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R Software Module

rwasp_arimaforecasting.wasp

Title produced by software

ARIMA Forecasting

Date of computation

Wed, 29 Dec 2010 19:15:17 +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/29/t12936500468kgpg542ic00gne.htm/, Retrieved Fri, 03 May 2024 05:50:32 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=117052, Retrieved Fri, 03 May 2024 05:50:32 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

127

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

-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [Univariate Data Series] [Identifying Integ...] [2009-11-22 12:08:06] [b98453cac15ba1066b407e146608df68]
- RMP         [Standard Deviation-Mean Plot] [Births] [2010-11-29 10:52:49] [b98453cac15ba1066b407e146608df68]
- RMP           [ARIMA Forecasting] [Births] [2010-11-29 20:53:49] [b98453cac15ba1066b407e146608df68]
-   PD            [ARIMA Forecasting] [Paper - ARIMA for...] [2010-12-21 13:32:32] [8677c3f87cec9201607d40be65aa9670]
-                     [ARIMA Forecasting] [paper (12)] [2010-12-29 19:15:17] [f420459ea4e1f042529d081e77704a0f] [Current]

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Dataseries X:

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Histogram

Boxplots

9.3
14.2
17.3
23
16.3
18.4
14.2
9.1
5.9
7.2
6.8
8
14.3
14.6
17.5
17.2
17.2
14.1
10.4
6.8
4.1
6.5
6.1
6.3
9.3
16.4
16.1
18
17.6
14
10.5
6.9
2.8
0.7
3.6
6.7
12.5
14.4
16.5
18.7
19.4
15.8
11.3
9.7
2.9
0.1
2.5
6.7
10.3
11.2
17.4
20.5
17
14.2
10.6
6.1

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	14 seconds
R Server	'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 14 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117052&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]14 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117052&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117052&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	14 seconds
R Server	'George Udny Yule' @ 72.249.76.132

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[44])
32	6.9	-	-	-	-	-	-	-
33	2.8	-	-	-	-	-	-	-
34	0.7	-	-	-	-	-	-	-
35	3.6	-	-	-	-	-	-	-
36	6.7	-	-	-	-	-	-	-
37	12.5	-	-	-	-	-	-	-
38	14.4	-	-	-	-	-	-	-
39	16.5	-	-	-	-	-	-	-
40	18.7	-	-	-	-	-	-	-
41	19.4	-	-	-	-	-	-	-
42	15.8	-	-	-	-	-	-	-
43	11.3	-	-	-	-	-	-	-
44	9.7	-	-	-	-	-	-	-
45	2.9	4.824	0.8268	8.8213	0.1727	0.0084	0.8395	0.0084
46	0.1	5.0639	0.861	9.2667	0.0103	0.8435	0.9791	0.0153
47	2.5	5.8665	1.5353	10.1976	0.0638	0.9955	0.8475	0.0414
48	6.7	7.1379	2.7254	11.5503	0.4229	0.9803	0.5771	0.1275
49	10.3	11.198	6.7336	15.6625	0.3467	0.9759	0.2838	0.7446
50	11.2	15.9838	11.4859	20.4816	0.0186	0.9934	0.7549	0.9969
51	17.4	16.6194	12.1	21.1389	0.3675	0.9906	0.5207	0.9987
52	20.5	18.5791	14.0456	23.1125	0.2031	0.6949	0.4791	0.9999
53	17	18.5918	14.0494	23.1343	0.2461	0.2052	0.3637	0.9999
54	14.2	14.9478	10.3994	19.4961	0.3736	0.1882	0.3567	0.9881
55	10.6	10.9873	6.4352	15.5394	0.4338	0.0833	0.4464	0.7103
56	6.1	8.2086	3.654	12.7632	0.1821	0.1517	0.2605	0.2605

