Free Statistics

of Irreproducible Research!

Author's title

Wisselkoersen - Referentiewisselkoersen voor de euro in nationale munteenhe...

Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sat, 31 May 2008 13:30:47 -0600

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/2008/May/31/t1212262327mivzrtt9secimgr.htm/, Retrieved Wed, 15 May 2024 06:21:24 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13625, Retrieved Wed, 15 May 2024 06:21:24 +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

165

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

-       [Exponential Smoothing] [Wisselkoersen - R...] [2008-05-31 19:30:47] [d41d8cd98f00b204e9800998ecf8427e] [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	6 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 6 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13625&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]6 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13625&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13625&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	6 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	-2.88939878967387e-17
gamma	0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & -2.88939878967387e-17 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13625&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]-2.88939878967387e-17[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13625&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13625&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	-2.88939878967387e-17
gamma	0

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	0.9095	0.9217	-0.0122
4	0.892	0.9095	-0.0175000000000000
5	0.8742	0.892	-0.0178000000000000
6	0.8532	0.8742	-0.021
7	0.8607	0.8532	0.00750000000000006
8	0.9005	0.8607	0.0397999999999999
9	0.9111	0.9005	0.0106000000000001
10	0.9059	0.9111	-0.00519999999999998
11	0.8883	0.9059	-0.0176000000000001
12	0.8924	0.8883	0.00409999999999999
13	0.8833	0.8924	-0.0091
14	0.87	0.8833	-0.0133000000000000
15	0.8758	0.87	0.00580000000000003
16	0.8858	0.8758	0.01
17	0.917	0.8858	0.0312
18	0.9554	0.917	0.0384
19	0.9922	0.9554	0.0367999999999999
20	0.9778	0.9922	-0.0144000000000000
21	0.9808	0.9778	0.003
22	0.9811	0.9808	0.000299999999999967
23	1.0014	0.9811	0.0203000000000001
24	1.0183	1.0014	0.0168999999999999
25	1.0622	1.0183	0.0439000000000001
26	1.0773	1.0622	0.0150999999999999
27	1.0807	1.0773	0.00340000000000007
28	1.0848	1.0807	0.00409999999999999
29	1.1582	1.0848	0.0733999999999999
30	1.1663	1.1582	0.0081
31	1.1372	1.1663	-0.0290999999999999
32	1.1139	1.1372	-0.0233000000000001
33	1.1222	1.1139	0.0083000000000002
34	1.1692	1.1222	0.0469999999999999
35	1.1702	1.1692	0.00099999999999989
36	1.2286	1.1702	0.0584
37	1.2613	1.2286	0.0327000000000002
38	1.2646	1.2613	0.00329999999999986
39	1.2262	1.2646	-0.0384
40	1.1985	1.2262	-0.0277000000000001
41	1.2007	1.1985	0.0022000000000002
42	1.2138	1.2007	0.0130999999999999
43	1.2266	1.2138	0.0127999999999999
44	1.2176	1.2266	-0.0089999999999999
45	1.2218	1.2176	0.00419999999999998
46	1.249	1.2218	0.0272000000000001
47	1.2991	1.249	0.0500999999999998
48	1.3408	1.2991	0.0417000000000001
49	1.3119	1.3408	-0.0288999999999999
50	1.3014	1.3119	-0.0105000000000002
51	1.3201	1.3014	0.0187000000000002
52	1.2938	1.3201	-0.0263
53	1.2694	1.2938	-0.0244
54	1.2165	1.2694	-0.0529000000000002
55	1.2037	1.2165	-0.0127999999999999
56	1.2292	1.2037	0.0255000000000001
57	1.2256	1.2292	-0.00360000000000005
58	1.2015	1.2256	-0.0241
59	1.1786	1.2015	-0.0228999999999999
60	1.1856	1.1786	0.0069999999999999
61	1.2103	1.1856	0.0246999999999999
62	1.1938	1.2103	-0.0165000000000000
63	1.202	1.1938	0.00819999999999999
64	1.2271	1.202	0.0251000000000001
65	1.277	1.2271	0.0498999999999998
66	1.265	1.277	-0.012
67	1.2684	1.265	0.00340000000000007
68	1.2811	1.2684	0.0126999999999999
69	1.2727	1.2811	-0.00839999999999996
70	1.2611	1.2727	-0.0115999999999998
71	1.2881	1.2611	0.0269999999999999
72	1.3213	1.2881	0.0331999999999999
73	1.2999	1.3213	-0.0213999999999999
74	1.3074	1.2999	0.00749999999999984
75	1.3242	1.3074	0.0168000000000001
76	1.3516	1.3242	0.0273999999999999
77	1.3511	1.3516	-0.000499999999999945
78	1.3419	1.3511	-0.00919999999999987
79	1.3716	1.3419	0.0296999999999998
80	1.3622	1.3716	-0.00939999999999985
81	1.3896	1.3622	0.0273999999999999
82	1.4227	1.3896	0.0331000000000001
83	1.4684	1.4227	0.0456999999999999
84	1.457	1.4684	-0.0113999999999999

