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Author

*The author of this computation has been verified*

R Software Module

rwasp_arimaforecasting.wasp

Title produced by software

ARIMA Forecasting

Date of computation

Mon, 20 Dec 2010 19:46:41 +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/20/t1292874289ngyyp5yk62ejh4f.htm/, Retrieved Sat, 04 May 2024 03:45:50 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=113095, Retrieved Sat, 04 May 2024 03:45:50 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

160

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

F     [Univariate Data Series] [HPC Retail Sales] [2008-03-02 15:42:48] [74be16979710d4c4e7c6647856088456]
-  MPD  [Univariate Data Series] [WS8 1] [2010-11-30 15:47:30] [07a238a5afc23eb944f8545182f29d5a]
- RMP     [Classical Decomposition] [WS8 2] [2010-11-30 15:54:02] [07a238a5afc23eb944f8545182f29d5a]
- RMPD      [Univariate Data Series] [Statistiek: Werkl...] [2010-12-12 15:20:09] [07a238a5afc23eb944f8545182f29d5a]
-    D        [Univariate Data Series] [Statistiek: Werkl...] [2010-12-14 09:08:05] [07a238a5afc23eb944f8545182f29d5a]
-               [Univariate Data Series] [Statistiek: Werkl...] [2010-12-14 09:12:36] [07a238a5afc23eb944f8545182f29d5a]
- RMPD            [Classical Decomposition] [statistiek classi...] [2010-12-19 09:09:14] [07a238a5afc23eb944f8545182f29d5a]
- RMP               [(Partial) Autocorrelation Function] [Statistiek: ACF D...] [2010-12-19 10:44:26] [07a238a5afc23eb944f8545182f29d5a]
-   P                 [(Partial) Autocorrelation Function] [Statistiek: ACF D...] [2010-12-19 12:30:15] [07a238a5afc23eb944f8545182f29d5a]
-   P                   [(Partial) Autocorrelation Function] [Statistiek: ACF D...] [2010-12-19 12:34:49] [07a238a5afc23eb944f8545182f29d5a]
- RMP                     [Standard Deviation-Mean Plot] [statistiek: stada...] [2010-12-19 15:02:29] [07a238a5afc23eb944f8545182f29d5a]
- RMP                       [ARIMA Backward Selection] [Statistiek: Arima...] [2010-12-20 19:29:57] [07a238a5afc23eb944f8545182f29d5a]
- RMP                           [ARIMA Forecasting] [statistiek: Arima...] [2010-12-20 19:46:41] [67e3c2d70de1dbb070b545ca6c893d5e] [Current]

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Dataseries X:

Download CSV

Histogram

Boxplots

6.5
6.3
5.9
5.5
5.2
4.9
5.4
5.8
5.7
5.6
5.5
5.4
5.4
5.4
5.5
5.8
5.7
5.4
5.6
5.8
6.2
6.8
6.7
6.7
6.4
6.3
6.3
6.4
6.3
6
6.3
6.3
6.6
7.5
7.8
7.9
7.8
7.6
7.5
7.6
7.5
7.3
7.6
7.5
7.6
7.9
7.9
8.1
8.2
8
7.5
6.8
6.5
6.6
7.6
8
8.1
7.7
7.5
7.6
7.8
7.8
7.8
7.5
7.5
7.1
7.5
7.5
7.6
7.7
7.7
7.9
8.1
8.2
8.2
8.2
7.9
7.3
6.9
6.6
6.7
6.9
7
7.1
7.2
7.1
6.9
7
6.8
6.4
6.7
6.6
6.4
6.3
6.2
6.5
6.8
6.8
6.4
6.1
5.8
6.1
7.2
7.3
6.9
6.1
5.8
6.2
7.1
7.7
8
7.8
7.4
7.4
7.7
7.8
7.8
8
8.1
8.4

