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R Software Module

rwasp_arimaforecasting.wasp

Title produced by software

ARIMA Forecasting

Date of computation

Mon, 06 Dec 2010 20:49:59 +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/06/t129166849636q62p1wlj07k3u.htm/, Retrieved Mon, 29 Apr 2024 02:47:49 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=105880, Retrieved Mon, 29 Apr 2024 02:47:49 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

143

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 Forecasting] [2010-12-06 20:49:59] [3ee4962e6ce79244b15c133e74cea133] [Current]
-   P                 [ARIMA Forecasting] [WS9 - Review] [2010-12-10 15:45:41] [4a7069087cf9e0eda253aeed7d8c30d6] 
-   PD                  [ARIMA Forecasting] [WS9 - Review] [2010-12-10 16:21:51] [4a7069087cf9e0eda253aeed7d8c30d6] 
-    D                    [ARIMA Forecasting] [WS9 - Review] [2010-12-10 17:02:50] [4a7069087cf9e0eda253aeed7d8c30d6] 

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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=105880&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=105880&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105880&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	53.0402	35.8131	70.2673	0.0551	0.2863	0.2142	0.2863
62	49	52.4	35.1713	69.6287	0.3495	0.9363	0.3411	0.262
63	58	65.8	48.5713	83.0287	0.1874	0.972	0.8126	0.8126
64	47	50.8	33.5713	68.0287	0.3328	0.2064	0.5363	0.2064
65	42	51.2	33.9713	68.4287	0.1476	0.6836	0.5091	0.2196
66	62	59.2	41.9713	76.4287	0.375	0.9748	0.7597	0.5543
67	39	38.8	21.5713	56.0287	0.4909	0.0042	0.5811	0.0145
68	40	28.4	11.1713	45.6287	0.0935	0.1139	0.7667	4e-04
69	72	54.8	37.5713	72.0287	0.0252	0.9539	0.4909	0.3579
70	70	62.6	45.3713	79.8287	0.1999	0.1424	0.1999	0.6996
71	54	48.4	31.1713	65.6287	0.262	0.007	0.0609	0.1374
72	65	55.3803	38.1517	72.609	0.1369	0.5624	0.3828	0.3828

\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 & 53.0402 & 35.8131 & 70.2673 & 0.0551 & 0.2863 & 0.2142 & 0.2863 \tabularnewline
62 & 49 & 52.4 & 35.1713 & 69.6287 & 0.3495 & 0.9363 & 0.3411 & 0.262 \tabularnewline
63 & 58 & 65.8 & 48.5713 & 83.0287 & 0.1874 & 0.972 & 0.8126 & 0.8126 \tabularnewline
64 & 47 & 50.8 & 33.5713 & 68.0287 & 0.3328 & 0.2064 & 0.5363 & 0.2064 \tabularnewline
65 & 42 & 51.2 & 33.9713 & 68.4287 & 0.1476 & 0.6836 & 0.5091 & 0.2196 \tabularnewline
66 & 62 & 59.2 & 41.9713 & 76.4287 & 0.375 & 0.9748 & 0.7597 & 0.5543 \tabularnewline
67 & 39 & 38.8 & 21.5713 & 56.0287 & 0.4909 & 0.0042 & 0.5811 & 0.0145 \tabularnewline
68 & 40 & 28.4 & 11.1713 & 45.6287 & 0.0935 & 0.1139 & 0.7667 & 4e-04 \tabularnewline
69 & 72 & 54.8 & 37.5713 & 72.0287 & 0.0252 & 0.9539 & 0.4909 & 0.3579 \tabularnewline
70 & 70 & 62.6 & 45.3713 & 79.8287 & 0.1999 & 0.1424 & 0.1999 & 0.6996 \tabularnewline
71 & 54 & 48.4 & 31.1713 & 65.6287 & 0.262 & 0.007 & 0.0609 & 0.1374 \tabularnewline
72 & 65 & 55.3803 & 38.1517 & 72.609 & 0.1369 & 0.5624 & 0.3828 & 0.3828 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105880&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]53.0402[/C][C]35.8131[/C][C]70.2673[/C][C]0.0551[/C][C]0.2863[/C][C]0.2142[/C][C]0.2863[/C][/ROW]
[ROW][C]62[/C][C]49[/C][C]52.4[/C][C]35.1713[/C][C]69.6287[/C][C]0.3495[/C][C]0.9363[/C][C]0.3411[/C][C]0.262[/C][/ROW]
[ROW][C]63[/C][C]58[/C][C]65.8[/C][C]48.5713[/C][C]83.0287[/C][C]0.1874[/C][C]0.972[/C][C]0.8126[/C][C]0.8126[/C][/ROW]
[ROW][C]64[/C][C]47[/C][C]50.8[/C][C]33.5713[/C][C]68.0287[/C][C]0.3328[/C][C]0.2064[/C][C]0.5363[/C][C]0.2064[/C][/ROW]
[ROW][C]65[/C][C]42[/C][C]51.2[/C][C]33.9713[/C][C]68.4287[/C][C]0.1476[/C][C]0.6836[/C][C]0.5091[/C][C]0.2196[/C][/ROW]
[ROW][C]66[/C][C]62[/C][C]59.2[/C][C]41.9713[/C][C]76.4287[/C][C]0.375[/C][C]0.9748[/C][C]0.7597[/C][C]0.5543[/C][/ROW]
[ROW][C]67[/C][C]39[/C][C]38.8[/C][C]21.5713[/C][C]56.0287[/C][C]0.4909[/C][C]0.0042[/C][C]0.5811[/C][C]0.0145[/C][/ROW]
[ROW][C]68[/C][C]40[/C][C]28.4[/C][C]11.1713[/C][C]45.6287[/C][C]0.0935[/C][C]0.1139[/C][C]0.7667[/C][C]4e-04[/C][/ROW]
[ROW][C]69[/C][C]72[/C][C]54.8[/C][C]37.5713[/C][C]72.0287[/C][C]0.0252[/C][C]0.9539[/C][C]0.4909[/C][C]0.3579[/C][/ROW]
[ROW][C]70[/C][C]70[/C][C]62.6[/C][C]45.3713[/C][C]79.8287[/C][C]0.1999[/C][C]0.1424[/C][C]0.1999[/C][C]0.6996[/C][/ROW]
[ROW][C]71[/C][C]54[/C][C]48.4[/C][C]31.1713[/C][C]65.6287[/C][C]0.262[/C][C]0.007[/C][C]0.0609[/C][C]0.1374[/C][/ROW]
[ROW][C]72[/C][C]65[/C][C]55.3803[/C][C]38.1517[/C][C]72.609[/C][C]0.1369[/C][C]0.5624[/C][C]0.3828[/C][C]0.3828[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105880&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105880&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	53.0402	35.8131	70.2673	0.0551	0.2863	0.2142	0.2863
62	49	52.4	35.1713	69.6287	0.3495	0.9363	0.3411	0.262
63	58	65.8	48.5713	83.0287	0.1874	0.972	0.8126	0.8126
64	47	50.8	33.5713	68.0287	0.3328	0.2064	0.5363	0.2064
65	42	51.2	33.9713	68.4287	0.1476	0.6836	0.5091	0.2196
66	62	59.2	41.9713	76.4287	0.375	0.9748	0.7597	0.5543
67	39	38.8	21.5713	56.0287	0.4909	0.0042	0.5811	0.0145
68	40	28.4	11.1713	45.6287	0.0935	0.1139	0.7667	4e-04
69	72	54.8	37.5713	72.0287	0.0252	0.9539	0.4909	0.3579
70	70	62.6	45.3713	79.8287	0.1999	0.1424	0.1999	0.6996
71	54	48.4	31.1713	65.6287	0.262	0.007	0.0609	0.1374
72	65	55.3803	38.1517	72.609	0.1369	0.5624	0.3828	0.3828

