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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

Fri, 24 Dec 2010 14:15:31 +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/24/t1293200091qu2ox902amg4154.htm/, Retrieved Tue, 30 Apr 2024 06:07:01 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=114985, Retrieved Tue, 30 Apr 2024 06:07:01 +0000

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Original text written by user:

Prijsverandering in België

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

148

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

F     [Univariate Data Series] [Airline data] [2007-10-18 09:58:47] [42daae401fd3def69a25014f2252b4c2]
F RMPD  [Cross Correlation Function] [Q7 - zonder trans...] [2008-12-01 20:04:13] [299afd6311e4c20059ea2f05c8dd029d]
F RM D    [Variance Reduction Matrix] [Q8] [2008-12-01 20:20:44] [299afd6311e4c20059ea2f05c8dd029d]
F    D      [Variance Reduction Matrix] [Q8 - 2] [2008-12-01 20:25:07] [299afd6311e4c20059ea2f05c8dd029d]
F RM D        [Standard Deviation-Mean Plot] [Deel 2: Step 1] [2008-12-08 20:09:35] [299afd6311e4c20059ea2f05c8dd029d]
-    D          [Standard Deviation-Mean Plot] [Totale Uitvoer - SMP] [2008-12-17 15:57:12] [299afd6311e4c20059ea2f05c8dd029d]
- RMPD              [ARIMA Forecasting] [ARIMA Forecasting] [2010-12-24 14:15:31] [fba9c6aa004af59d8497d682e70ddad5] [Current]
- RMPD                [Standard Deviation-Mean Plot] [Standard Deviatio...] [2010-12-27 09:50:14] [9f313cc7203314d73bf17d2b325aee79] 
- RMPD                [Variance Reduction Matrix] [Variance Reductio...] [2010-12-27 09:53:20] [9f313cc7203314d73bf17d2b325aee79] 
- RMPD                [Spectral Analysis] [Spectral Analysis] [2010-12-27 10:01:30] [9f313cc7203314d73bf17d2b325aee79] 
- RMPD                [Spectral Analysis] [Spectral Analysis] [2010-12-27 10:03:10] [9f313cc7203314d73bf17d2b325aee79] 
- RMPD                [Classical Decomposition] [Classical Decompo...] [2010-12-27 10:06:19] [9f313cc7203314d73bf17d2b325aee79] 
- RMPD                [Decomposition by Loess] [Decomposition by ...] [2010-12-27 10:08:53] [9f313cc7203314d73bf17d2b325aee79] 
- RMPD                [ARIMA Backward Selection] [ARIMA Backward Se...] [2010-12-27 10:15:12] [9f313cc7203314d73bf17d2b325aee79] 
-   PD                [ARIMA Forecasting] [ARIMA Forecasting] [2010-12-27 10:20:40] [9f313cc7203314d73bf17d2b325aee79] 

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Dataseries X:

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Histogram

Boxplots

3.4
3.4
3.4
-3.5
-3.5
-3.5
-8.3
-8.3
-8.3
-16.7
-16.7
-16.7
-11.6
-11.6
-11.6
-8.4
-8.4
-8.4
-8.6
-8.6
-8.6
0.6
0.6
0.6
-1.5
-1.5
-1.5
9.3
9.3
9.3
2.0
2.0
2.0
-5.5
-5.5
-5.5
4.0
4.0
4.0
-0.5
-0.5
-0.5
10.9
10.9
10.9
19.4
19.4
19.4
13.9
13.9
13.9
10.6
10.6
10.6
4.8
4.8
4.8
4.7
4.7
4.7
-3.9
-3.9
-3.9
-0.2
-0.2
-0.2

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114985&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114985&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114985&T=0

As an alternative you can also use a QR Code:

