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*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Mon, 23 May 2016 21:24:57 +0100

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/May/23/t1464035186a45sfy2kevefbea.htm/, Retrieved Wed, 08 May 2024 02:34:00 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=295532, Retrieved Wed, 08 May 2024 02:34:00 +0000

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single gaf slechte voorspelling.

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No (this computation is public)

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Estimated Impact

133

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

-       [Exponential Smoothing] [Opgave 10 oef 2 D...] [2016-05-23 20:24:57] [8fd6d867e46a5221be3e0a22eb2f8c7a] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'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 & 1 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295532&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295532&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295532&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Sir Maurice George Kendall' @ kendall.wessa.net

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

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295532&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[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295532&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295532&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
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	96.61	92.59	4.02
4	99.69	96.2	3.48999999999999
5	101.05	99.28	1.77
6	98	100.64	-2.64
7	97.32	97.59	-0.27000000000001
8	97.83	96.91	0.920000000000002
9	99.57	97.42	2.14999999999999
10	97.63	99.16	-1.53
11	96.68	97.22	-0.539999999999992
12	96.28	96.27	0.00999999999999091
13	99.81	95.87	3.94
14	101.43	99.4	2.03
15	105.59	101.02	4.56999999999999
16	108.86	105.18	3.67999999999999
17	104.01	108.45	-4.44
18	101.95	103.6	-1.65000000000001
19	101.52	101.54	-0.0200000000000102
20	105.61	101.11	4.5
21	108.43	105.2	3.23
22	105.54	108.02	-2.48
23	100.11	105.13	-5.02000000000001
24	99.93	99.7	0.230000000000004
25	99.88	99.52	0.359999999999985
26	102.71	99.47	3.23999999999999
27	101.89	102.3	-0.409999999999997
28	101.93	101.48	0.450000000000003
29	99.49	101.52	-2.03000000000002
30	99.87	99.08	0.790000000000006
31	100.33	99.46	0.86999999999999
32	101.5	99.92	1.58
33	102.29	101.09	1.2
34	97.04	101.88	-4.84
35	95.71	96.63	-0.920000000000016
36	97.37	95.3	2.07000000000001
37	96.51	96.96	-0.450000000000003
38	96.33	96.1	0.22999999999999
39	96.88	95.92	0.959999999999994
40	97.59	96.47	1.12
41	98.96	97.18	1.77999999999999
42	99.93	98.55	1.38000000000001
43	101.34	99.52	1.81999999999999
44	98.04	100.93	-2.89
45	98.56	97.63	0.929999999999993
46	96.73	98.15	-1.42
47	92.36	96.32	-3.96000000000001
48	87.88	91.95	-4.07000000000001
49	79.84	87.47	-7.63
50	82.91	79.43	3.47999999999999
51	87.78	82.5	5.28
52	89.36	87.37	1.98999999999999
53	91.86	88.95	2.91
54	92.48	91.45	1.03
55	93.4	92.07	1.33
56	89.97	92.99	-3.02000000000001
57	83.96	89.56	-5.60000000000001
58	82.76	83.55	-0.789999999999992
59	82.97	82.35	0.61999999999999
60	81.07	82.56	-1.49000000000001