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 0.9095 & 0.9217 & -0.0122 \tabularnewline
4 & 0.892 & 0.9095 & -0.0175000000000000 \tabularnewline
5 & 0.8742 & 0.892 & -0.0178000000000000 \tabularnewline
6 & 0.8532 & 0.8742 & -0.021 \tabularnewline
7 & 0.8607 & 0.8532 & 0.00750000000000006 \tabularnewline
8 & 0.9005 & 0.8607 & 0.0397999999999999 \tabularnewline
9 & 0.9111 & 0.9005 & 0.0106000000000001 \tabularnewline
10 & 0.9059 & 0.9111 & -0.00519999999999998 \tabularnewline
11 & 0.8883 & 0.9059 & -0.0176000000000001 \tabularnewline
12 & 0.8924 & 0.8883 & 0.00409999999999999 \tabularnewline
13 & 0.8833 & 0.8924 & -0.0091 \tabularnewline
14 & 0.87 & 0.8833 & -0.0133000000000000 \tabularnewline
15 & 0.8758 & 0.87 & 0.00580000000000003 \tabularnewline
16 & 0.8858 & 0.8758 & 0.01 \tabularnewline
17 & 0.917 & 0.8858 & 0.0312 \tabularnewline
18 & 0.9554 & 0.917 & 0.0384 \tabularnewline
19 & 0.9922 & 0.9554 & 0.0367999999999999 \tabularnewline
20 & 0.9778 & 0.9922 & -0.0144000000000000 \tabularnewline
21 & 0.9808 & 0.9778 & 0.003 \tabularnewline
22 & 0.9811 & 0.9808 & 0.000299999999999967 \tabularnewline
23 & 1.0014 & 0.9811 & 0.0203000000000001 \tabularnewline
24 & 1.0183 & 1.0014 & 0.0168999999999999 \tabularnewline
25 & 1.0622 & 1.0183 & 0.0439000000000001 \tabularnewline
26 & 1.0773 & 1.0622 & 0.0150999999999999 \tabularnewline
27 & 1.0807 & 1.0773 & 0.00340000000000007 \tabularnewline
28 & 1.0848 & 1.0807 & 0.00409999999999999 \tabularnewline
29 & 1.1582 & 1.0848 & 0.0733999999999999 \tabularnewline
30 & 1.1663 & 1.1582 & 0.0081 \tabularnewline
31 & 1.1372 & 1.1663 & -0.0290999999999999 \tabularnewline
32 & 1.1139 & 1.1372 & -0.0233000000000001 \tabularnewline
33 & 1.1222 & 1.1139 & 0.0083000000000002 \tabularnewline
34 & 1.1692 & 1.1222 & 0.0469999999999999 \tabularnewline
35 & 1.1702 & 1.1692 & 0.00099999999999989 \tabularnewline
36 & 1.2286 & 1.1702 & 0.0584 \tabularnewline
37 & 1.2613 & 1.2286 & 0.0327000000000002 \tabularnewline
38 & 1.2646 & 1.2613 & 0.00329999999999986 \tabularnewline
39 & 1.2262 & 1.2646 & -0.0384 \tabularnewline
40 & 1.1985 & 1.2262 & -0.0277000000000001 \tabularnewline
41 & 1.2007 & 1.1985 & 0.0022000000000002 \tabularnewline
42 & 1.2138 & 1.2007 & 0.0130999999999999 \tabularnewline