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	'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 & 6 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113095&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113095&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113095&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Univariate ARIMA Extrapolation Forecast
time	Y[t]	F[t]	95% LB	95% UB	p-value(H0: Y[t] = F[t])	P(F[t]>Y[t-1])	P(F[t]>Y[t-s])	P(F[t]>Y[96])
84	7.1	-	-	-	-	-	-	-
85	7.2	-	-	-	-	-	-	-
86	7.1	-	-	-	-	-	-	-
87	6.9	-	-	-	-	-	-	-
88	7	-	-	-	-	-	-	-
89	6.8	-	-	-	-	-	-	-
90	6.4	-	-	-	-	-	-	-
91	6.7	-	-	-	-	-	-	-
92	6.6	-	-	-	-	-	-	-
93	6.4	-	-	-	-	-	-	-
94	6.3	-	-	-	-	-	-	-
95	6.2	-	-	-	-	-	-	-
96	6.5	-	-	-	-	-	-	-
97	6.8	6.779	6.405	7.1529	0.4561	0.9281	0.0137	0.9281
98	6.8	6.8373	6.1514	7.5231	0.4576	0.5424	0.2264	0.8324
99	6.4	6.6717	5.7389	7.6046	0.284	0.3938	0.3158	0.6409
100	6.1	6.5179	5.456	7.5798	0.2203	0.5861	0.1868	0.5131
101	5.8	6.2556	5.1338	7.3773	0.213	0.6071	0.1707	0.3347
102	6.1	5.9389	4.783	7.0949	0.3924	0.5931	0.2172	0.1707
103	7.2	6.25	5.0564	7.4436	0.0594	0.5973	0.23	0.3407
104	7.3	6.3236	5.074	7.5733	0.0628	0.0846	0.3323	0.391
105	6.9	6.3666	5.0432	7.6899	0.2147	0.0834	0.4803	0.4217
106	6.1	6.4569	5.0576	7.8562	0.3086	0.2674	0.587	0.4759
107	5.8	6.4108	4.9464	7.8753	0.2068	0.6613	0.6111	0.4525
108	6.2	6.5388	5.0222	8.0553	0.3308	0.8302	0.52	0.52
109	7.1	6.6387	5.0458	8.2316	0.2851	0.7053	0.4213	0.5677
110	7.7	6.6098	4.9258	8.2939	0.1023	0.2842	0.4124	0.5509
111	8	6.4904	4.7087	8.2721	0.0484	0.0917	0.5396	0.4958
112	7.8	6.394	4.5264	8.2616	0.07	0.046	0.6212	0.4557
113	7.4	6.2157	4.2768	8.1545	0.1156	0.0546	0.6628	0.3869
114	7.4	5.9411	3.9415	7.9408	0.0764	0.0764	0.4381	0.2919
115	7.7	6.2151	4.1576	8.2727	0.0786	0.1295	0.1741	0.3931
116	7.8	6.2684	4.1509	8.3859	0.0781	0.0926	0.1698	0.4151
117	7.8	6.33	4.1493	8.5108	0.0932	0.0932	0.3042	0.4393
118	8	6.4649	4.2197	8.71	0.0901	0.1219	0.625	0.4878
119	8.1	6.4569	4.1494	8.7644	0.0814	0.095	0.7116	0.4854
120	8.4	6.573	4.2072	8.9388	0.0651	0.1029	0.6213	0.5241

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast \tabularnewline
time & Y[t] & F[t] & 95% LB & 95% UB & p-value(H0: Y[t] = F[t]) & P(F[t]>Y[t-1]) & P(F[t]>Y[t-s]) & P(F[t]>Y[96]) \tabularnewline
84 & 7.1 & - & - & - & - & - & - & - \tabularnewline
85 & 7.2 & - & - & - & - & - & - & - \tabularnewline
86 & 7.1 & - & - & - & - & - & - & - \tabularnewline
87 & 6.9 & - & - & - & - & - & - & - \tabularnewline
88 & 7 & - & - & - & - & - & - & - \tabularnewline
89 & 6.8 & - & - & - & - & - & - & - \tabularnewline
90 & 6.4 & - & - & - & - & - & - & - \tabularnewline
91 & 6.7 & - & - & - & - & - & - & - \tabularnewline
92 & 6.6 & - & - & - & - & - & - & - \tabularnewline
93 & 6.4 & - & - & - & - & - & - & - \tabularnewline
94 & 6.3 & - & - & - & - & - & - & - \tabularnewline
95 & 6.2 & - & - & - & - & - & - & - \tabularnewline
96 & 6.5 & - & - & - & - & - & - & - \tabularnewline
97 & 6.8 & 6.779 & 6.405 & 7.1529 & 0.4561 & 0.9281 & 0.0137 & 0.9281 \tabularnewline
98 & 6.8 & 6.8373 & 6.1514 & 7.5231 & 0.4576 & 0.5424 & 0.2264 & 0.8324 \tabularnewline
99 & 6.4 & 6.6717 & 5.7389 & 7.6046 & 0.284 & 0.3938 & 0.3158 & 0.6409 \tabularnewline
100 & 6.1 & 6.5179 & 5.456 & 7.5798 & 0.2203 & 0.5861 & 0.1868 & 0.5131 \tabularnewline
101 & 5.8 & 6.2556 & 5.1338 & 7.3773 & 0.213 & 0.6071 & 0.1707 & 0.3347 \tabularnewline
102 & 6.1 & 5.9389 & 4.783 & 7.0949 & 0.3924 & 0.5931 & 0.2172 & 0.1707 \tabularnewline
103 & 7.2 & 6.25 & 5.0564 & 7.4436 & 0.0594 & 0.5973 & 0.23 & 0.3407 \tabularnewline
104 & 7.3 & 6.3236 & 5.074 & 7.5733 & 0.0628 & 0.0846 & 0.3323 & 0.391 \tabularnewline
105 & 6.9 & 6.3666 & 5.0432 & 7.6899 & 0.2147 & 0.0834 & 0.4803 & 0.4217 \tabularnewline
106 & 6.1 & 6.4569 & 5.0576 & 7.8562 & 0.3086 & 0.2674 & 0.587 & 0.4759 \tabularnewline
107 & 5.8 & 6.4108 & 4.9464 & 7.8753 & 0.2068 & 0.6613 & 0.6111 & 0.4525 \tabularnewline
108 & 6.2 & 6.5388 & 5.0222 & 8.0553 & 0.3308 & 0.8302 & 0.52 & 0.52 \tabularnewline
109 & 7.1 & 6.6387 & 5.0458 & 8.2316 & 0.2851 & 0.7053 & 0.4213 & 0.5677 \tabularnewline
110 & 7.7 & 6.6098 & 4.9258 & 8.2939 & 0.1023 & 0.2842 & 0.4124 & 0.5509 \tabularnewline
111 & 8 & 6.4904 & 4.7087 & 8.2721 & 0.0484 & 0.0917 & 0.5396 & 0.4958 \tabularnewline
112 & 7.8 & 6.394 & 4.5264 & 8.2616 & 0.07 & 0.046 & 0.6212 & 0.4557 \tabularnewline
113 & 7.4 & 6.2157 & 4.2768 & 8.1545 & 0.1156 & 0.0546 & 0.6628 & 0.3869 \tabularnewline
114 & 7.4 & 5.9411 & 3.9415 & 7.9408 & 0.0764 & 0.0764 & 0.4381 & 0.2919 \tabularnewline
115 & 7.7 & 6.2151 & 4.1576 & 8.2727 & 0.0786 & 0.1295 & 0.1741 & 0.3931 \tabularnewline
116 & 7.8 & 6.2684 & 4.1509 & 8.3859 & 0.0781 & 0.0926 & 0.1698 & 0.4151 \tabularnewline
117 & 7.8 & 6.33 & 4.1493 & 8.5108 & 0.0932 & 0.0932 & 0.3042 & 0.4393 \tabularnewline
118 & 8 & 6.4649 & 4.2197 & 8.71 & 0.0901 & 0.1219 & 0.625 & 0.4878 \tabularnewline
119 & 8.1 & 6.4569 & 4.1494 & 8.7644 & 0.0814 & 0.095 & 0.7116 & 0.4854 \tabularnewline
120 & 8.4 & 6.573 & 4.2072 & 8.9388 & 0.0651 & 0.1029 & 0.6213 & 0.5241 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113095&T=1