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

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[51])
39	4	-	-	-	-	-	-	-
40	-0.5	-	-	-	-	-	-	-
41	-0.5	-	-	-	-	-	-	-
42	-0.5	-	-	-	-	-	-	-
43	10.9	-	-	-	-	-	-	-
44	10.9	-	-	-	-	-	-	-
45	10.9	-	-	-	-	-	-	-
46	19.4	-	-	-	-	-	-	-
47	19.4	-	-	-	-	-	-	-
48	19.4	-	-	-	-	-	-	-
49	13.9	-	-	-	-	-	-	-
50	13.9	-	-	-	-	-	-	-
51	13.9	-	-	-	-	-	-	-
52	10.6	11.12	5.1341	17.106	0.4324	0.1813	0.9999	0.1813
53	10.6	11.12	2.6546	19.5854	0.4521	0.5479	0.9964	0.2599
54	10.6	11.12	0.752	21.488	0.4608	0.5392	0.986	0.2996
55	4.8	7.42	-4.5519	19.3919	0.334	0.3013	0.2844	0.1444
56	4.8	7.42	-5.965	20.805	0.3506	0.6494	0.3052	0.1713
57	4.8	7.42	-7.2425	22.0825	0.3631	0.6369	0.3209	0.1932
58	4.7	3.12	-12.7173	18.9573	0.4225	0.4176	0.022	0.0911
59	4.7	3.12	-13.8108	20.0508	0.4274	0.4274	0.0297	0.106
60	4.7	3.12	-14.8379	21.0779	0.4315	0.4315	0.0378	0.1197
61	-3.9	1.64	-17.2892	20.5693	0.2831	0.3757	0.1021	0.1021
62	-3.9	1.64	-18.1881	21.4681	0.292	0.708	0.1128	0.1128
63	-3.9	1.64	-19.0479	22.3279	0.2998	0.7002	0.1227	0.1227
64	-0.2	1.64	-19.0479	22.3279	0.4308	0.7002	0.198	0.1227
65	-0.2	1.64	-19.0479	22.3279	0.4308	0.5692	0.198	0.1227
66	-0.2	1.64	-19.0479	22.3279	0.4308	0.5692	0.198	0.1227