43 & 1.2266 & 1.2138 & 0.0127999999999999 \tabularnewline
44 & 1.2176 & 1.2266 & -0.0089999999999999 \tabularnewline
45 & 1.2218 & 1.2176 & 0.00419999999999998 \tabularnewline
46 & 1.249 & 1.2218 & 0.0272000000000001 \tabularnewline
47 & 1.2991 & 1.249 & 0.0500999999999998 \tabularnewline
48 & 1.3408 & 1.2991 & 0.0417000000000001 \tabularnewline
49 & 1.3119 & 1.3408 & -0.0288999999999999 \tabularnewline
50 & 1.3014 & 1.3119 & -0.0105000000000002 \tabularnewline
51 & 1.3201 & 1.3014 & 0.0187000000000002 \tabularnewline
52 & 1.2938 & 1.3201 & -0.0263 \tabularnewline
53 & 1.2694 & 1.2938 & -0.0244 \tabularnewline
54 & 1.2165 & 1.2694 & -0.0529000000000002 \tabularnewline
55 & 1.2037 & 1.2165 & -0.0127999999999999 \tabularnewline
56 & 1.2292 & 1.2037 & 0.0255000000000001 \tabularnewline
57 & 1.2256 & 1.2292 & -0.00360000000000005 \tabularnewline
58 & 1.2015 & 1.2256 & -0.0241 \tabularnewline
59 & 1.1786 & 1.2015 & -0.0228999999999999 \tabularnewline
60 & 1.1856 & 1.1786 & 0.0069999999999999 \tabularnewline
61 & 1.2103 & 1.1856 & 0.0246999999999999 \tabularnewline
62 & 1.1938 & 1.2103 & -0.0165000000000000 \tabularnewline
63 & 1.202 & 1.1938 & 0.00819999999999999 \tabularnewline
64 & 1.2271 & 1.202 & 0.0251000000000001 \tabularnewline
65 & 1.277 & 1.2271 & 0.0498999999999998 \tabularnewline
66 & 1.265 & 1.277 & -0.012 \tabularnewline
67 & 1.2684 & 1.265 & 0.00340000000000007 \tabularnewline
68 & 1.2811 & 1.2684 & 0.0126999999999999 \tabularnewline
69 & 1.2727 & 1.2811 & -0.00839999999999996 \tabularnewline
70 & 1.2611 & 1.2727 & -0.0115999999999998 \tabularnewline
71 & 1.2881 & 1.2611 & 0.0269999999999999 \tabularnewline
72 & 1.3213 & 1.2881 & 0.0331999999999999 \tabularnewline
73 & 1.2999 & 1.3213 & -0.0213999999999999 \tabularnewline
74 & 1.3074 & 1.2999 & 0.00749999999999984 \tabularnewline
75 & 1.3242 & 1.3074 & 0.0168000000000001 \tabularnewline
76 & 1.3516 & 1.3242 & 0.0273999999999999 \tabularnewline
77 & 1.3511 & 1.3516 & -0.000499999999999945 \tabularnewline
78 & 1.3419 & 1.3511 & -0.00919999999999987 \tabularnewline
79 & 1.3716 & 1.3419 & 0.0296999999999998 \tabularnewline
80 & 1.3622 & 1.3716 & -0.00939999999999985 \tabularnewline
81 & 1.3896 & 1.3622 & 0.0273999999999999 \tabularnewline