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 96.61 & 92.59 & 4.02 \tabularnewline
4 & 99.69 & 96.2 & 3.48999999999999 \tabularnewline
5 & 101.05 & 99.28 & 1.77 \tabularnewline
6 & 98 & 100.64 & -2.64 \tabularnewline
7 & 97.32 & 97.59 & -0.27000000000001 \tabularnewline
8 & 97.83 & 96.91 & 0.920000000000002 \tabularnewline
9 & 99.57 & 97.42 & 2.14999999999999 \tabularnewline
10 & 97.63 & 99.16 & -1.53 \tabularnewline
11 & 96.68 & 97.22 & -0.539999999999992 \tabularnewline
12 & 96.28 & 96.27 & 0.00999999999999091 \tabularnewline
13 & 99.81 & 95.87 & 3.94 \tabularnewline
14 & 101.43 & 99.4 & 2.03 \tabularnewline
15 & 105.59 & 101.02 & 4.56999999999999 \tabularnewline
16 & 108.86 & 105.18 & 3.67999999999999 \tabularnewline
17 & 104.01 & 108.45 & -4.44 \tabularnewline
18 & 101.95 & 103.6 & -1.65000000000001 \tabularnewline
19 & 101.52 & 101.54 & -0.0200000000000102 \tabularnewline
20 & 105.61 & 101.11 & 4.5 \tabularnewline
21 & 108.43 & 105.2 & 3.23 \tabularnewline
22 & 105.54 & 108.02 & -2.48 \tabularnewline
23 & 100.11 & 105.13 & -5.02000000000001 \tabularnewline
24 & 99.93 & 99.7 & 0.230000000000004 \tabularnewline
25 & 99.88 & 99.52 & 0.359999999999985 \tabularnewline
26 & 102.71 & 99.47 & 3.23999999999999 \tabularnewline
27 & 101.89 & 102.3 & -0.409999999999997 \tabularnewline
28 & 101.93 & 101.48 & 0.450000000000003 \tabularnewline
29 & 99.49 & 101.52 & -2.03000000000002 \tabularnewline
30 & 99.87 & 99.08 & 0.790000000000006 \tabularnewline
31 & 100.33 & 99.46 & 0.86999999999999 \tabularnewline
32 & 101.5 & 99.92 & 1.58 \tabularnewline
33 & 102.29 & 101.09 & 1.2 \tabularnewline
34 & 97.04 & 101.88 & -4.84 \tabularnewline
35 & 95.71 & 96.63 & -0.920000000000016 \tabularnewline
36 & 97.37 & 95.3 & 2.07000000000001 \tabularnewline
37 & 96.51 & 96.96 & -0.450000000000003 \tabularnewline
38 & 96.33 & 96.1 & 0.22999999999999 \tabularnewline
39 & 96.88 & 95.92 & 0.959999999999994 \tabularnewline
40 & 97.59 & 96.47 & 1.12 \tabularnewline
41 & 98.96 & 97.18 & 1.77999999999999 \tabularnewline
42 & 99.93 & 98.55 & 1.38000000000001 \tabularnewline
43 & 101.34 & 99.52 & 1.81999999999999 \tabularnewline
44 & 98.04 & 100.93 & -2.89 \tabularnewline
45 & 98.56 & 97.63 & 0.929999999999993 \tabularnewline
46 & 96.73 & 98.15 & -1.42 \tabularnewline
47 & 92.36 & 96.32 & -3.96000000000001 \tabularnewline
48 & 87.88 & 91.95 & -4.07000000000001 \tabularnewline
49 & 79.84 & 87.47 & -7.63 \tabularnewline
50 & 82.91 & 79.43 & 3.47999999999999 \tabularnewline
51 & 87.78 & 82.5 & 5.28 \tabularnewline
52 & 89.36 & 87.37 & 1.98999999999999 \tabularnewline
53 & 91.86 & 88.95 & 2.91 \tabularnewline
54 & 92.48 & 91.45 & 1.03 \tabularnewline
55 & 93.4 & 92.07 & 1.33 \tabularnewline
56 & 89.97 & 92.99 & -3.02000000000001 \tabularnewline
57 & 83.96 & 89.56 & -5.60000000000001 \tabularnewline
58 & 82.76 & 83.55 & -0.789999999999992 \tabularnewline