\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[44]) \tabularnewline
32 & 6.9 & - & - & - & - & - & - & - \tabularnewline
33 & 2.8 & - & - & - & - & - & - & - \tabularnewline
34 & 0.7 & - & - & - & - & - & - & - \tabularnewline
35 & 3.6 & - & - & - & - & - & - & - \tabularnewline
36 & 6.7 & - & - & - & - & - & - & - \tabularnewline
37 & 12.5 & - & - & - & - & - & - & - \tabularnewline
38 & 14.4 & - & - & - & - & - & - & - \tabularnewline
39 & 16.5 & - & - & - & - & - & - & - \tabularnewline
40 & 18.7 & - & - & - & - & - & - & - \tabularnewline
41 & 19.4 & - & - & - & - & - & - & - \tabularnewline
42 & 15.8 & - & - & - & - & - & - & - \tabularnewline
43 & 11.3 & - & - & - & - & - & - & - \tabularnewline
44 & 9.7 & - & - & - & - & - & - & - \tabularnewline
45 & 2.9 & 4.824 & 0.8268 & 8.8213 & 0.1727 & 0.0084 & 0.8395 & 0.0084 \tabularnewline
46 & 0.1 & 5.0639 & 0.861 & 9.2667 & 0.0103 & 0.8435 & 0.9791 & 0.0153 \tabularnewline
47 & 2.5 & 5.8665 & 1.5353 & 10.1976 & 0.0638 & 0.9955 & 0.8475 & 0.0414 \tabularnewline
48 & 6.7 & 7.1379 & 2.7254 & 11.5503 & 0.4229 & 0.9803 & 0.5771 & 0.1275 \tabularnewline
49 & 10.3 & 11.198 & 6.7336 & 15.6625 & 0.3467 & 0.9759 & 0.2838 & 0.7446 \tabularnewline
50 & 11.2 & 15.9838 & 11.4859 & 20.4816 & 0.0186 & 0.9934 & 0.7549 & 0.9969 \tabularnewline
51 & 17.4 & 16.6194 & 12.1 & 21.1389 & 0.3675 & 0.9906 & 0.5207 & 0.9987 \tabularnewline
52 & 20.5 & 18.5791 & 14.0456 & 23.1125 & 0.2031 & 0.6949 & 0.4791 & 0.9999 \tabularnewline
53 & 17 & 18.5918 & 14.0494 & 23.1343 & 0.2461 & 0.2052 & 0.3637 & 0.9999 \tabularnewline
54 & 14.2 & 14.9478 & 10.3994 & 19.4961 & 0.3736 & 0.1882 & 0.3567 & 0.9881 \tabularnewline
55 & 10.6 & 10.9873 & 6.4352 & 15.5394 & 0.4338 & 0.0833 & 0.4464 & 0.7103 \tabularnewline
56 & 6.1 & 8.2086 & 3.654 & 12.7632 & 0.1821 & 0.1517 & 0.2605 & 0.2605 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117052&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[44])[/C][/ROW]
[ROW][C]32[/C][C]6.9[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]33[/C][C]2.8[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]34[/C][C]0.7[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]35[/C][C]3.6[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]36[/C][C]6.7[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]37[/C][C]12.5[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]38[/C][C]14.4[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]39[/C][C]16.5[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]40[/C][C]18.7[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]41[/C][C]19.4[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]42[/C][C]15.8[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]43[/C][C]11.3[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]44[/C][C]9.7[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]45[/C][C]2.9[/C][C]4.824[/C][C]0.8268[/C][C]8.8213[/C][C]0.1727[/C][C]0.0084[/C][C]0.8395[/C][C]0.0084[/C][/ROW]