82 & 1.4227 & 1.3896 & 0.0331000000000001 \tabularnewline
83 & 1.4684 & 1.4227 & 0.0456999999999999 \tabularnewline
84 & 1.457 & 1.4684 & -0.0113999999999999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13625&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]0.9095[/C][C]0.9217[/C][C]-0.0122[/C][/ROW]
[ROW][C]4[/C][C]0.892[/C][C]0.9095[/C][C]-0.0175000000000000[/C][/ROW]
[ROW][C]5[/C][C]0.8742[/C][C]0.892[/C][C]-0.0178000000000000[/C][/ROW]
[ROW][C]6[/C][C]0.8532[/C][C]0.8742[/C][C]-0.021[/C][/ROW]
[ROW][C]7[/C][C]0.8607[/C][C]0.8532[/C][C]0.00750000000000006[/C][/ROW]
[ROW][C]8[/C][C]0.9005[/C][C]0.8607[/C][C]0.0397999999999999[/C][/ROW]
[ROW][C]9[/C][C]0.9111[/C][C]0.9005[/C][C]0.0106000000000001[/C][/ROW]
[ROW][C]10[/C][C]0.9059[/C][C]0.9111[/C][C]-0.00519999999999998[/C][/ROW]
[ROW][C]11[/C][C]0.8883[/C][C]0.9059[/C][C]-0.0176000000000001[/C][/ROW]
[ROW][C]12[/C][C]0.8924[/C][C]0.8883[/C][C]0.00409999999999999[/C][/ROW]
[ROW][C]13[/C][C]0.8833[/C][C]0.8924[/C][C]-0.0091[/C][/ROW]
[ROW][C]14[/C][C]0.87[/C][C]0.8833[/C][C]-0.0133000000000000[/C][/ROW]
[ROW][C]15[/C][C]0.8758[/C][C]0.87[/C][C]0.00580000000000003[/C][/ROW]
[ROW][C]16[/C][C]0.8858[/C][C]0.8758[/C][C]0.01[/C][/ROW]
[ROW][C]17[/C][C]0.917[/C][C]0.8858[/C][C]0.0312[/C][/ROW]
[ROW][C]18[/C][C]0.9554[/C][C]0.917[/C][C]0.0384[/C][/ROW]
[ROW][C]19[/C][C]0.9922[/C][C]0.9554[/C][C]0.0367999999999999[/C][/ROW]
[ROW][C]20[/C][C]0.9778[/C][C]0.9922[/C][C]-0.0144000000000000[/C][/ROW]
[ROW][C]21[/C][C]0.9808[/C][C]0.9778[/C][C]0.003[/C][/ROW]
[ROW][C]22[/C][C]0.9811[/C][C]0.9808[/C][C]0.000299999999999967[/C][/ROW]
[ROW][C]23[/C][C]1.0014[/C][C]0.9811[/C][C]0.0203000000000001[/C][/ROW]
[ROW][C]24[/C][C]1.0183[/C][C]1.0014[/C][C]0.0168999999999999[/C][/ROW]
[ROW][C]25[/C][C]1.0622[/C][C]1.0183[/C][C]0.0439000000000001[/C][/ROW]
[ROW][C]26[/C][C]1.0773[/C][C]1.0622[/C][C]0.0150999999999999[/C][/ROW]
[ROW][C]27[/C][C]1.0807[/C][C]1.0773[/C][C]0.00340000000000007[/C][/ROW]
[ROW][C]28[/C][C]1.0848[/C][C]1.0807[/C][C]0.00409999999999999[/C][/ROW]
[ROW][C]29[/C][C]1.1582[/C][C]1.0848[/C][C]0.0733999999999999[/C][/ROW]
[ROW][C]30[/C][C]1.1663[/C][C]1.1582[/C][C]0.0081[/C][/ROW]
[ROW][C]31[/C][C]1.1372[/C][C]1.1663[/C][C]-0.0290999999999999[/C][/ROW]