\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[51]) \tabularnewline
39 & 4 & - & - & - & - & - & - & - \tabularnewline
40 & -0.5 & - & - & - & - & - & - & - \tabularnewline
41 & -0.5 & - & - & - & - & - & - & - \tabularnewline
42 & -0.5 & - & - & - & - & - & - & - \tabularnewline
43 & 10.9 & - & - & - & - & - & - & - \tabularnewline
44 & 10.9 & - & - & - & - & - & - & - \tabularnewline
45 & 10.9 & - & - & - & - & - & - & - \tabularnewline
46 & 19.4 & - & - & - & - & - & - & - \tabularnewline
47 & 19.4 & - & - & - & - & - & - & - \tabularnewline
48 & 19.4 & - & - & - & - & - & - & - \tabularnewline
49 & 13.9 & - & - & - & - & - & - & - \tabularnewline
50 & 13.9 & - & - & - & - & - & - & - \tabularnewline
51 & 13.9 & - & - & - & - & - & - & - \tabularnewline
52 & 10.6 & 11.12 & 5.1341 & 17.106 & 0.4324 & 0.1813 & 0.9999 & 0.1813 \tabularnewline
53 & 10.6 & 11.12 & 2.6546 & 19.5854 & 0.4521 & 0.5479 & 0.9964 & 0.2599 \tabularnewline
54 & 10.6 & 11.12 & 0.752 & 21.488 & 0.4608 & 0.5392 & 0.986 & 0.2996 \tabularnewline
55 & 4.8 & 7.42 & -4.5519 & 19.3919 & 0.334 & 0.3013 & 0.2844 & 0.1444 \tabularnewline
56 & 4.8 & 7.42 & -5.965 & 20.805 & 0.3506 & 0.6494 & 0.3052 & 0.1713 \tabularnewline
57 & 4.8 & 7.42 & -7.2425 & 22.0825 & 0.3631 & 0.6369 & 0.3209 & 0.1932 \tabularnewline
58 & 4.7 & 3.12 & -12.7173 & 18.9573 & 0.4225 & 0.4176 & 0.022 & 0.0911 \tabularnewline
59 & 4.7 & 3.12 & -13.8108 & 20.0508 & 0.4274 & 0.4274 & 0.0297 & 0.106 \tabularnewline
60 & 4.7 & 3.12 & -14.8379 & 21.0779 & 0.4315 & 0.4315 & 0.0378 & 0.1197 \tabularnewline
61 & -3.9 & 1.64 & -17.2892 & 20.5693 & 0.2831 & 0.3757 & 0.1021 & 0.1021 \tabularnewline
62 & -3.9 & 1.64 & -18.1881 & 21.4681 & 0.292 & 0.708 & 0.1128 & 0.1128 \tabularnewline
63 & -3.9 & 1.64 & -19.0479 & 22.3279 & 0.2998 & 0.7002 & 0.1227 & 0.1227 \tabularnewline
64 & -0.2 & 1.64 & -19.0479 & 22.3279 & 0.4308 & 0.7002 & 0.198 & 0.1227 \tabularnewline
65 & -0.2 & 1.64 & -19.0479 & 22.3279 & 0.4308 & 0.5692 & 0.198 & 0.1227 \tabularnewline
66 & -0.2 & 1.64 & -19.0479 & 22.3279 & 0.4308 & 0.5692 & 0.198 & 0.1227 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114985&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[51])[/C][/ROW]
[ROW][C]39[/C][C]4[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]40[/C][C]-0.5[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]41[/C][C]-0.5[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]42[/C][C]-0.5[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]43[/C][C]10.9[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]44[/C][C]10.9[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]45[/C][C]10.9[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]46[/C][C]19.4[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]47[/C][C]19.4[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]48[/C][C]19.4[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]49[/C][C]13.9[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]50[/C][C]13.9[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]51[/C][C]13.9[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]52[/C][C]10.6[/C][C]11.12[/C][C]5.1341[/C][C]17.106[/C][C]0.4324[/C][C]0.1813[/C][C]0.9999[/C][C]0.1813[/C][/ROW]
[ROW][C]53[/C][C]10.6[/C][C]11.12[/C][C]2.6546[/C][C]19.5854[/C][C]0.4521[/C][C]0.5479[/C][C]0.9964[/C][C]0.2599[/C][/ROW]
[ROW][C]54[/C][C]10.6[/C][C]11.12[/C][C]0.752[/C][C]21.488[/C][C]0.4608[/C][C]0.5392[/C][C]0.986[/C][C]0.2996[/C][/ROW]
[ROW][C]55[/C][C]4.8[/C][C]7.42[/C][C]-4.5519[/C][C]19.3919[/C][C]0.334[/C][C]0.3013[/C][C]0.2844[/C][C]0.1444[/C][/ROW]
[ROW][C]56[/C][C]4.8[/C][C]7.42[/C][C]-5.965[/C][C]20.805[/C][C]0.3506[/C][C]0.6494[/C][C]0.3052[/C][C]0.1713[/C][/ROW]
[ROW][C]57[/C][C]4.8[/C][C]7.42[/C][C]-7.2425[/C][C]22.0825[/C][C]0.3631[/C][C]0.6369[/C][C]0.3209[/C][C]0.1932[/C][/ROW]
[ROW][C]58[/C][C]4.7[/C][C]3.12[/C][C]-12.7173[/C][C]18.9573[/C][C]0.4225[/C][C]0.4176[/C][C]0.022[/C][C]0.0911[/C][/ROW]
[ROW][C]59[/C][C]4.7[/C][C]3.12[/C][C]-13.8108[/C][C]20.0508[/C][C]0.4274[/C][C]0.4274[/C][C]0.0297[/C][C]0.106[/C][/ROW]
[ROW][C]60[/C][C]4.7[/C][C]3.12[/C][C]-14.8379[/C][C]21.0779[/C][C]0.4315[/C][C]0.4315[/C][C]0.0378[/C][C]0.1197[/C][/ROW]
[ROW][C]61[/C][C]-3.9[/C][C]1.64[/C][C]-17.2892[/C][C]20.5693[/C][C]0.2831[/C][C]0.3757[/C][C]0.1021[/C][C]0.1021[/C][/ROW]
[ROW][C]62[/C][C]-3.9[/C][C]1.64[/C][C]-18.1881[/C][C]21.4681[/C][C]0.292[/C][C]0.708[/C][C]0.1128[/C][C]0.1128[/C][/ROW]
[ROW][C]63[/C][C]-3.9[/C][C]1.64[/C][C]-19.0479[/C][C]22.3279[/C][C]0.2998[/C][C]0.7002[/C][C]0.1227[/C][C]0.1227[/C][/ROW]
[ROW][C]64[/C][C]-0.2[/C][C]1.64[/C][C]-19.0479[/C][C]22.3279[/C][C]0.4308[/C][C]0.7002[/C][C]0.198[/C][C]0.1227[/C][/ROW]
[ROW][C]65[/C][C]-0.2[/C][C]1.64[/C][C]-19.0479[/C][C]22.3279[/C][C]0.4308[/C][C]0.5692[/C][C]0.198[/C][C]0.1227[/C][/ROW]
[ROW][C]66[/C][C]-0.2[/C][C]1.64[/C][C]-19.0479[/C][C]22.3279[/C][C]0.4308[/C][C]0.5692[/C][C]0.198[/C][C]0.1227[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114985&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114985&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[51])
39	4	-	-	-	-	-	-	-
40	-0.5	-	-	-	-	-	-	-
41	-0.5	-	-	-	-	-	-	-
42	-0.5	-	-	-	-	-	-	-
43	10.9	-	-	-	-	-	-	-
44	10.9	-	-	-	-	-	-	-
45	10.9	-	-	-	-	-	-	-
46	19.4	-	-	-	-	-	-	-
47	19.4	-	-	-	-	-	-	-
48	19.4	-	-	-	-	-	-	-
49	13.9	-	-	-	-	-	-	-
50	13.9	-	-	-	-	-	-	-
51	13.9	-	-	-	-	-	-	-
52	10.6	11.12	5.1341	17.106	0.4324	0.1813	0.9999	0.1813
53	10.6	11.12	2.6546	19.5854	0.4521	0.5479	0.9964	0.2599
54	10.6	11.12	0.752	21.488	0.4608	0.5392	0.986	0.2996
55	4.8	7.42	-4.5519	19.3919	0.334	0.3013	0.2844	0.1444
56	4.8	7.42	-5.965	20.805	0.3506	0.6494	0.3052	0.1713
57	4.8	7.42	-7.2425	22.0825	0.3631	0.6369	0.3209	0.1932
58	4.7	3.12	-12.7173	18.9573	0.4225	0.4176	0.022	0.0911
59	4.7	3.12	-13.8108	20.0508	0.4274	0.4274	0.0297	0.106
60	4.7	3.12	-14.8379	21.0779	0.4315	0.4315	0.0378	0.1197
61	-3.9	1.64	-17.2892	20.5693	0.2831	0.3757	0.1021	0.1021
62	-3.9	1.64	-18.1881	21.4681	0.292	0.708	0.1128	0.1128
63	-3.9	1.64	-19.0479	22.3279	0.2998	0.7002	0.1227	0.1227
64	-0.2	1.64	-19.0479	22.3279	0.4308	0.7002	0.198	0.1227
65	-0.2	1.64	-19.0479	22.3279	0.4308	0.5692	0.198	0.1227
66	-0.2	1.64	-19.0479	22.3279	0.4308	0.5692	0.198	0.1227