[ROW][C]46[/C][C]0.1[/C][C]5.0639[/C][C]0.861[/C][C]9.2667[/C][C]0.0103[/C][C]0.8435[/C][C]0.9791[/C][C]0.0153[/C][/ROW]
[ROW][C]47[/C][C]2.5[/C][C]5.8665[/C][C]1.5353[/C][C]10.1976[/C][C]0.0638[/C][C]0.9955[/C][C]0.8475[/C][C]0.0414[/C][/ROW]
[ROW][C]48[/C][C]6.7[/C][C]7.1379[/C][C]2.7254[/C][C]11.5503[/C][C]0.4229[/C][C]0.9803[/C][C]0.5771[/C][C]0.1275[/C][/ROW]
[ROW][C]49[/C][C]10.3[/C][C]11.198[/C][C]6.7336[/C][C]15.6625[/C][C]0.3467[/C][C]0.9759[/C][C]0.2838[/C][C]0.7446[/C][/ROW]
[ROW][C]50[/C][C]11.2[/C][C]15.9838[/C][C]11.4859[/C][C]20.4816[/C][C]0.0186[/C][C]0.9934[/C][C]0.7549[/C][C]0.9969[/C][/ROW]
[ROW][C]51[/C][C]17.4[/C][C]16.6194[/C][C]12.1[/C][C]21.1389[/C][C]0.3675[/C][C]0.9906[/C][C]0.5207[/C][C]0.9987[/C][/ROW]
[ROW][C]52[/C][C]20.5[/C][C]18.5791[/C][C]14.0456[/C][C]23.1125[/C][C]0.2031[/C][C]0.6949[/C][C]0.4791[/C][C]0.9999[/C][/ROW]
[ROW][C]53[/C][C]17[/C][C]18.5918[/C][C]14.0494[/C][C]23.1343[/C][C]0.2461[/C][C]0.2052[/C][C]0.3637[/C][C]0.9999[/C][/ROW]
[ROW][C]54[/C][C]14.2[/C][C]14.9478[/C][C]10.3994[/C][C]19.4961[/C][C]0.3736[/C][C]0.1882[/C][C]0.3567[/C][C]0.9881[/C][/ROW]
[ROW][C]55[/C][C]10.6[/C][C]10.9873[/C][C]6.4352[/C][C]15.5394[/C][C]0.4338[/C][C]0.0833[/C][C]0.4464[/C][C]0.7103[/C][/ROW]
[ROW][C]56[/C][C]6.1[/C][C]8.2086[/C][C]3.654[/C][C]12.7632[/C][C]0.1821[/C][C]0.1517[/C][C]0.2605[/C][C]0.2605[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117052&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117052&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[44])
32	6.9	-	-	-	-	-	-	-
33	2.8	-	-	-	-	-	-	-
34	0.7	-	-	-	-	-	-	-
35	3.6	-	-	-	-	-	-	-
36	6.7	-	-	-	-	-	-	-
37	12.5	-	-	-	-	-	-	-
38	14.4	-	-	-	-	-	-	-
39	16.5	-	-	-	-	-	-	-
40	18.7	-	-	-	-	-	-	-
41	19.4	-	-	-	-	-	-	-
42	15.8	-	-	-	-	-	-	-
43	11.3	-	-	-	-	-	-	-
44	9.7	-	-	-	-	-	-	-
45	2.9	4.824	0.8268	8.8213	0.1727	0.0084	0.8395	0.0084
46	0.1	5.0639	0.861	9.2667	0.0103	0.8435	0.9791	0.0153
47	2.5	5.8665	1.5353	10.1976	0.0638	0.9955	0.8475	0.0414
48	6.7	7.1379	2.7254	11.5503	0.4229	0.9803	0.5771	0.1275
49	10.3	11.198	6.7336	15.6625	0.3467	0.9759	0.2838	0.7446
50	11.2	15.9838	11.4859	20.4816	0.0186	0.9934	0.7549	0.9969
51	17.4	16.6194	12.1	21.1389	0.3675	0.9906	0.5207	0.9987
52	20.5	18.5791	14.0456	23.1125	0.2031	0.6949	0.4791	0.9999
53	17	18.5918	14.0494	23.1343	0.2461	0.2052	0.3637	0.9999
54	14.2	14.9478	10.3994	19.4961	0.3736	0.1882	0.3567	0.9881
55	10.6	10.9873	6.4352	15.5394	0.4338	0.0833	0.4464	0.7103
56	6.1	8.2086	3.654	12.7632	0.1821	0.1517	0.2605	0.2605

