1.98152310910064 \tabularnewline
43 & -8 & -13.3126123341545 & 5.31261233415455 \tabularnewline
44 & -13 & -8.83813715550967 & -4.16186284449033 \tabularnewline
45 & -9 & -12.3434092934512 & 3.34340929345118 \tabularnewline
46 & -7 & -9.5274684804126 & 2.52746848041261 \tabularnewline
47 & -4 & -7.39874267301502 & 3.39874267301502 \tabularnewline
48 & -4 & -4.53619807678353 & 0.536198076783532 \tabularnewline
49 & -2 & -4.08459257001982 & 2.08459257001982 \tabularnewline
50 & 0 & -2.32887294933991 & 2.32887294933991 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108946&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]2[/C][C]1[/C][C]2[/C][C]-1[/C][/ROW]
[ROW][C]3[/C][C]-8[/C][C]1.15776365802589[/C][C]-9.15776365802589[/C][/ROW]
[ROW][C]4[/C][C]-1[/C][C]-6.5552377059733[/C][C]5.5552377059733[/C][/ROW]
[ROW][C]5[/C][C]1[/C][C]-1.87641462169769[/C][C]2.87641462169769[/C][/ROW]
[ROW][C]6[/C][C]-1[/C][C]0.546206307281824[/C][C]-1.54620630728182[/C][/ROW]
[ROW][C]7[/C][C]2[/C][C]-0.75606483690052[/C][C]2.75606483690052[/C][/ROW]
[ROW][C]8[/C][C]2[/C][C]1.56519312957405[/C][C]0.434806870425947[/C][/ROW]
[ROW][C]9[/C][C]1[/C][C]1.93140327758681[/C][C]-0.931403277586815[/C][/ROW]
[ROW][C]10[/C][C]-1[/C][C]1.14694158816940[/C][C]-2.14694158816940[/C][/ROW]
[ROW][C]11[/C][C]-2[/C][C]-0.661290641482488[/C][C]-1.33870935851751[/C][/ROW]
[ROW][C]12[/C][C]-2[/C][C]-1.78880031456679[/C][C]-0.211199685433212[/C][/ROW]
[ROW][C]13[/C][C]-1[/C][C]-1.96668036505214[/C][C]0.96668036505214[/C][/ROW]
[ROW][C]14[/C][C]-8[/C][C]-1.15250703053243[/C][C]-6.84749296946757[/C][/ROW]
[ROW][C]15[/C][C]-4[/C][C]-6.91971446083025[/C][C]2.91971446083025[/C][/ROW]
[ROW][C]16[/C][C]-6[/C][C]-4.46062483373166[/C][C]-1.53937516626834[/C][/ROW]
[ROW][C]17[/C][C]-3[/C][C]-5.7571425426953[/C][C]2.7571425426953[/C][/ROW]
[ROW][C]18[/C][C]-3[/C][C]-3.43497689323441[/C][C]0.434976893234406[/C][/ROW]
[ROW][C]19[/C][C]-7[/C][C]-3.06862354583340[/C][C]-3.9313764541666[/C][/ROW]
[ROW][C]20[/C][C]-9[/C][C]-6.37977166951383[/C][C]-2.62022833048617[/C][/ROW]
[ROW][C]21[/C][C]-11[/C][C]-8.58662319371944[/C][C]-2.41337680628056[/C][/ROW]
[ROW][C]22[/C][C]-13[/C][C]-10.6192568468463[/C][C]-2.38074315315366[/C][/ROW]
[ROW][C]23[/C][C]-11[/C][C]-12.6244052513384[/C][C]1.62440525133839[/C][/ROW]
[ROW][C]24[/C][C]-9[/C][C]-11.2562721145676[/C][C]2.25627211456760[/C][/ROW]
[ROW][C]25[/C][C]-17[/C][C]-9.35595774229599[/C][C]-7.64404225770401[/C][/ROW]
[ROW][C]26[/C][C]-22[/C][C]-15.7940479313202[/C][C]-6.20595206867985[/C][/ROW]
[ROW][C]27[/C][C]-25[/C][C]-21.0209263001117[/C][C]-3.97907369988826[/C][/ROW]
[ROW][C]28[/C][C]-20[/C][C]-24.372246777551[/C][C]4.37224677755103[/C][/ROW]
[ROW][C]29[/C][C]-24[/C][C]-20.6897816454183[/C][C]-3.31021835458165[/C][/ROW]
[ROW][C]30[/C][C]-24[/C][C]-23.4777678435168[/C][C]-0.522232156483238[/C][/ROW]
[ROW][C]31[/C][C]-22[/C][C]-23.9176107446545[/C][C]1.91761074465446[/C][/ROW]
[ROW][C]32[/C][C]-19[/C][C]-22.3025292857464[/C][C]3.30252928574643[/C][/ROW]
[ROW][C]33[/C][C]-18[/C][C]-19.5210191008570[/C][C]1.52101910085698[/C][/ROW]
[ROW][C]34[/C][C]-17[/C][C]-18.2399615372784[/C][C]1.23996153727844[/C][/ROW]
[ROW][C]35[/C][C]-11[/C][C]-17.1956208679325[/C][C]6.19562086793245[/C][/ROW]
[ROW][C]36[/C][C]-11[/C][C]-11.9774438118665[/C][C]0.977443811866546[/C][/ROW]
[ROW][C]37[/C][C]-12[/C][C]-11.1542051112748[/C][C]-0.845794888725166[/C][/ROW]
[ROW][C]38[/C][C]-10[/C][C]-11.8665643044151[/C][C]1.86656430441512[/C][/ROW]
[ROW][C]39[/C][C]-15[/C][C]-10.2944760126051[/C][C]-4.70552398739493[/C][/ROW]