Univariate ARIMA Extrapolation Forecast Performance
time	% S.E.	PE	MAPE	Sq.E	MSE	RMSE
52	0.2746	-0.0468	0	0.2704	0	0
53	0.3884	-0.0468	0.0468	0.2704	0.2704	0.52
54	0.4757	-0.0468	0.0468	0.2704	0.2704	0.52
55	0.8232	-0.3531	0.1233	6.8644	1.9189	1.3852
56	0.9204	-0.3531	0.1693	6.8644	2.908	1.7053
57	1.0082	-0.3531	0.1999	6.8644	3.5674	1.8888
58	2.5898	0.5064	0.2437	2.4964	3.4144	1.8478
59	2.7686	0.5064	0.2766	2.4964	3.2997	1.8165
60	2.9366	0.5064	0.3021	2.4964	3.2104	1.7918
61	5.8889	-3.378	0.6097	30.6917	5.9585	2.441
62	6.1685	-3.378	0.8614	30.6917	8.207	2.8648
63	6.436	-3.378	1.0711	30.6917	10.0807	3.175
64	6.436	-1.122	1.075	3.3856	9.5657	3.0928
65	6.436	-1.122	1.0783	3.3856	9.1243	3.0206
66	6.436	-1.122	1.0813	3.3856	8.7417	2.9566

