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R Software Module

rwasp_arimaforecasting.wasp

Title produced by software

ARIMA Forecasting

Date of computation

Sat, 04 Dec 2010 17:55:48 +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/04/t1291485275nzzp63lx728705u.htm/, Retrieved Sat, 04 May 2024 21:59:11 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=105238, Retrieved Sat, 04 May 2024 21:59:11 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

200

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] [WS9 Arima forecast] [2010-12-04 17:55:48] [8b27277f7b82c0354d659d066108e38e] [Current]
-   P                 [ARIMA Forecasting] [WS9 Arima forecast] [2010-12-04 22:07:21] [65eb19f81eab2b6e672eafaed2a27190] 

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Dataseries X:

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105238&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105238&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105238&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	'Gwilym Jenkins' @ 72.249.127.135

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[60])
48	69	-	-	-	-	-	-	-
49	60	-	-	-	-	-	-	-
50	56	-	-	-	-	-	-	-
51	58	-	-	-	-	-	-	-
52	50	-	-	-	-	-	-	-
53	51	-	-	-	-	-	-	-
54	53	-	-	-	-	-	-	-
55	37	-	-	-	-	-	-	-
56	22	-	-	-	-	-	-	-
57	55	-	-	-	-	-	-	-
58	70	-	-	-	-	-	-	-
59	62	-	-	-	-	-	-	-
60	58	-	-	-	-	-	-	-
61	39	58.0001	33.2393	82.761	0.0663	0.5	0.4371	0.5
62	49	57.4002	22.7349	92.0654	0.3174	0.8509	0.5315	0.4865
63	58	70.8002	28.4888	113.1116	0.2766	0.8437	0.7234	0.7234
64	47	55.8002	7.027	104.5735	0.3618	0.4648	0.5922	0.4648
65	42	56.2003	1.7264	110.6742	0.3047	0.6297	0.5742	0.4742
66	62	64.2003	4.5683	123.8324	0.4712	0.7672	0.6436	0.5807
67	39	43.8004	-20.5779	108.1786	0.4419	0.2898	0.582	0.3328
68	40	33.4005	-35.3973	102.1982	0.4254	0.4366	0.6273	0.2417
69	72	59.8005	-13.1495	132.7506	0.3715	0.7026	0.5513	0.5193
70	70	67.6006	-9.2777	144.479	0.4756	0.4553	0.4756	0.5967
71	54	53.4007	-27.2148	134.0162	0.4942	0.3433	0.4172	0.4555
72	65	60.4008	-23.7861	144.5877	0.4574	0.5592	0.5223	0.5223