[ROW][C]40[/C][C]-15[/C][C]-14.2576393228200[/C][C]-0.742360677179983[/C][/ROW]
[ROW][C]41[/C][C]-15[/C][C]-14.8828824639935[/C][C]-0.117117536006489[/C][/ROW]
[ROW][C]42[/C][C]-13[/C][C]-14.9815231091006[/C][C]1.98152310910064[/C][/ROW]
[ROW][C]43[/C][C]-8[/C][C]-13.3126123341545[/C][C]5.31261233415455[/C][/ROW]
[ROW][C]44[/C][C]-13[/C][C]-8.83813715550967[/C][C]-4.16186284449033[/C][/ROW]
[ROW][C]45[/C][C]-9[/C][C]-12.3434092934512[/C][C]3.34340929345118[/C][/ROW]
[ROW][C]46[/C][C]-7[/C][C]-9.5274684804126[/C][C]2.52746848041261[/C][/ROW]
[ROW][C]47[/C][C]-4[/C][C]-7.39874267301502[/C][C]3.39874267301502[/C][/ROW]
[ROW][C]48[/C][C]-4[/C][C]-4.53619807678353[/C][C]0.536198076783532[/C][/ROW]
[ROW][C]49[/C][C]-2[/C][C]-4.08459257001982[/C][C]2.08459257001982[/C][/ROW]
[ROW][C]50[/C][C]0[/C][C]-2.32887294933991[/C][C]2.32887294933991[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108946&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108946&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
2	1	2	-1
3	-8	1.15776365802589	-9.15776365802589
4	-1	-6.5552377059733	5.5552377059733
5	1	-1.87641462169769	2.87641462169769
6	-1	0.546206307281824	-1.54620630728182
7	2	-0.75606483690052	2.75606483690052
8	2	1.56519312957405	0.434806870425947
9	1	1.93140327758681	-0.931403277586815
10	-1	1.14694158816940	-2.14694158816940
11	-2	-0.661290641482488	-1.33870935851751
12	-2	-1.78880031456679	-0.211199685433212
13	-1	-1.96668036505214	0.96668036505214
14	-8	-1.15250703053243	-6.84749296946757
15	-4	-6.91971446083025	2.91971446083025
16	-6	-4.46062483373166	-1.53937516626834
17	-3	-5.7571425426953	2.7571425426953
18	-3	-3.43497689323441	0.434976893234406
19	-7	-3.06862354583340	-3.9313764541666
20	-9	-6.37977166951383	-2.62022833048617
21	-11	-8.58662319371944	-2.41337680628056
22	-13	-10.6192568468463	-2.38074315315366
23	-11	-12.6244052513384	1.62440525133839
24	-9	-11.2562721145676	2.25627211456760
25	-17	-9.35595774229599	-7.64404225770401
26	-22	-15.7940479313202	-6.20595206867985
27	-25	-21.0209263001117	-3.97907369988826
28	-20	-24.372246777551	4.37224677755103
29	-24	-20.6897816454183	-3.31021835458165
30	-24	-23.4777678435168	-0.522232156483238
31	-22	-23.9176107446545	1.91761074465446
32	-19	-22.3025292857464	3.30252928574643
33	-18	-19.5210191008570	1.52101910085698
34	-17	-18.2399615372784	1.23996153727844
35	-11	-17.1956208679325	6.19562086793245
36	-11	-11.9774438118665	0.977443811866546
37	-12	-11.1542051112748	-0.845794888725166
38	-10	-11.8665643044151	1.86656430441512
39	-15	-10.2944760126051	-4.70552398739493
40	-15	-14.2576393228200	-0.742360677179983
41	-15	-14.8828824639935	-0.117117536006489
42	-13	-14.9815231091006	1.98152310910064
43	-8	-13.3126123341545	5.31261233415455
44	-13	-8.83813715550967	-4.16186284449033
45	-9	-12.3434092934512	3.34340929345118
46	-7	-9.5274684804126	2.52746848041261
47	-4	-7.39874267301502	3.39874267301502
48	-4	-4.53619807678353	0.536198076783532
49	-2	-4.08459257001982	2.08459257001982
50	0	-2.32887294933991	2.32887294933991

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
51	-0.367411515565401	-7.09673005461784	6.36190702348704
52	-0.367411515565401	-9.1654957607746	8.43067272964379
53	-0.367411515565401	-10.8330144495373	10.0981914184065
54	-0.367411515565401	-12.2691510168873	11.5343279857565
55	-0.367411515565401	-13.5497467238314	12.8149236927006
56	-0.367411515565401	-14.7165062580518	13.9816832269210
57	-0.367411515565401	-15.7952784554445	15.0604554243137