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
52 & 0.2746 & -0.0468 & 0 & 0.2704 & 0 & 0 \tabularnewline
53 & 0.3884 & -0.0468 & 0.0468 & 0.2704 & 0.2704 & 0.52 \tabularnewline
54 & 0.4757 & -0.0468 & 0.0468 & 0.2704 & 0.2704 & 0.52 \tabularnewline
55 & 0.8232 & -0.3531 & 0.1233 & 6.8644 & 1.9189 & 1.3852 \tabularnewline
56 & 0.9204 & -0.3531 & 0.1693 & 6.8644 & 2.908 & 1.7053 \tabularnewline
57 & 1.0082 & -0.3531 & 0.1999 & 6.8644 & 3.5674 & 1.8888 \tabularnewline
58 & 2.5898 & 0.5064 & 0.2437 & 2.4964 & 3.4144 & 1.8478 \tabularnewline
59 & 2.7686 & 0.5064 & 0.2766 & 2.4964 & 3.2997 & 1.8165 \tabularnewline
60 & 2.9366 & 0.5064 & 0.3021 & 2.4964 & 3.2104 & 1.7918 \tabularnewline
61 & 5.8889 & -3.378 & 0.6097 & 30.6917 & 5.9585 & 2.441 \tabularnewline
62 & 6.1685 & -3.378 & 0.8614 & 30.6917 & 8.207 & 2.8648 \tabularnewline
63 & 6.436 & -3.378 & 1.0711 & 30.6917 & 10.0807 & 3.175 \tabularnewline
64 & 6.436 & -1.122 & 1.075 & 3.3856 & 9.5657 & 3.0928 \tabularnewline
65 & 6.436 & -1.122 & 1.0783 & 3.3856 & 9.1243 & 3.0206 \tabularnewline
66 & 6.436 & -1.122 & 1.0813 & 3.3856 & 8.7417 & 2.9566 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114985&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]52[/C][C]0.2746[/C][C]-0.0468[/C][C]0[/C][C]0.2704[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]53[/C][C]0.3884[/C][C]-0.0468[/C][C]0.0468[/C][C]0.2704[/C][C]0.2704[/C][C]0.52[/C][/ROW]
[ROW][C]54[/C][C]0.4757[/C][C]-0.0468[/C][C]0.0468[/C][C]0.2704[/C][C]0.2704[/C][C]0.52[/C][/ROW]
[ROW][C]55[/C][C]0.8232[/C][C]-0.3531[/C][C]0.1233[/C][C]6.8644[/C][C]1.9189[/C][C]1.3852[/C][/ROW]
[ROW][C]56[/C][C]0.9204[/C][C]-0.3531[/C][C]0.1693[/C][C]6.8644[/C][C]2.908[/C][C]1.7053[/C][/ROW]
[ROW][C]57[/C][C]1.0082[/C][C]-0.3531[/C][C]0.1999[/C][C]6.8644[/C][C]3.5674[/C][C]1.8888[/C][/ROW]
[ROW][C]58[/C][C]2.5898[/C][C]0.5064[/C][C]0.2437[/C][C]2.4964[/C][C]3.4144[/C][C]1.8478[/C][/ROW]
[ROW][C]59[/C][C]2.7686[/C][C]0.5064[/C][C]0.2766[/C][C]2.4964[/C][C]3.2997[/C][C]1.8165[/C][/ROW]
[ROW][C]60[/C][C]2.9366[/C][C]0.5064[/C][C]0.3021[/C][C]2.4964[/C][C]3.2104[/C][C]1.7918[/C][/ROW]
[ROW][C]61[/C][C]5.8889[/C][C]-3.378[/C][C]0.6097[/C][C]30.6917[/C][C]5.9585[/C][C]2.441[/C][/ROW]
[ROW][C]62[/C][C]6.1685[/C][C]-3.378[/C][C]0.8614[/C][C]30.6917[/C][C]8.207[/C][C]2.8648[/C][/ROW]
[ROW][C]63[/C][C]6.436[/C][C]-3.378[/C][C]1.0711[/C][C]30.6917[/C][C]10.0807[/C][C]3.175[/C][/ROW]
[ROW][C]64[/C][C]6.436[/C][C]-1.122[/C][C]1.075[/C][C]3.3856[/C][C]9.5657[/C][C]3.0928[/C][/ROW]
[ROW][C]65[/C][C]6.436[/C][C]-1.122[/C][C]1.0783[/C][C]3.3856[/C][C]9.1243[/C][C]3.0206[/C][/ROW]
[ROW][C]66[/C][C]6.436[/C][C]-1.122[/C][C]1.0813[/C][C]3.3856[/C][C]8.7417[/C][C]2.9566[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114985&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114985&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
52	0.2746	-0.0468	0	0.2704	0	0
53	0.3884	-0.0468	0.0468	0.2704	0.2704	0.52
54	0.4757	-0.0468	0.0468	0.2704	0.2704	0.52
55	0.8232	-0.3531	0.1233	6.8644	1.9189	1.3852
56	0.9204	-0.3531	0.1693	6.8644	2.908	1.7053
57	1.0082	-0.3531	0.1999	6.8644	3.5674	1.8888
58	2.5898	0.5064	0.2437	2.4964	3.4144	1.8478
59	2.7686	0.5064	0.2766	2.4964	3.2997	1.8165
60	2.9366	0.5064	0.3021	2.4964	3.2104	1.7918
61	5.8889	-3.378	0.6097	30.6917	5.9585	2.441
62	6.1685	-3.378	0.8614	30.6917	8.207	2.8648
63	6.436	-3.378	1.0711	30.6917	10.0807	3.175
64	6.436	-1.122	1.075	3.3856	9.5657	3.0928
65	6.436	-1.122	1.0783	3.3856	9.1243	3.0206
66	6.436	-1.122	1.0813	3.3856	8.7417	2.9566

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 15 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 0 ; par7 = 0 ; par8 = 0 ; par9 = 1 ; par10 = FALSE ;

Parameters (R input):

par1 = 15 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 0 ; par7 = 0 ; par8 = 0 ; 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