\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[60]) \tabularnewline
48 & 69 & - & - & - & - & - & - & - \tabularnewline
49 & 60 & - & - & - & - & - & - & - \tabularnewline
50 & 56 & - & - & - & - & - & - & - \tabularnewline
51 & 58 & - & - & - & - & - & - & - \tabularnewline
52 & 50 & - & - & - & - & - & - & - \tabularnewline
53 & 51 & - & - & - & - & - & - & - \tabularnewline
54 & 53 & - & - & - & - & - & - & - \tabularnewline
55 & 37 & - & - & - & - & - & - & - \tabularnewline
56 & 22 & - & - & - & - & - & - & - \tabularnewline
57 & 55 & - & - & - & - & - & - & - \tabularnewline
58 & 70 & - & - & - & - & - & - & - \tabularnewline
59 & 62 & - & - & - & - & - & - & - \tabularnewline
60 & 58 & - & - & - & - & - & - & - \tabularnewline
61 & 39 & 58.0001 & 33.2393 & 82.761 & 0.0663 & 0.5 & 0.4371 & 0.5 \tabularnewline
62 & 49 & 57.4002 & 22.7349 & 92.0654 & 0.3174 & 0.8509 & 0.5315 & 0.4865 \tabularnewline
63 & 58 & 70.8002 & 28.4888 & 113.1116 & 0.2766 & 0.8437 & 0.7234 & 0.7234 \tabularnewline
64 & 47 & 55.8002 & 7.027 & 104.5735 & 0.3618 & 0.4648 & 0.5922 & 0.4648 \tabularnewline
65 & 42 & 56.2003 & 1.7264 & 110.6742 & 0.3047 & 0.6297 & 0.5742 & 0.4742 \tabularnewline
66 & 62 & 64.2003 & 4.5683 & 123.8324 & 0.4712 & 0.7672 & 0.6436 & 0.5807 \tabularnewline
67 & 39 & 43.8004 & -20.5779 & 108.1786 & 0.4419 & 0.2898 & 0.582 & 0.3328 \tabularnewline
68 & 40 & 33.4005 & -35.3973 & 102.1982 & 0.4254 & 0.4366 & 0.6273 & 0.2417 \tabularnewline
69 & 72 & 59.8005 & -13.1495 & 132.7506 & 0.3715 & 0.7026 & 0.5513 & 0.5193 \tabularnewline
70 & 70 & 67.6006 & -9.2777 & 144.479 & 0.4756 & 0.4553 & 0.4756 & 0.5967 \tabularnewline
71 & 54 & 53.4007 & -27.2148 & 134.0162 & 0.4942 & 0.3433 & 0.4172 & 0.4555 \tabularnewline
72 & 65 & 60.4008 & -23.7861 & 144.5877 & 0.4574 & 0.5592 & 0.5223 & 0.5223 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105238&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[60])[/C][/ROW]
[ROW][C]48[/C][C]69[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]49[/C][C]60[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]50[/C][C]56[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]51[/C][C]58[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]52[/C][C]50[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]53[/C][C]51[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]54[/C][C]53[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]55[/C][C]37[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]56[/C][C]22[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]57[/C][C]55[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]58[/C][C]70[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]59[/C][C]62[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]60[/C][C]58[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]61[/C][C]39[/C][C]58.0001[/C][C]33.2393[/C][C]82.761[/C][C]0.0663[/C][C]0.5[/C][C]0.4371[/C][C]0.5[/C][/ROW]