[TABLE]
[ROW][C]Univariate ARIMA Extrapolation Forecast[/C][/ROW]
[ROW][C]time[/C][C]Y[t][/C][C]F[t][/C][C]95% LB[/C][C]95% UB[/C][C]p-value(H0: Y[t] = F[t])[/C][C]P(F[t]>Y[t-1])[/C][C]P(F[t]>Y[t-s])[/C][C]P(F[t]>Y[96])[/C][/ROW]
[ROW][C]84[/C][C]7.1[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]85[/C][C]7.2[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]86[/C][C]7.1[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]87[/C][C]6.9[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]88[/C][C]7[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]89[/C][C]6.8[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]90[/C][C]6.4[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]91[/C][C]6.7[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]92[/C][C]6.6[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]93[/C][C]6.4[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]94[/C][C]6.3[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]95[/C][C]6.2[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]96[/C][C]6.5[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]97[/C][C]6.8[/C][C]6.779[/C][C]6.405[/C][C]7.1529[/C][C]0.4561[/C][C]0.9281[/C][C]0.0137[/C][C]0.9281[/C][/ROW]
[ROW][C]98[/C][C]6.8[/C][C]6.8373[/C][C]6.1514[/C][C]7.5231[/C][C]0.4576[/C][C]0.5424[/C][C]0.2264[/C][C]0.8324[/C][/ROW]
[ROW][C]99[/C][C]6.4[/C][C]6.6717[/C][C]5.7389[/C][C]7.6046[/C][C]0.284[/C][C]0.3938[/C][C]0.3158[/C][C]0.6409[/C][/ROW]
[ROW][C]100[/C][C]6.1[/C][C]6.5179[/C][C]5.456[/C][C]7.5798[/C][C]0.2203[/C][C]0.5861[/C][C]0.1868[/C][C]0.5131[/C][/ROW]
[ROW][C]101[/C][C]5.8[/C][C]6.2556[/C][C]5.1338[/C][C]7.3773[/C][C]0.213[/C][C]0.6071[/C][C]0.1707[/C][C]0.3347[/C][/ROW]
[ROW][C]102[/C][C]6.1[/C][C]5.9389[/C][C]4.783[/C][C]7.0949[/C][C]0.3924[/C][C]0.5931[/C][C]0.2172[/C][C]0.1707[/C][/ROW]
[ROW][C]103[/C][C]7.2[/C][C]6.25[/C][C]5.0564[/C][C]7.4436[/C][C]0.0594[/C][C]0.5973[/C][C]0.23[/C][C]0.3407[/C][/ROW]
[ROW][C]104[/C][C]7.3[/C][C]6.3236[/C][C]5.074[/C][C]7.5733[/C][C]0.0628[/C][C]0.0846[/C][C]0.3323[/C][C]0.391[/C][/ROW]
[ROW][C]105[/C][C]6.9[/C][C]6.3666[/C][C]5.0432[/C][C]7.6899[/C][C]0.2147[/C][C]0.0834[/C][C]0.4803[/C][C]0.4217[/C][/ROW]
[ROW][C]106[/C][C]6.1[/C][C]6.4569[/C][C]5.0576[/C][C]7.8562[/C][C]0.3086[/C][C]0.2674[/C][C]0.587[/C][C]0.4759[/C][/ROW]
[ROW][C]107[/C][C]5.8[/C][C]6.4108[/C][C]4.9464[/C][C]7.8753[/C][C]0.2068[/C][C]0.6613[/C][C]0.6111[/C][C]0.4525[/C][/ROW]
[ROW][C]108[/C][C]6.2[/C][C]6.5388[/C][C]5.0222[/C][C]8.0553[/C][C]0.3308[/C][C]0.8302[/C][C]0.52[/C][C]0.52[/C][/ROW]
[ROW][C]109[/C][C]7.1[/C][C]6.6387[/C][C]5.0458[/C][C]8.2316[/C][C]0.2851[/C][C]0.7053[/C][C]0.4213[/C][C]0.5677[/C][/ROW]
[ROW][C]110[/C][C]7.7[/C][C]6.6098[/C][C]4.9258[/C][C]8.2939[/C][C]0.1023[/C][C]0.2842[/C][C]0.4124[/C][C]0.5509[/C][/ROW]
[ROW][C]111[/C][C]8[/C][C]6.4904[/C][C]4.7087[/C][C]8.2721[/C][C]0.0484[/C][C]0.0917[/C][C]0.5396[/C][C]0.4958[/C][/ROW]
[ROW][C]112[/C][C]7.8[/C][C]6.394[/C][C]4.5264[/C][C]8.2616[/C][C]0.07[/C][C]0.046[/C][C]0.6212[/C][C]0.4557[/C][/ROW]
[ROW][C]113[/C][C]7.4[/C][C]6.2157[/C][C]4.2768[/C][C]8.1545[/C][C]0.1156[/C][C]0.0546[/C][C]0.6628[/C][C]0.3869[/C][/ROW]
[ROW][C]114[/C][C]7.4[/C][C]5.9411[/C][C]3.9415[/C][C]7.9408[/C][C]0.0764[/C][C]0.0764[/C][C]0.4381[/C][C]0.2919[/C][/ROW]
[ROW][C]115[/C][C]7.7[/C][C]6.2151[/C][C]4.1576[/C][C]8.2727[/C][C]0.0786[/C][C]0.1295[/C][C]0.1741[/C][C]0.3931[/C][/ROW]
[ROW][C]116[/C][C]7.8[/C][C]6.2684[/C][C]4.1509[/C][C]8.3859[/C][C]0.0781[/C][C]0.0926[/C][C]0.1698[/C][C]0.4151[/C][/ROW]
[ROW][C]117[/C][C]7.8[/C][C]6.33[/C][C]4.1493[/C][C]8.5108[/C][C]0.0932[/C][C]0.0932[/C][C]0.3042[/C][C]0.4393[/C][/ROW]
[ROW][C]118[/C][C]8[/C][C]6.4649[/C][C]4.2197[/C][C]8.71[/C][C]0.0901[/C][C]0.1219[/C][C]0.625[/C][C]0.4878[/C][/ROW]
[ROW][C]119[/C][C]8.1[/C][C]6.4569[/C][C]4.1494[/C][C]8.7644[/C][C]0.0814[/C][C]0.095[/C][C]0.7116[/C][C]0.4854[/C][/ROW]
[ROW][C]120[/C][C]8.4[/C][C]6.573[/C][C]4.2072[/C][C]8.9388[/C][C]0.0651[/C][C]0.1029[/C][C]0.6213[/C][C]0.5241[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113095&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113095&T=1