59 & 82.97 & 82.35 & 0.61999999999999 \tabularnewline
60 & 81.07 & 82.56 & -1.49000000000001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295532&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]3[/C][C]96.61[/C][C]92.59[/C][C]4.02[/C][/ROW]
[ROW][C]4[/C][C]99.69[/C][C]96.2[/C][C]3.48999999999999[/C][/ROW]
[ROW][C]5[/C][C]101.05[/C][C]99.28[/C][C]1.77[/C][/ROW]
[ROW][C]6[/C][C]98[/C][C]100.64[/C][C]-2.64[/C][/ROW]
[ROW][C]7[/C][C]97.32[/C][C]97.59[/C][C]-0.27000000000001[/C][/ROW]
[ROW][C]8[/C][C]97.83[/C][C]96.91[/C][C]0.920000000000002[/C][/ROW]
[ROW][C]9[/C][C]99.57[/C][C]97.42[/C][C]2.14999999999999[/C][/ROW]
[ROW][C]10[/C][C]97.63[/C][C]99.16[/C][C]-1.53[/C][/ROW]
[ROW][C]11[/C][C]96.68[/C][C]97.22[/C][C]-0.539999999999992[/C][/ROW]
[ROW][C]12[/C][C]96.28[/C][C]96.27[/C][C]0.00999999999999091[/C][/ROW]
[ROW][C]13[/C][C]99.81[/C][C]95.87[/C][C]3.94[/C][/ROW]
[ROW][C]14[/C][C]101.43[/C][C]99.4[/C][C]2.03[/C][/ROW]
[ROW][C]15[/C][C]105.59[/C][C]101.02[/C][C]4.56999999999999[/C][/ROW]
[ROW][C]16[/C][C]108.86[/C][C]105.18[/C][C]3.67999999999999[/C][/ROW]
[ROW][C]17[/C][C]104.01[/C][C]108.45[/C][C]-4.44[/C][/ROW]
[ROW][C]18[/C][C]101.95[/C][C]103.6[/C][C]-1.65000000000001[/C][/ROW]
[ROW][C]19[/C][C]101.52[/C][C]101.54[/C][C]-0.0200000000000102[/C][/ROW]
[ROW][C]20[/C][C]105.61[/C][C]101.11[/C][C]4.5[/C][/ROW]
[ROW][C]21[/C][C]108.43[/C][C]105.2[/C][C]3.23[/C][/ROW]
[ROW][C]22[/C][C]105.54[/C][C]108.02[/C][C]-2.48[/C][/ROW]
[ROW][C]23[/C][C]100.11[/C][C]105.13[/C][C]-5.02000000000001[/C][/ROW]
[ROW][C]24[/C][C]99.93[/C][C]99.7[/C][C]0.230000000000004[/C][/ROW]
[ROW][C]25[/C][C]99.88[/C][C]99.52[/C][C]0.359999999999985[/C][/ROW]
[ROW][C]26[/C][C]102.71[/C][C]99.47[/C][C]3.23999999999999[/C][/ROW]
[ROW][C]27[/C][C]101.89[/C][C]102.3[/C][C]-0.409999999999997[/C][/ROW]
[ROW][C]28[/C][C]101.93[/C][C]101.48[/C][C]0.450000000000003[/C][/ROW]
[ROW][C]29[/C][C]99.49[/C][C]101.52[/C][C]-2.03000000000002[/C][/ROW]
[ROW][C]30[/C][C]99.87[/C][C]99.08[/C][C]0.790000000000006[/C][/ROW]
[ROW][C]31[/C][C]100.33[/C][C]99.46[/C][C]0.86999999999999[/C][/ROW]
[ROW][C]32[/C][C]101.5[/C][C]99.92[/C][C]1.58[/C][/ROW]
[ROW][C]33[/C][C]102.29[/C][C]101.09[/C][C]1.2[/C][/ROW]
[ROW][C]34[/C][C]97.04[/C][C]101.88[/C][C]-4.84[/C][/ROW]
[ROW][C]35[/C][C]95.71[/C][C]96.63[/C][C]-0.920000000000016[/C][/ROW]
[ROW][C]36[/C][C]97.37[/C][C]95.3[/C][C]2.07000000000001[/C][/ROW]
[ROW][C]37[/C][C]96.51[/C][C]96.96[/C][C]-0.450000000000003[/C][/ROW]
[ROW][C]38[/C][C]96.33[/C][C]96.1[/C][C]0.22999999999999[/C][/ROW]
[ROW][C]39[/C][C]96.88[/C][C]95.92[/C][C]0.959999999999994[/C][/ROW]
[ROW][C]40[/C][C]97.59[/C][C]96.47[/C][C]1.12[/C][/ROW]
[ROW][C]41[/C][C]98.96[/C][C]97.18[/C][C]1.77999999999999[/C][/ROW]
[ROW][C]42[/C][C]99.93[/C][C]98.55[/C][C]1.38000000000001[/C][/ROW]
[ROW][C]43[/C][C]101.34[/C][C]99.52[/C][C]1.81999999999999[/C][/ROW]