[ROW][C]62[/C][C]49[/C][C]57.4002[/C][C]22.7349[/C][C]92.0654[/C][C]0.3174[/C][C]0.8509[/C][C]0.5315[/C][C]0.4865[/C][/ROW]
[ROW][C]63[/C][C]58[/C][C]70.8002[/C][C]28.4888[/C][C]113.1116[/C][C]0.2766[/C][C]0.8437[/C][C]0.7234[/C][C]0.7234[/C][/ROW]
[ROW][C]64[/C][C]47[/C][C]55.8002[/C][C]7.027[/C][C]104.5735[/C][C]0.3618[/C][C]0.4648[/C][C]0.5922[/C][C]0.4648[/C][/ROW]
[ROW][C]65[/C][C]42[/C][C]56.2003[/C][C]1.7264[/C][C]110.6742[/C][C]0.3047[/C][C]0.6297[/C][C]0.5742[/C][C]0.4742[/C][/ROW]
[ROW][C]66[/C][C]62[/C][C]64.2003[/C][C]4.5683[/C][C]123.8324[/C][C]0.4712[/C][C]0.7672[/C][C]0.6436[/C][C]0.5807[/C][/ROW]
[ROW][C]67[/C][C]39[/C][C]43.8004[/C][C]-20.5779[/C][C]108.1786[/C][C]0.4419[/C][C]0.2898[/C][C]0.582[/C][C]0.3328[/C][/ROW]
[ROW][C]68[/C][C]40[/C][C]33.4005[/C][C]-35.3973[/C][C]102.1982[/C][C]0.4254[/C][C]0.4366[/C][C]0.6273[/C][C]0.2417[/C][/ROW]
[ROW][C]69[/C][C]72[/C][C]59.8005[/C][C]-13.1495[/C][C]132.7506[/C][C]0.3715[/C][C]0.7026[/C][C]0.5513[/C][C]0.5193[/C][/ROW]
[ROW][C]70[/C][C]70[/C][C]67.6006[/C][C]-9.2777[/C][C]144.479[/C][C]0.4756[/C][C]0.4553[/C][C]0.4756[/C][C]0.5967[/C][/ROW]
[ROW][C]71[/C][C]54[/C][C]53.4007[/C][C]-27.2148[/C][C]134.0162[/C][C]0.4942[/C][C]0.3433[/C][C]0.4172[/C][C]0.4555[/C][/ROW]
[ROW][C]72[/C][C]65[/C][C]60.4008[/C][C]-23.7861[/C][C]144.5877[/C][C]0.4574[/C][C]0.5592[/C][C]0.5223[/C][C]0.5223[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105238&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105238&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[60])
48	69	-	-	-	-	-	-	-
49	60	-	-	-	-	-	-	-
50	56	-	-	-	-	-	-	-
51	58	-	-	-	-	-	-	-
52	50	-	-	-	-	-	-	-
53	51	-	-	-	-	-	-	-
54	53	-	-	-	-	-	-	-
55	37	-	-	-	-	-	-	-
56	22	-	-	-	-	-	-	-
57	55	-	-	-	-	-	-	-
58	70	-	-	-	-	-	-	-
59	62	-	-	-	-	-	-	-
60	58	-	-	-	-	-	-	-
61	39	58.0001	33.2393	82.761	0.0663	0.5	0.4371	0.5
62	49	57.4002	22.7349	92.0654	0.3174	0.8509	0.5315	0.4865
63	58	70.8002	28.4888	113.1116	0.2766	0.8437	0.7234	0.7234
64	47	55.8002	7.027	104.5735	0.3618	0.4648	0.5922	0.4648
65	42	56.2003	1.7264	110.6742	0.3047	0.6297	0.5742	0.4742
66	62	64.2003	4.5683	123.8324	0.4712	0.7672	0.6436	0.5807
67	39	43.8004	-20.5779	108.1786	0.4419	0.2898	0.582	0.3328
68	40	33.4005	-35.3973	102.1982	0.4254	0.4366	0.6273	0.2417
69	72	59.8005	-13.1495	132.7506	0.3715	0.7026	0.5513	0.5193
70	70	67.6006	-9.2777	144.479	0.4756	0.4553	0.4756	0.5967
71	54	53.4007	-27.2148	134.0162	0.4942	0.3433	0.4172	0.4555
72	65	60.4008	-23.7861	144.5877	0.4574	0.5592	0.5223	0.5223