As an alternative you can also use a QR Code:

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

Univariate ARIMA Extrapolation Forecast
time	Y[t]	F[t]	95% LB	95% UB	p-value(H0: Y[t] = F[t])	P(F[t]>Y[t-1])	P(F[t]>Y[t-s])	P(F[t]>Y[96])
84	7.1	-	-	-	-	-	-	-
85	7.2	-	-	-	-	-	-	-
86	7.1	-	-	-	-	-	-	-
87	6.9	-	-	-	-	-	-	-
88	7	-	-	-	-	-	-	-
89	6.8	-	-	-	-	-	-	-
90	6.4	-	-	-	-	-	-	-
91	6.7	-	-	-	-	-	-	-
92	6.6	-	-	-	-	-	-	-
93	6.4	-	-	-	-	-	-	-
94	6.3	-	-	-	-	-	-	-
95	6.2	-	-	-	-	-	-	-
96	6.5	-	-	-	-	-	-	-
97	6.8	6.779	6.405	7.1529	0.4561	0.9281	0.0137	0.9281
98	6.8	6.8373	6.1514	7.5231	0.4576	0.5424	0.2264	0.8324
99	6.4	6.6717	5.7389	7.6046	0.284	0.3938	0.3158	0.6409
100	6.1	6.5179	5.456	7.5798	0.2203	0.5861	0.1868	0.5131
101	5.8	6.2556	5.1338	7.3773	0.213	0.6071	0.1707	0.3347
102	6.1	5.9389	4.783	7.0949	0.3924	0.5931	0.2172	0.1707
103	7.2	6.25	5.0564	7.4436	0.0594	0.5973	0.23	0.3407
104	7.3	6.3236	5.074	7.5733	0.0628	0.0846	0.3323	0.391
105	6.9	6.3666	5.0432	7.6899	0.2147	0.0834	0.4803	0.4217
106	6.1	6.4569	5.0576	7.8562	0.3086	0.2674	0.587	0.4759
107	5.8	6.4108	4.9464	7.8753	0.2068	0.6613	0.6111	0.4525
108	6.2	6.5388	5.0222	8.0553	0.3308	0.8302	0.52	0.52
109	7.1	6.6387	5.0458	8.2316	0.2851	0.7053	0.4213	0.5677
110	7.7	6.6098	4.9258	8.2939	0.1023	0.2842	0.4124	0.5509
111	8	6.4904	4.7087	8.2721	0.0484	0.0917	0.5396	0.4958
112	7.8	6.394	4.5264	8.2616	0.07	0.046	0.6212	0.4557
113	7.4	6.2157	4.2768	8.1545	0.1156	0.0546	0.6628	0.3869
114	7.4	5.9411	3.9415	7.9408	0.0764	0.0764	0.4381	0.2919
115	7.7	6.2151	4.1576	8.2727	0.0786	0.1295	0.1741	0.3931
116	7.8	6.2684	4.1509	8.3859	0.0781	0.0926	0.1698	0.4151
117	7.8	6.33	4.1493	8.5108	0.0932	0.0932	0.3042	0.4393
118	8	6.4649	4.2197	8.71	0.0901	0.1219	0.625	0.4878
119	8.1	6.4569	4.1494	8.7644	0.0814	0.095	0.7116	0.4854
120	8.4	6.573	4.2072	8.9388	0.0651	0.1029	0.6213	0.5241