[ROW][C]44[/C][C]98.04[/C][C]100.93[/C][C]-2.89[/C][/ROW]
[ROW][C]45[/C][C]98.56[/C][C]97.63[/C][C]0.929999999999993[/C][/ROW]
[ROW][C]46[/C][C]96.73[/C][C]98.15[/C][C]-1.42[/C][/ROW]
[ROW][C]47[/C][C]92.36[/C][C]96.32[/C][C]-3.96000000000001[/C][/ROW]
[ROW][C]48[/C][C]87.88[/C][C]91.95[/C][C]-4.07000000000001[/C][/ROW]
[ROW][C]49[/C][C]79.84[/C][C]87.47[/C][C]-7.63[/C][/ROW]
[ROW][C]50[/C][C]82.91[/C][C]79.43[/C][C]3.47999999999999[/C][/ROW]
[ROW][C]51[/C][C]87.78[/C][C]82.5[/C][C]5.28[/C][/ROW]
[ROW][C]52[/C][C]89.36[/C][C]87.37[/C][C]1.98999999999999[/C][/ROW]
[ROW][C]53[/C][C]91.86[/C][C]88.95[/C][C]2.91[/C][/ROW]
[ROW][C]54[/C][C]92.48[/C][C]91.45[/C][C]1.03[/C][/ROW]
[ROW][C]55[/C][C]93.4[/C][C]92.07[/C][C]1.33[/C][/ROW]
[ROW][C]56[/C][C]89.97[/C][C]92.99[/C][C]-3.02000000000001[/C][/ROW]
[ROW][C]57[/C][C]83.96[/C][C]89.56[/C][C]-5.60000000000001[/C][/ROW]
[ROW][C]58[/C][C]82.76[/C][C]83.55[/C][C]-0.789999999999992[/C][/ROW]
[ROW][C]59[/C][C]82.97[/C][C]82.35[/C][C]0.61999999999999[/C][/ROW]
[ROW][C]60[/C][C]81.07[/C][C]82.56[/C][C]-1.49000000000001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295532&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295532&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
3	96.61	92.59	4.02
4	99.69	96.2	3.48999999999999
5	101.05	99.28	1.77
6	98	100.64	-2.64
7	97.32	97.59	-0.27000000000001
8	97.83	96.91	0.920000000000002
9	99.57	97.42	2.14999999999999
10	97.63	99.16	-1.53
11	96.68	97.22	-0.539999999999992
12	96.28	96.27	0.00999999999999091
13	99.81	95.87	3.94
14	101.43	99.4	2.03
15	105.59	101.02	4.56999999999999
16	108.86	105.18	3.67999999999999
17	104.01	108.45	-4.44
18	101.95	103.6	-1.65000000000001
19	101.52	101.54	-0.0200000000000102
20	105.61	101.11	4.5
21	108.43	105.2	3.23
22	105.54	108.02	-2.48
23	100.11	105.13	-5.02000000000001
24	99.93	99.7	0.230000000000004
25	99.88	99.52	0.359999999999985
26	102.71	99.47	3.23999999999999
27	101.89	102.3	-0.409999999999997
28	101.93	101.48	0.450000000000003
29	99.49	101.52	-2.03000000000002
30	99.87	99.08	0.790000000000006
31	100.33	99.46	0.86999999999999
32	101.5	99.92	1.58
33	102.29	101.09	1.2
34	97.04	101.88	-4.84
35	95.71	96.63	-0.920000000000016
36	97.37	95.3	2.07000000000001
37	96.51	96.96	-0.450000000000003
38	96.33	96.1	0.22999999999999
39	96.88	95.92	0.959999999999994
40	97.59	96.47	1.12
41	98.96	97.18	1.77999999999999
42	99.93	98.55	1.38000000000001
43	101.34	99.52	1.81999999999999
44	98.04	100.93	-2.89
45	98.56	97.63	0.929999999999993
46	96.73	98.15	-1.42
47	92.36	96.32	-3.96000000000001
48	87.88	91.95	-4.07000000000001
49	79.84	87.47	-7.63
50	82.91	79.43	3.47999999999999
51	87.78	82.5	5.28
52	89.36	87.37	1.98999999999999
53	91.86	88.95	2.91
54	92.48	91.45	1.03
55	93.4	92.07	1.33
56	89.97	92.99	-3.02000000000001
57	83.96	89.56	-5.60000000000001
58	82.76	83.55	-0.789999999999992
59	82.97	82.35	0.61999999999999
60	81.07	82.56	-1.49000000000001