Univariate ARIMA Extrapolation Forecast Performance
time	% S.E.	PE	MAPE	Sq.E	MSE	RMSE
45	0.4228	-0.3988	0	3.7019	0	0
46	0.4235	-0.9803	0.6895	24.6398	14.1709	3.7644
47	0.3767	-0.5738	0.651	11.333	13.2249	3.6366
48	0.3154	-0.0613	0.5036	0.1917	9.9666	3.157
49	0.2034	-0.0802	0.4189	0.8065	8.1346	2.8521
50	0.1436	-0.2993	0.399	22.8843	10.5929	3.2547
51	0.1387	0.047	0.3487	0.6093	9.1666	3.0276
52	0.1245	0.1034	0.318	3.69	8.4821	2.9124
53	0.1247	-0.0856	0.2922	2.5339	7.8212	2.7966
54	0.1552	-0.05	0.268	0.5591	7.095	2.6636
55	0.2114	-0.0352	0.2468	0.15	6.4636	2.5424
56	0.2831	-0.2569	0.2477	4.4462	6.2955	2.5091

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
45 & 0.4228 & -0.3988 & 0 & 3.7019 & 0 & 0 \tabularnewline
46 & 0.4235 & -0.9803 & 0.6895 & 24.6398 & 14.1709 & 3.7644 \tabularnewline
47 & 0.3767 & -0.5738 & 0.651 & 11.333 & 13.2249 & 3.6366 \tabularnewline
48 & 0.3154 & -0.0613 & 0.5036 & 0.1917 & 9.9666 & 3.157 \tabularnewline
49 & 0.2034 & -0.0802 & 0.4189 & 0.8065 & 8.1346 & 2.8521 \tabularnewline
50 & 0.1436 & -0.2993 & 0.399 & 22.8843 & 10.5929 & 3.2547 \tabularnewline
51 & 0.1387 & 0.047 & 0.3487 & 0.6093 & 9.1666 & 3.0276 \tabularnewline
52 & 0.1245 & 0.1034 & 0.318 & 3.69 & 8.4821 & 2.9124 \tabularnewline
53 & 0.1247 & -0.0856 & 0.2922 & 2.5339 & 7.8212 & 2.7966 \tabularnewline
54 & 0.1552 & -0.05 & 0.268 & 0.5591 & 7.095 & 2.6636 \tabularnewline
55 & 0.2114 & -0.0352 & 0.2468 & 0.15 & 6.4636 & 2.5424 \tabularnewline
56 & 0.2831 & -0.2569 & 0.2477 & 4.4462 & 6.2955 & 2.5091 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117052&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]45[/C][C]0.4228[/C][C]-0.3988[/C][C]0[/C][C]3.7019[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]46[/C][C]0.4235[/C][C]-0.9803[/C][C]0.6895[/C][C]24.6398[/C][C]14.1709[/C][C]3.7644[/C][/ROW]
[ROW][C]47[/C][C]0.3767[/C][C]-0.5738[/C][C]0.651[/C][C]11.333[/C][C]13.2249[/C][C]3.6366[/C][/ROW]
[ROW][C]48[/C][C]0.3154[/C][C]-0.0613[/C][C]0.5036[/C][C]0.1917[/C][C]9.9666[/C][C]3.157[/C][/ROW]
[ROW][C]49[/C][C]0.2034[/C][C]-0.0802[/C][C]0.4189[/C][C]0.8065[/C][C]8.1346[/C][C]2.8521[/C][/ROW]
[ROW][C]50[/C][C]0.1436[/C][C]-0.2993[/C][C]0.399[/C][C]22.8843[/C][C]10.5929[/C][C]3.2547[/C][/ROW]
[ROW][C]51[/C][C]0.1387[/C][C]0.047[/C][C]0.3487[/C][C]0.6093[/C][C]9.1666[/C][C]3.0276[/C][/ROW]
[ROW][C]52[/C][C]0.1245[/C][C]0.1034[/C][C]0.318[/C][C]3.69[/C][C]8.4821[/C][C]2.9124[/C][/ROW]
[ROW][C]53[/C][C]0.1247[/C][C]-0.0856[/C][C]0.2922[/C][C]2.5339[/C][C]7.8212[/C][C]2.7966[/C][/ROW]
[ROW][C]54[/C][C]0.1552[/C][C]-0.05[/C][C]0.268[/C][C]0.5591[/C][C]7.095[/C][C]2.6636[/C][/ROW]
[ROW][C]55[/C][C]0.2114[/C][C]-0.0352[/C][C]0.2468[/C][C]0.15[/C][C]6.4636[/C][C]2.5424[/C][/ROW]
[ROW][C]56[/C][C]0.2831[/C][C]-0.2569[/C][C]0.2477[/C][C]4.4462[/C][C]6.2955[/C][C]2.5091[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117052&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117052&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
45	0.4228	-0.3988	0	3.7019	0	0
46	0.4235	-0.9803	0.6895	24.6398	14.1709	3.7644
47	0.3767	-0.5738	0.651	11.333	13.2249	3.6366
48	0.3154	-0.0613	0.5036	0.1917	9.9666	3.157
49	0.2034	-0.0802	0.4189	0.8065	8.1346	2.8521
50	0.1436	-0.2993	0.399	22.8843	10.5929	3.2547
51	0.1387	0.047	0.3487	0.6093	9.1666	3.0276
52	0.1245	0.1034	0.318	3.69	8.4821	2.9124
53	0.1247	-0.0856	0.2922	2.5339	7.8212	2.7966
54	0.1552	-0.05	0.268	0.5591	7.095	2.6636
55	0.2114	-0.0352	0.2468	0.15	6.4636	2.5424
56	0.2831	-0.2569	0.2477	4.4462	6.2955	2.5091

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

par1 = 12 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = 1 ; par7 = 1 ; par8 = 1 ; par9 = 0 ; par10 = FALSE ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;

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