Univariate ARIMA Extrapolation Forecast Performance
time	% S.E.	PE	MAPE	Sq.E	MSE	RMSE
97	0.0281	0.0031	0	4e-04	0	0
98	0.0512	-0.0054	0.0043	0.0014	9e-04	0.0302
99	0.0713	-0.0407	0.0164	0.0738	0.0252	0.1588
100	0.0831	-0.0641	0.0283	0.1746	0.0626	0.2501
101	0.0915	-0.0728	0.0372	0.2075	0.0916	0.3026
102	0.0993	0.0271	0.0356	0.0259	0.0806	0.2839
103	0.0974	0.152	0.0522	0.9025	0.198	0.445
104	0.1008	0.1544	0.065	0.9533	0.2924	0.5408
105	0.106	0.0838	0.0671	0.2846	0.2916	0.54
106	0.1106	-0.0553	0.0659	0.1274	0.2752	0.5245
107	0.1165	-0.0953	0.0686	0.3731	0.2841	0.533
108	0.1183	-0.0518	0.0672	0.1148	0.27	0.5196
109	0.1224	0.0695	0.0673	0.2128	0.2656	0.5153
110	0.13	0.1649	0.0743	1.1885	0.3315	0.5757
111	0.1401	0.2326	0.0849	2.2788	0.4613	0.6792
112	0.149	0.2199	0.0933	1.9768	0.556	0.7457
113	0.1591	0.1905	0.099	1.4027	0.6058	0.7783
114	0.1717	0.2456	0.1072	2.1284	0.6904	0.8309
115	0.1689	0.2389	0.1141	2.2049	0.7701	0.8776
116	0.1723	0.2443	0.1206	2.3458	0.8489	0.9214
117	0.1758	0.2322	0.1259	2.1608	0.9114	0.9547
118	0.1772	0.2375	0.131	2.3567	0.9771	0.9885
119	0.1823	0.2545	0.1364	2.6997	1.052	1.0257
120	0.1836	0.278	0.1423	3.338	1.1472	1.0711

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
97 & 0.0281 & 0.0031 & 0 & 4e-04 & 0 & 0 \tabularnewline
98 & 0.0512 & -0.0054 & 0.0043 & 0.0014 & 9e-04 & 0.0302 \tabularnewline
99 & 0.0713 & -0.0407 & 0.0164 & 0.0738 & 0.0252 & 0.1588 \tabularnewline
100 & 0.0831 & -0.0641 & 0.0283 & 0.1746 & 0.0626 & 0.2501 \tabularnewline
101 & 0.0915 & -0.0728 & 0.0372 & 0.2075 & 0.0916 & 0.3026 \tabularnewline
102 & 0.0993 & 0.0271 & 0.0356 & 0.0259 & 0.0806 & 0.2839 \tabularnewline
103 & 0.0974 & 0.152 & 0.0522 & 0.9025 & 0.198 & 0.445 \tabularnewline
104 & 0.1008 & 0.1544 & 0.065 & 0.9533 & 0.2924 & 0.5408 \tabularnewline
105 & 0.106 & 0.0838 & 0.0671 & 0.2846 & 0.2916 & 0.54 \tabularnewline
106 & 0.1106 & -0.0553 & 0.0659 & 0.1274 & 0.2752 & 0.5245 \tabularnewline
107 & 0.1165 & -0.0953 & 0.0686 & 0.3731 & 0.2841 & 0.533 \tabularnewline
108 & 0.1183 & -0.0518 & 0.0672 & 0.1148 & 0.27 & 0.5196 \tabularnewline
109 & 0.1224 & 0.0695 & 0.0673 & 0.2128 & 0.2656 & 0.5153 \tabularnewline
110 & 0.13 & 0.1649 & 0.0743 & 1.1885 & 0.3315 & 0.5757 \tabularnewline
111 & 0.1401 & 0.2326 & 0.0849 & 2.2788 & 0.4613 & 0.6792 \tabularnewline
112 & 0.149 & 0.2199 & 0.0933 & 1.9768 & 0.556 & 0.7457 \tabularnewline
113 & 0.1591 & 0.1905 & 0.099 & 1.4027 & 0.6058 & 0.7783 \tabularnewline
114 & 0.1717 & 0.2456 & 0.1072 & 2.1284 & 0.6904 & 0.8309 \tabularnewline
115 & 0.1689 & 0.2389 & 0.1141 & 2.2049 & 0.7701 & 0.8776 \tabularnewline
116 & 0.1723 & 0.2443 & 0.1206 & 2.3458 & 0.8489 & 0.9214 \tabularnewline
117 & 0.1758 & 0.2322 & 0.1259 & 2.1608 & 0.9114 & 0.9547 \tabularnewline
118 & 0.1772 & 0.2375 & 0.131 & 2.3567 & 0.9771 & 0.9885 \tabularnewline
119 & 0.1823 & 0.2545 & 0.1364 & 2.6997 & 1.052 & 1.0257 \tabularnewline
120 & 0.1836 & 0.278 & 0.1423 & 3.338 & 1.1472 & 1.0711 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113095&T=2