[ROW][C]32[/C][C]1.1139[/C][C]1.1372[/C][C]-0.0233000000000001[/C][/ROW]
[ROW][C]33[/C][C]1.1222[/C][C]1.1139[/C][C]0.0083000000000002[/C][/ROW]
[ROW][C]34[/C][C]1.1692[/C][C]1.1222[/C][C]0.0469999999999999[/C][/ROW]
[ROW][C]35[/C][C]1.1702[/C][C]1.1692[/C][C]0.00099999999999989[/C][/ROW]
[ROW][C]36[/C][C]1.2286[/C][C]1.1702[/C][C]0.0584[/C][/ROW]
[ROW][C]37[/C][C]1.2613[/C][C]1.2286[/C][C]0.0327000000000002[/C][/ROW]
[ROW][C]38[/C][C]1.2646[/C][C]1.2613[/C][C]0.00329999999999986[/C][/ROW]
[ROW][C]39[/C][C]1.2262[/C][C]1.2646[/C][C]-0.0384[/C][/ROW]
[ROW][C]40[/C][C]1.1985[/C][C]1.2262[/C][C]-0.0277000000000001[/C][/ROW]
[ROW][C]41[/C][C]1.2007[/C][C]1.1985[/C][C]0.0022000000000002[/C][/ROW]
[ROW][C]42[/C][C]1.2138[/C][C]1.2007[/C][C]0.0130999999999999[/C][/ROW]
[ROW][C]43[/C][C]1.2266[/C][C]1.2138[/C][C]0.0127999999999999[/C][/ROW]
[ROW][C]44[/C][C]1.2176[/C][C]1.2266[/C][C]-0.0089999999999999[/C][/ROW]
[ROW][C]45[/C][C]1.2218[/C][C]1.2176[/C][C]0.00419999999999998[/C][/ROW]
[ROW][C]46[/C][C]1.249[/C][C]1.2218[/C][C]0.0272000000000001[/C][/ROW]
[ROW][C]47[/C][C]1.2991[/C][C]1.249[/C][C]0.0500999999999998[/C][/ROW]
[ROW][C]48[/C][C]1.3408[/C][C]1.2991[/C][C]0.0417000000000001[/C][/ROW]
[ROW][C]49[/C][C]1.3119[/C][C]1.3408[/C][C]-0.0288999999999999[/C][/ROW]
[ROW][C]50[/C][C]1.3014[/C][C]1.3119[/C][C]-0.0105000000000002[/C][/ROW]
[ROW][C]51[/C][C]1.3201[/C][C]1.3014[/C][C]0.0187000000000002[/C][/ROW]
[ROW][C]52[/C][C]1.2938[/C][C]1.3201[/C][C]-0.0263[/C][/ROW]
[ROW][C]53[/C][C]1.2694[/C][C]1.2938[/C][C]-0.0244[/C][/ROW]
[ROW][C]54[/C][C]1.2165[/C][C]1.2694[/C][C]-0.0529000000000002[/C][/ROW]
[ROW][C]55[/C][C]1.2037[/C][C]1.2165[/C][C]-0.0127999999999999[/C][/ROW]
[ROW][C]56[/C][C]1.2292[/C][C]1.2037[/C][C]0.0255000000000001[/C][/ROW]
[ROW][C]57[/C][C]1.2256[/C][C]1.2292[/C][C]-0.00360000000000005[/C][/ROW]
[ROW][C]58[/C][C]1.2015[/C][C]1.2256[/C][C]-0.0241[/C][/ROW]
[ROW][C]59[/C][C]1.1786[/C][C]1.2015[/C][C]-0.0228999999999999[/C][/ROW]
[ROW][C]60[/C][C]1.1856[/C][C]1.1786[/C][C]0.0069999999999999[/C][/ROW]
[ROW][C]61[/C][C]1.2103[/C][C]1.1856[/C][C]0.0246999999999999[/C][/ROW]
[ROW][C]62[/C][C]1.1938[/C][C]1.2103[/C][C]-0.0165000000000000[/C][/ROW]
[ROW][C]63[/C][C]1.202[/C][C]1.1938[/C][C]0.00819999999999999[/C][/ROW]