Univariate ARIMA Extrapolation Forecast Performance
time	% S.E.	PE	MAPE	Sq.E	MSE	RMSE
61	0.2178	-0.3276	0	361.0057	0	0
62	0.3081	-0.1463	0.237	70.5628	215.7842	14.6896
63	0.3049	-0.1808	0.2182	163.8449	198.4711	14.088
64	0.446	-0.1577	0.2031	77.444	168.2144	12.9697
65	0.4945	-0.2527	0.213	201.6478	174.901	13.225
66	0.4739	-0.0343	0.1832	4.8414	146.5578	12.1061
67	0.7499	-0.1096	0.1727	23.0438	128.9129	11.354
68	1.0509	0.1976	0.1758	43.5539	118.243	10.874
69	0.6224	0.204	0.179	148.8269	121.6412	11.0291
70	0.5802	0.0355	0.1646	5.757	110.0528	10.4906
71	0.7702	0.0112	0.1507	0.3591	100.0807	10.004
72	0.7111	0.0761	0.1445	21.1525	93.5033	9.6697

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
61 & 0.2178 & -0.3276 & 0 & 361.0057 & 0 & 0 \tabularnewline
62 & 0.3081 & -0.1463 & 0.237 & 70.5628 & 215.7842 & 14.6896 \tabularnewline
63 & 0.3049 & -0.1808 & 0.2182 & 163.8449 & 198.4711 & 14.088 \tabularnewline
64 & 0.446 & -0.1577 & 0.2031 & 77.444 & 168.2144 & 12.9697 \tabularnewline
65 & 0.4945 & -0.2527 & 0.213 & 201.6478 & 174.901 & 13.225 \tabularnewline
66 & 0.4739 & -0.0343 & 0.1832 & 4.8414 & 146.5578 & 12.1061 \tabularnewline
67 & 0.7499 & -0.1096 & 0.1727 & 23.0438 & 128.9129 & 11.354 \tabularnewline
68 & 1.0509 & 0.1976 & 0.1758 & 43.5539 & 118.243 & 10.874 \tabularnewline
69 & 0.6224 & 0.204 & 0.179 & 148.8269 & 121.6412 & 11.0291 \tabularnewline
70 & 0.5802 & 0.0355 & 0.1646 & 5.757 & 110.0528 & 10.4906 \tabularnewline
71 & 0.7702 & 0.0112 & 0.1507 & 0.3591 & 100.0807 & 10.004 \tabularnewline
72 & 0.7111 & 0.0761 & 0.1445 & 21.1525 & 93.5033 & 9.6697 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105238&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]61[/C][C]0.2178[/C][C]-0.3276[/C][C]0[/C][C]361.0057[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]62[/C][C]0.3081[/C][C]-0.1463[/C][C]0.237[/C][C]70.5628[/C][C]215.7842[/C][C]14.6896[/C][/ROW]
[ROW][C]63[/C][C]0.3049[/C][C]-0.1808[/C][C]0.2182[/C][C]163.8449[/C][C]198.4711[/C][C]14.088[/C][/ROW]
[ROW][C]64[/C][C]0.446[/C][C]-0.1577[/C][C]0.2031[/C][C]77.444[/C][C]168.2144[/C][C]12.9697[/C][/ROW]
[ROW][C]65[/C][C]0.4945[/C][C]-0.2527[/C][C]0.213[/C][C]201.6478[/C][C]174.901[/C][C]13.225[/C][/ROW]
[ROW][C]66[/C][C]0.4739[/C][C]-0.0343[/C][C]0.1832[/C][C]4.8414[/C][C]146.5578[/C][C]12.1061[/C][/ROW]
[ROW][C]67[/C][C]0.7499[/C][C]-0.1096[/C][C]0.1727[/C][C]23.0438[/C][C]128.9129[/C][C]11.354[/C][/ROW]
[ROW][C]68[/C][C]1.0509[/C][C]0.1976[/C][C]0.1758[/C][C]43.5539[/C][C]118.243[/C][C]10.874[/C][/ROW]
[ROW][C]69[/C][C]0.6224[/C][C]0.204[/C][C]0.179[/C][C]148.8269[/C][C]121.6412[/C][C]11.0291[/C][/ROW]
[ROW][C]70[/C][C]0.5802[/C][C]0.0355[/C][C]0.1646[/C][C]5.757[/C][C]110.0528[/C][C]10.4906[/C][/ROW]
[ROW][C]71[/C][C]0.7702[/C][C]0.0112[/C][C]0.1507[/C][C]0.3591[/C][C]100.0807[/C][C]10.004[/C][/ROW]
[ROW][C]72[/C][C]0.7111[/C][C]0.0761[/C][C]0.1445[/C][C]21.1525[/C][C]93.5033[/C][C]9.6697[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105238&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105238&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
61	0.2178	-0.3276	0	361.0057	0	0
62	0.3081	-0.1463	0.237	70.5628	215.7842	14.6896
63	0.3049	-0.1808	0.2182	163.8449	198.4711	14.088
64	0.446	-0.1577	0.2031	77.444	168.2144	12.9697
65	0.4945	-0.2527	0.213	201.6478	174.901	13.225
66	0.4739	-0.0343	0.1832	4.8414	146.5578	12.1061
67	0.7499	-0.1096	0.1727	23.0438	128.9129	11.354
68	1.0509	0.1976	0.1758	43.5539	118.243	10.874
69	0.6224	0.204	0.179	148.8269	121.6412	11.0291
70	0.5802	0.0355	0.1646	5.757	110.0528	10.4906
71	0.7702	0.0112	0.1507	0.3591	100.0807	10.004
72	0.7111	0.0761	0.1445	21.1525	93.5033	9.6697

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

par1 = 12 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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