[TABLE]
[ROW][C]Univariate ARIMA Extrapolation Forecast Performance[/C][/ROW]
[ROW][C]time[/C][C]% S.E.[/C][C]PE[/C][C]MAPE[/C][C]Sq.E[/C][C]MSE[/C][C]RMSE[/C][/ROW]
[ROW][C]97[/C][C]0.0281[/C][C]0.0031[/C][C]0[/C][C]4e-04[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]98[/C][C]0.0512[/C][C]-0.0054[/C][C]0.0043[/C][C]0.0014[/C][C]9e-04[/C][C]0.0302[/C][/ROW]
[ROW][C]99[/C][C]0.0713[/C][C]-0.0407[/C][C]0.0164[/C][C]0.0738[/C][C]0.0252[/C][C]0.1588[/C][/ROW]
[ROW][C]100[/C][C]0.0831[/C][C]-0.0641[/C][C]0.0283[/C][C]0.1746[/C][C]0.0626[/C][C]0.2501[/C][/ROW]
[ROW][C]101[/C][C]0.0915[/C][C]-0.0728[/C][C]0.0372[/C][C]0.2075[/C][C]0.0916[/C][C]0.3026[/C][/ROW]
[ROW][C]102[/C][C]0.0993[/C][C]0.0271[/C][C]0.0356[/C][C]0.0259[/C][C]0.0806[/C][C]0.2839[/C][/ROW]
[ROW][C]103[/C][C]0.0974[/C][C]0.152[/C][C]0.0522[/C][C]0.9025[/C][C]0.198[/C][C]0.445[/C][/ROW]
[ROW][C]104[/C][C]0.1008[/C][C]0.1544[/C][C]0.065[/C][C]0.9533[/C][C]0.2924[/C][C]0.5408[/C][/ROW]
[ROW][C]105[/C][C]0.106[/C][C]0.0838[/C][C]0.0671[/C][C]0.2846[/C][C]0.2916[/C][C]0.54[/C][/ROW]
[ROW][C]106[/C][C]0.1106[/C][C]-0.0553[/C][C]0.0659[/C][C]0.1274[/C][C]0.2752[/C][C]0.5245[/C][/ROW]
[ROW][C]107[/C][C]0.1165[/C][C]-0.0953[/C][C]0.0686[/C][C]0.3731[/C][C]0.2841[/C][C]0.533[/C][/ROW]
[ROW][C]108[/C][C]0.1183[/C][C]-0.0518[/C][C]0.0672[/C][C]0.1148[/C][C]0.27[/C][C]0.5196[/C][/ROW]
[ROW][C]109[/C][C]0.1224[/C][C]0.0695[/C][C]0.0673[/C][C]0.2128[/C][C]0.2656[/C][C]0.5153[/C][/ROW]
[ROW][C]110[/C][C]0.13[/C][C]0.1649[/C][C]0.0743[/C][C]1.1885[/C][C]0.3315[/C][C]0.5757[/C][/ROW]
[ROW][C]111[/C][C]0.1401[/C][C]0.2326[/C][C]0.0849[/C][C]2.2788[/C][C]0.4613[/C][C]0.6792[/C][/ROW]
[ROW][C]112[/C][C]0.149[/C][C]0.2199[/C][C]0.0933[/C][C]1.9768[/C][C]0.556[/C][C]0.7457[/C][/ROW]
[ROW][C]113[/C][C]0.1591[/C][C]0.1905[/C][C]0.099[/C][C]1.4027[/C][C]0.6058[/C][C]0.7783[/C][/ROW]
[ROW][C]114[/C][C]0.1717[/C][C]0.2456[/C][C]0.1072[/C][C]2.1284[/C][C]0.6904[/C][C]0.8309[/C][/ROW]
[ROW][C]115[/C][C]0.1689[/C][C]0.2389[/C][C]0.1141[/C][C]2.2049[/C][C]0.7701[/C][C]0.8776[/C][/ROW]
[ROW][C]116[/C][C]0.1723[/C][C]0.2443[/C][C]0.1206[/C][C]2.3458[/C][C]0.8489[/C][C]0.9214[/C][/ROW]
[ROW][C]117[/C][C]0.1758[/C][C]0.2322[/C][C]0.1259[/C][C]2.1608[/C][C]0.9114[/C][C]0.9547[/C][/ROW]
[ROW][C]118[/C][C]0.1772[/C][C]0.2375[/C][C]0.131[/C][C]2.3567[/C][C]0.9771[/C][C]0.9885[/C][/ROW]
[ROW][C]119[/C][C]0.1823[/C][C]0.2545[/C][C]0.1364[/C][C]2.6997[/C][C]1.052[/C][C]1.0257[/C][/ROW]
[ROW][C]120[/C][C]0.1836[/C][C]0.278[/C][C]0.1423[/C][C]3.338[/C][C]1.1472[/C][C]1.0711[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113095&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113095&T=2