[ROW][C]64[/C][C]1.2271[/C][C]1.202[/C][C]0.0251000000000001[/C][/ROW]
[ROW][C]65[/C][C]1.277[/C][C]1.2271[/C][C]0.0498999999999998[/C][/ROW]
[ROW][C]66[/C][C]1.265[/C][C]1.277[/C][C]-0.012[/C][/ROW]
[ROW][C]67[/C][C]1.2684[/C][C]1.265[/C][C]0.00340000000000007[/C][/ROW]
[ROW][C]68[/C][C]1.2811[/C][C]1.2684[/C][C]0.0126999999999999[/C][/ROW]
[ROW][C]69[/C][C]1.2727[/C][C]1.2811[/C][C]-0.00839999999999996[/C][/ROW]
[ROW][C]70[/C][C]1.2611[/C][C]1.2727[/C][C]-0.0115999999999998[/C][/ROW]
[ROW][C]71[/C][C]1.2881[/C][C]1.2611[/C][C]0.0269999999999999[/C][/ROW]
[ROW][C]72[/C][C]1.3213[/C][C]1.2881[/C][C]0.0331999999999999[/C][/ROW]
[ROW][C]73[/C][C]1.2999[/C][C]1.3213[/C][C]-0.0213999999999999[/C][/ROW]
[ROW][C]74[/C][C]1.3074[/C][C]1.2999[/C][C]0.00749999999999984[/C][/ROW]
[ROW][C]75[/C][C]1.3242[/C][C]1.3074[/C][C]0.0168000000000001[/C][/ROW]
[ROW][C]76[/C][C]1.3516[/C][C]1.3242[/C][C]0.0273999999999999[/C][/ROW]
[ROW][C]77[/C][C]1.3511[/C][C]1.3516[/C][C]-0.000499999999999945[/C][/ROW]
[ROW][C]78[/C][C]1.3419[/C][C]1.3511[/C][C]-0.00919999999999987[/C][/ROW]
[ROW][C]79[/C][C]1.3716[/C][C]1.3419[/C][C]0.0296999999999998[/C][/ROW]
[ROW][C]80[/C][C]1.3622[/C][C]1.3716[/C][C]-0.00939999999999985[/C][/ROW]
[ROW][C]81[/C][C]1.3896[/C][C]1.3622[/C][C]0.0273999999999999[/C][/ROW]
[ROW][C]82[/C][C]1.4227[/C][C]1.3896[/C][C]0.0331000000000001[/C][/ROW]
[ROW][C]83[/C][C]1.4684[/C][C]1.4227[/C][C]0.0456999999999999[/C][/ROW]
[ROW][C]84[/C][C]1.457[/C][C]1.4684[/C][C]-0.0113999999999999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13625&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13625&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	0.9095	0.9217	-0.0122
4	0.892	0.9095	-0.0175000000000000
5	0.8742	0.892	-0.0178000000000000
6	0.8532	0.8742	-0.021
7	0.8607	0.8532	0.00750000000000006
8	0.9005	0.8607	0.0397999999999999
9	0.9111	0.9005	0.0106000000000001
10	0.9059	0.9111	-0.00519999999999998
11	0.8883	0.9059	-0.0176000000000001
12	0.8924	0.8883	0.00409999999999999
13	0.8833	0.8924	-0.0091
14	0.87	0.8833	-0.0133000000000000
15	0.8758	0.87	0.00580000000000003
16	0.8858	0.8758	0.01
17	0.917	0.8858	0.0312
18	0.9554	0.917	0.0384
19	0.9922	0.9554	0.0367999999999999
20	0.9778	0.9922	-0.0144000000000000