58	-0.367411515565401	-16.8033975431933	16.0685745120625
59	-0.367411515565401	-17.7531584102531	17.0183353791223
60	-0.367411515565401	-18.6536564409705	17.9188334098397
61	-0.367411515565401	-19.5118444363303	18.7770214051995
62	-0.367411515565401	-20.3331789749803	19.5983559438495

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
51 & -0.367411515565401 & -7.09673005461784 & 6.36190702348704 \tabularnewline
52 & -0.367411515565401 & -9.1654957607746 & 8.43067272964379 \tabularnewline
53 & -0.367411515565401 & -10.8330144495373 & 10.0981914184065 \tabularnewline
54 & -0.367411515565401 & -12.2691510168873 & 11.5343279857565 \tabularnewline
55 & -0.367411515565401 & -13.5497467238314 & 12.8149236927006 \tabularnewline
56 & -0.367411515565401 & -14.7165062580518 & 13.9816832269210 \tabularnewline
57 & -0.367411515565401 & -15.7952784554445 & 15.0604554243137 \tabularnewline
58 & -0.367411515565401 & -16.8033975431933 & 16.0685745120625 \tabularnewline
59 & -0.367411515565401 & -17.7531584102531 & 17.0183353791223 \tabularnewline
60 & -0.367411515565401 & -18.6536564409705 & 17.9188334098397 \tabularnewline
61 & -0.367411515565401 & -19.5118444363303 & 18.7770214051995 \tabularnewline
62 & -0.367411515565401 & -20.3331789749803 & 19.5983559438495 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108946&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]51[/C][C]-0.367411515565401[/C][C]-7.09673005461784[/C][C]6.36190702348704[/C][/ROW]
[ROW][C]52[/C][C]-0.367411515565401[/C][C]-9.1654957607746[/C][C]8.43067272964379[/C][/ROW]
[ROW][C]53[/C][C]-0.367411515565401[/C][C]-10.8330144495373[/C][C]10.0981914184065[/C][/ROW]
[ROW][C]54[/C][C]-0.367411515565401[/C][C]-12.2691510168873[/C][C]11.5343279857565[/C][/ROW]
[ROW][C]55[/C][C]-0.367411515565401[/C][C]-13.5497467238314[/C][C]12.8149236927006[/C][/ROW]
[ROW][C]56[/C][C]-0.367411515565401[/C][C]-14.7165062580518[/C][C]13.9816832269210[/C][/ROW]
[ROW][C]57[/C][C]-0.367411515565401[/C][C]-15.7952784554445[/C][C]15.0604554243137[/C][/ROW]
[ROW][C]58[/C][C]-0.367411515565401[/C][C]-16.8033975431933[/C][C]16.0685745120625[/C][/ROW]
[ROW][C]59[/C][C]-0.367411515565401[/C][C]-17.7531584102531[/C][C]17.0183353791223[/C][/ROW]
[ROW][C]60[/C][C]-0.367411515565401[/C][C]-18.6536564409705[/C][C]17.9188334098397[/C][/ROW]
[ROW][C]61[/C][C]-0.367411515565401[/C][C]-19.5118444363303[/C][C]18.7770214051995[/C][/ROW]
[ROW][C]62[/C][C]-0.367411515565401[/C][C]-20.3331789749803[/C][C]19.5983559438495[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108946&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108946&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
51	-0.367411515565401	-7.09673005461784	6.36190702348704
52	-0.367411515565401	-9.1654957607746	8.43067272964379
53	-0.367411515565401	-10.8330144495373	10.0981914184065
54	-0.367411515565401	-12.2691510168873	11.5343279857565
55	-0.367411515565401	-13.5497467238314	12.8149236927006
56	-0.367411515565401	-14.7165062580518	13.9816832269210
57	-0.367411515565401	-15.7952784554445	15.0604554243137
58	-0.367411515565401	-16.8033975431933	16.0685745120625
59	-0.367411515565401	-17.7531584102531	17.0183353791223
60	-0.367411515565401	-18.6536564409705	17.9188334098397
61	-0.367411515565401	-19.5118444363303	18.7770214051995
62	-0.367411515565401	-20.3331789749803	19.5983559438495

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 = Single ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Single ; 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