As an alternative you can also use a QR Code:

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

Univariate ARIMA Extrapolation Forecast Performance
time	% S.E.	PE	MAPE	Sq.E	MSE	RMSE
97	0.0281	0.0031	0	4e-04	0	0
98	0.0512	-0.0054	0.0043	0.0014	9e-04	0.0302
99	0.0713	-0.0407	0.0164	0.0738	0.0252	0.1588
100	0.0831	-0.0641	0.0283	0.1746	0.0626	0.2501
101	0.0915	-0.0728	0.0372	0.2075	0.0916	0.3026
102	0.0993	0.0271	0.0356	0.0259	0.0806	0.2839
103	0.0974	0.152	0.0522	0.9025	0.198	0.445
104	0.1008	0.1544	0.065	0.9533	0.2924	0.5408
105	0.106	0.0838	0.0671	0.2846	0.2916	0.54
106	0.1106	-0.0553	0.0659	0.1274	0.2752	0.5245
107	0.1165	-0.0953	0.0686	0.3731	0.2841	0.533
108	0.1183	-0.0518	0.0672	0.1148	0.27	0.5196
109	0.1224	0.0695	0.0673	0.2128	0.2656	0.5153
110	0.13	0.1649	0.0743	1.1885	0.3315	0.5757
111	0.1401	0.2326	0.0849	2.2788	0.4613	0.6792
112	0.149	0.2199	0.0933	1.9768	0.556	0.7457
113	0.1591	0.1905	0.099	1.4027	0.6058	0.7783
114	0.1717	0.2456	0.1072	2.1284	0.6904	0.8309
115	0.1689	0.2389	0.1141	2.2049	0.7701	0.8776
116	0.1723	0.2443	0.1206	2.3458	0.8489	0.9214
117	0.1758	0.2322	0.1259	2.1608	0.9114	0.9547
118	0.1772	0.2375	0.131	2.3567	0.9771	0.9885
119	0.1823	0.2545	0.1364	2.6997	1.052	1.0257
120	0.1836	0.278	0.1423	3.338	1.1472	1.0711

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 24 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 3 ; par7 = 0 ; par8 = 2 ; par9 = 1 ; par10 = FALSE ;

Parameters (R input):

par1 = 24 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 3 ; par7 = 0 ; par8 = 2 ; par9 = 1 ; par10 = FALSE ;