21	0.9808	0.9778	0.003
22	0.9811	0.9808	0.000299999999999967
23	1.0014	0.9811	0.0203000000000001
24	1.0183	1.0014	0.0168999999999999
25	1.0622	1.0183	0.0439000000000001
26	1.0773	1.0622	0.0150999999999999
27	1.0807	1.0773	0.00340000000000007
28	1.0848	1.0807	0.00409999999999999
29	1.1582	1.0848	0.0733999999999999
30	1.1663	1.1582	0.0081
31	1.1372	1.1663	-0.0290999999999999
32	1.1139	1.1372	-0.0233000000000001
33	1.1222	1.1139	0.0083000000000002
34	1.1692	1.1222	0.0469999999999999
35	1.1702	1.1692	0.00099999999999989
36	1.2286	1.1702	0.0584
37	1.2613	1.2286	0.0327000000000002
38	1.2646	1.2613	0.00329999999999986
39	1.2262	1.2646	-0.0384
40	1.1985	1.2262	-0.0277000000000001
41	1.2007	1.1985	0.0022000000000002
42	1.2138	1.2007	0.0130999999999999
43	1.2266	1.2138	0.0127999999999999
44	1.2176	1.2266	-0.0089999999999999
45	1.2218	1.2176	0.00419999999999998
46	1.249	1.2218	0.0272000000000001
47	1.2991	1.249	0.0500999999999998
48	1.3408	1.2991	0.0417000000000001
49	1.3119	1.3408	-0.0288999999999999
50	1.3014	1.3119	-0.0105000000000002
51	1.3201	1.3014	0.0187000000000002
52	1.2938	1.3201	-0.0263
53	1.2694	1.2938	-0.0244
54	1.2165	1.2694	-0.0529000000000002
55	1.2037	1.2165	-0.0127999999999999
56	1.2292	1.2037	0.0255000000000001
57	1.2256	1.2292	-0.00360000000000005
58	1.2015	1.2256	-0.0241
59	1.1786	1.2015	-0.0228999999999999
60	1.1856	1.1786	0.0069999999999999
61	1.2103	1.1856	0.0246999999999999
62	1.1938	1.2103	-0.0165000000000000
63	1.202	1.1938	0.00819999999999999
64	1.2271	1.202	0.0251000000000001
65	1.277	1.2271	0.0498999999999998
66	1.265	1.277	-0.012
67	1.2684	1.265	0.00340000000000007
68	1.2811	1.2684	0.0126999999999999
69	1.2727	1.2811	-0.00839999999999996
70	1.2611	1.2727	-0.0115999999999998
71	1.2881	1.2611	0.0269999999999999
72	1.3213	1.2881	0.0331999999999999
73	1.2999	1.3213	-0.0213999999999999
74	1.3074	1.2999	0.00749999999999984
75	1.3242	1.3074	0.0168000000000001
76	1.3516	1.3242	0.0273999999999999
77	1.3511	1.3516	-0.000499999999999945
78	1.3419	1.3511	-0.00919999999999987
79	1.3716	1.3419	0.0296999999999998
80	1.3622	1.3716	-0.00939999999999985
81	1.3896	1.3622	0.0273999999999999
82	1.4227	1.3896	0.0331000000000001
83	1.4684	1.4227	0.0456999999999999
84	1.457	1.4684	-0.0113999999999999