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	80.66	75.1944142553445	86.1255857446555
62	80.25	72.5204945135952	87.9795054864048
63	79.84	70.3733277971325	89.3066722028675
64	79.43	68.4988285106891	90.3611714893109
65	79.02	66.7985787380966	91.2414212619035
66	78.61	65.2221037801645	91.9978962198356
67	78.2	63.7394193503419	92.6605806496582
68	77.79	62.3309890271904	93.2490109728097
69	77.38	60.9832427660336	93.7767572339664
70	76.97	59.6863002999413	94.2536997000588
71	76.56	58.4327028254626	94.6872971745374
72	76.15	57.2166555942651	95.0833444057349

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 80.66 & 75.1944142553445 & 86.1255857446555 \tabularnewline
62 & 80.25 & 72.5204945135952 & 87.9795054864048 \tabularnewline
63 & 79.84 & 70.3733277971325 & 89.3066722028675 \tabularnewline
64 & 79.43 & 68.4988285106891 & 90.3611714893109 \tabularnewline
65 & 79.02 & 66.7985787380966 & 91.2414212619035 \tabularnewline
66 & 78.61 & 65.2221037801645 & 91.9978962198356 \tabularnewline
67 & 78.2 & 63.7394193503419 & 92.6605806496582 \tabularnewline
68 & 77.79 & 62.3309890271904 & 93.2490109728097 \tabularnewline
69 & 77.38 & 60.9832427660336 & 93.7767572339664 \tabularnewline
70 & 76.97 & 59.6863002999413 & 94.2536997000588 \tabularnewline
71 & 76.56 & 58.4327028254626 & 94.6872971745374 \tabularnewline
72 & 76.15 & 57.2166555942651 & 95.0833444057349 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295532&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]80.66[/C][C]75.1944142553445[/C][C]86.1255857446555[/C][/ROW]
[ROW][C]62[/C][C]80.25[/C][C]72.5204945135952[/C][C]87.9795054864048[/C][/ROW]
[ROW][C]63[/C][C]79.84[/C][C]70.3733277971325[/C][C]89.3066722028675[/C][/ROW]
[ROW][C]64[/C][C]79.43[/C][C]68.4988285106891[/C][C]90.3611714893109[/C][/ROW]
[ROW][C]65[/C][C]79.02[/C][C]66.7985787380966[/C][C]91.2414212619035[/C][/ROW]
[ROW][C]66[/C][C]78.61[/C][C]65.2221037801645[/C][C]91.9978962198356[/C][/ROW]
[ROW][C]67[/C][C]78.2[/C][C]63.7394193503419[/C][C]92.6605806496582[/C][/ROW]
[ROW][C]68[/C][C]77.79[/C][C]62.3309890271904[/C][C]93.2490109728097[/C][/ROW]
[ROW][C]69[/C][C]77.38[/C][C]60.9832427660336[/C][C]93.7767572339664[/C][/ROW]
[ROW][C]70[/C][C]76.97[/C][C]59.6863002999413[/C][C]94.2536997000588[/C][/ROW]
[ROW][C]71[/C][C]76.56[/C][C]58.4327028254626[/C][C]94.6872971745374[/C][/ROW]
[ROW][C]72[/C][C]76.15[/C][C]57.2166555942651[/C][C]95.0833444057349[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295532&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295532&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	80.66	75.1944142553445	86.1255857446555
62	80.25	72.5204945135952	87.9795054864048
63	79.84	70.3733277971325	89.3066722028675
64	79.43	68.4988285106891	90.3611714893109
65	79.02	66.7985787380966	91.2414212619035
66	78.61	65.2221037801645	91.9978962198356
67	78.2	63.7394193503419	92.6605806496582
68	77.79	62.3309890271904	93.2490109728097
69	77.38	60.9832427660336	93.7767572339664
70	76.97	59.6863002999413	94.2536997000588
71	76.56	58.4327028254626	94.6872971745374
72	76.15	57.2166555942651	95.0833444057349

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 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; par3 = additive ;

R code (references can be found in the software module):

par3 <- 'additive'
par2 <- 'Single'
par1 <- '12'
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