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

par1 <- as.numeric(par1) #cut off periods
par2 <- as.numeric(par2) #lambda
par3 <- as.numeric(par3) #degree of non-seasonal differencing
par4 <- as.numeric(par4) #degree of seasonal differencing
par5 <- as.numeric(par5) #seasonal period
par6 <- as.numeric(par6) #p
par7 <- as.numeric(par7) #q
par8 <- as.numeric(par8) #P
par9 <- as.numeric(par9) #Q
if (par10 == 'TRUE') par10 <- TRUE
if (par10 == 'FALSE') par10 <- FALSE
if (par2 == 0) x <- log(x)
if (par2 != 0) x <- x^par2
lx <- length(x)
first <- lx - 2*par1
nx <- lx - par1
nx1 <- nx + 1
fx <- lx - nx
if (fx < 1) {
fx <- par5
nx1 <- lx + fx - 1
first <- lx - 2*fx
}
first <- 1
if (fx < 3) fx <- round(lx/10,0)
(arima.out <- arima(x[1:nx], order=c(par6,par3,par7), seasonal=list(order=c(par8,par4,par9), period=par5), include.mean=par10, method='ML'))
(forecast <- predict(arima.out,par1))
(lb <- forecast$pred - 1.96 * forecast$se)
(ub <- forecast$pred + 1.96 * forecast$se)
if (par2 == 0) {
x <- exp(x)
forecast$pred <- exp(forecast$pred)
lb <- exp(lb)
ub <- exp(ub)
}
if (par2 != 0) {
x <- x^(1/par2)
forecast$pred <- forecast$pred^(1/par2)
lb <- lb^(1/par2)
ub <- ub^(1/par2)
}
if (par2 < 0) {
olb <- lb
lb <- ub
ub <- olb
}
(actandfor <- c(x[1:nx], forecast$pred))
(perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
bitmap(file='test1.png')
opar <- par(mar=c(4,4,2,2),las=1)
ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
plot(x,ylim=ylim,type='n',xlim=c(first,lx))
usr <- par('usr')
rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
abline(h= (-3:3)*2 , col ='gray', lty =3)
polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
lines(nx1:lx, lb , lty=2)
lines(nx1:lx, ub , lty=2)
lines(x, lwd=2)
lines(nx1:lx, forecast$pred , lwd=2 , col ='white')
box()
par(opar)
dev.off()
prob.dec <- array(NA, dim=fx)
prob.sdec <- array(NA, dim=fx)
prob.ldec <- array(NA, dim=fx)
prob.pval <- array(NA, dim=fx)
perf.pe <- array(0, dim=fx)
perf.mape <- array(0, dim=fx)
perf.mape1 <- array(0, dim=fx)
perf.se <- array(0, dim=fx)
perf.mse <- array(0, dim=fx)
perf.mse1 <- array(0, dim=fx)
perf.rmse <- array(0, dim=fx)
for (i in 1:fx) {
locSD <- (ub[i] - forecast$pred[i]) / 1.96
perf.pe[i] = (x[nx+i] - forecast$pred[i]) / forecast$pred[i]
perf.se[i] = (x[nx+i] - forecast$pred[i])^2
prob.dec[i] = pnorm((x[nx+i-1] - forecast$pred[i]) / locSD)
prob.sdec[i] = pnorm((x[nx+i-par5] - forecast$pred[i]) / locSD)
prob.ldec[i] = pnorm((x[nx] - forecast$pred[i]) / locSD)
prob.pval[i] = pnorm(abs(x[nx+i] - forecast$pred[i]) / locSD)
}
perf.mape[1] = abs(perf.pe[1])
perf.mse[1] = abs(perf.se[1])
for (i in 2:fx) {
perf.mape[i] = perf.mape[i-1] + abs(perf.pe[i])
perf.mape1[i] = perf.mape[i] / i
perf.mse[i] = perf.mse[i-1] + perf.se[i]
perf.mse1[i] = perf.mse[i] / i
}
perf.rmse = sqrt(perf.mse1)
bitmap(file='test2.png')
plot(forecast$pred, pch=19, type='b',main='ARIMA Extrapolation Forecast', ylab='Forecast and 95% CI', xlab='time',ylim=c(min(lb),max(ub)))
dum <- forecast$pred
dum[1:par1] <- x[(nx+1):lx]
lines(dum, lty=1)
lines(ub,lty=3)
lines(lb,lty=3)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Univariate ARIMA Extrapolation Forecast',9,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'time',1,header=TRUE)
a<-table.element(a,'Y[t]',1,header=TRUE)
a<-table.element(a,'F[t]',1,header=TRUE)
a<-table.element(a,'95% LB',1,header=TRUE)
a<-table.element(a,'95% UB',1,header=TRUE)
a<-table.element(a,'p-value
(H0: Y[t] = F[t])',1,header=TRUE)
a<-table.element(a,'P(F[t]>Y[t-1])',1,header=TRUE)
a<-table.element(a,'P(F[t]>Y[t-s])',1,header=TRUE)
mylab <- paste('P(F[t]>Y[',nx,sep='')
mylab <- paste(mylab,'])',sep='')
a<-table.element(a,mylab,1,header=TRUE)
a<-table.row.end(a)
for (i in (nx-par5):nx) {
a<-table.row.start(a)
a<-table.element(a,i,header=TRUE)
a<-table.element(a,x[i])
a<-table.element(a,'-')
a<-table.element(a,'-')
a<-table.element(a,'-')
a<-table.element(a,'-')
a<-table.element(a,'-')
a<-table.element(a,'-')
a<-table.element(a,'-')
a<-table.row.end(a)
}
for (i in 1:fx) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,round(x[nx+i],4))
a<-table.element(a,round(forecast$pred[i],4))
a<-table.element(a,round(lb[i],4))
a<-table.element(a,round(ub[i],4))
a<-table.element(a,round((1-prob.pval[i]),4))
a<-table.element(a,round((1-prob.dec[i]),4))
a<-table.element(a,round((1-prob.sdec[i]),4))
a<-table.element(a,round((1-prob.ldec[i]),4))
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,'Univariate ARIMA Extrapolation Forecast Performance',7,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'time',1,header=TRUE)
a<-table.element(a,'% S.E.',1,header=TRUE)
a<-table.element(a,'PE',1,header=TRUE)
a<-table.element(a,'MAPE',1,header=TRUE)
a<-table.element(a,'Sq.E',1,header=TRUE)
a<-table.element(a,'MSE',1,header=TRUE)
a<-table.element(a,'RMSE',1,header=TRUE)
a<-table.row.end(a)
for (i in 1:fx) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,round(perc.se[i],4))
a<-table.element(a,round(perf.pe[i],4))
a<-table.element(a,round(perf.mape1[i],4))
a<-table.element(a,round(perf.se[i],4))
a<-table.element(a,round(perf.mse1[i],4))
a<-table.element(a,round(perf.rmse[i],4))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code