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	1.457	1.40886651426556	1.50513348573444
86	1.457	1.38892897167006	1.52507102832994
87	1.457	1.37363035716255	1.54036964283745
88	1.457	1.36073302853111	1.55326697146889
89	1.457	1.34937025390377	1.56462974609623
90	1.457	1.33909752040908	1.57490247959092
91	1.457	1.32965076701199	1.58434923298801
92	1.457	1.32085794334011	1.59314205665989
93	1.457	1.31259954279667	1.60140045720333
94	1.457	1.30478855335593	1.60921144664407
95	1.457	1.29735928796692	1.61664071203308
96	1.457	1.29026071432510	1.6237392856749

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 1.457 & 1.40886651426556 & 1.50513348573444 \tabularnewline
86 & 1.457 & 1.38892897167006 & 1.52507102832994 \tabularnewline
87 & 1.457 & 1.37363035716255 & 1.54036964283745 \tabularnewline
88 & 1.457 & 1.36073302853111 & 1.55326697146889 \tabularnewline
89 & 1.457 & 1.34937025390377 & 1.56462974609623 \tabularnewline
90 & 1.457 & 1.33909752040908 & 1.57490247959092 \tabularnewline
91 & 1.457 & 1.32965076701199 & 1.58434923298801 \tabularnewline
92 & 1.457 & 1.32085794334011 & 1.59314205665989 \tabularnewline
93 & 1.457 & 1.31259954279667 & 1.60140045720333 \tabularnewline
94 & 1.457 & 1.30478855335593 & 1.60921144664407 \tabularnewline
95 & 1.457 & 1.29735928796692 & 1.61664071203308 \tabularnewline
96 & 1.457 & 1.29026071432510 & 1.6237392856749 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13625&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]85[/C][C]1.457[/C][C]1.40886651426556[/C][C]1.50513348573444[/C][/ROW]
[ROW][C]86[/C][C]1.457[/C][C]1.38892897167006[/C][C]1.52507102832994[/C][/ROW]
[ROW][C]87[/C][C]1.457[/C][C]1.37363035716255[/C][C]1.54036964283745[/C][/ROW]
[ROW][C]88[/C][C]1.457[/C][C]1.36073302853111[/C][C]1.55326697146889[/C][/ROW]
[ROW][C]89[/C][C]1.457[/C][C]1.34937025390377[/C][C]1.56462974609623[/C][/ROW]
[ROW][C]90[/C][C]1.457[/C][C]1.33909752040908[/C][C]1.57490247959092[/C][/ROW]
[ROW][C]91[/C][C]1.457[/C][C]1.32965076701199[/C][C]1.58434923298801[/C][/ROW]
[ROW][C]92[/C][C]1.457[/C][C]1.32085794334011[/C][C]1.59314205665989[/C][/ROW]
[ROW][C]93[/C][C]1.457[/C][C]1.31259954279667[/C][C]1.60140045720333[/C][/ROW]
[ROW][C]94[/C][C]1.457[/C][C]1.30478855335593[/C][C]1.60921144664407[/C][/ROW]
[ROW][C]95[/C][C]1.457[/C][C]1.29735928796692[/C][C]1.61664071203308[/C][/ROW]
[ROW][C]96[/C][C]1.457[/C][C]1.29026071432510[/C][C]1.6237392856749[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13625&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13625&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
85	1.457	1.40886651426556	1.50513348573444
86	1.457	1.38892897167006	1.52507102832994
87	1.457	1.37363035716255	1.54036964283745
88	1.457	1.36073302853111	1.55326697146889
89	1.457	1.34937025390377	1.56462974609623
90	1.457	1.33909752040908	1.57490247959092
91	1.457	1.32965076701199	1.58434923298801
92	1.457	1.32085794334011	1.59314205665989
93	1.457	1.31259954279667	1.60140045720333
94	1.457	1.30478855335593	1.60921144664407
95	1.457	1.29735928796692	1.61664071203308
96	1.457	1.29026071432510	1.6237392856749

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):

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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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

Wisselkoersen - Referentiewisselkoersen voor de euro in nationale munteenhe...

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code