Univariate ARIMA Extrapolation Forecast Performance
time	% S.E.	PE	MAPE	Sq.E	MSE	RMSE
61	0.1657	-0.2647	0	197.1271	0	0
62	0.1678	-0.0649	0.1648	11.5599	104.3435	10.2149
63	0.1336	-0.1185	0.1494	60.8397	89.8422	9.4785
64	0.173	-0.0748	0.1307	14.4399	70.9917	8.4257
65	0.1717	-0.1797	0.1405	84.6397	73.7213	8.5861
66	0.1485	0.0473	0.125	7.8401	62.7411	7.9209
67	0.2266	0.0052	0.1079	0.04	53.7838	7.3337
68	0.3095	0.4085	0.1454	134.5602	63.8808	7.9925
69	0.1604	0.3139	0.1642	295.8405	89.6541	9.4686
70	0.1404	0.1182	0.1596	54.7602	86.1647	9.2825
71	0.1816	0.1157	0.1556	31.3601	81.1825	9.0101
72	0.1587	0.1737	0.1571	92.5379	82.1288	9.0625

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
61 & 0.1657 & -0.2647 & 0 & 197.1271 & 0 & 0 \tabularnewline
62 & 0.1678 & -0.0649 & 0.1648 & 11.5599 & 104.3435 & 10.2149 \tabularnewline
63 & 0.1336 & -0.1185 & 0.1494 & 60.8397 & 89.8422 & 9.4785 \tabularnewline
64 & 0.173 & -0.0748 & 0.1307 & 14.4399 & 70.9917 & 8.4257 \tabularnewline
65 & 0.1717 & -0.1797 & 0.1405 & 84.6397 & 73.7213 & 8.5861 \tabularnewline
66 & 0.1485 & 0.0473 & 0.125 & 7.8401 & 62.7411 & 7.9209 \tabularnewline
67 & 0.2266 & 0.0052 & 0.1079 & 0.04 & 53.7838 & 7.3337 \tabularnewline
68 & 0.3095 & 0.4085 & 0.1454 & 134.5602 & 63.8808 & 7.9925 \tabularnewline
69 & 0.1604 & 0.3139 & 0.1642 & 295.8405 & 89.6541 & 9.4686 \tabularnewline
70 & 0.1404 & 0.1182 & 0.1596 & 54.7602 & 86.1647 & 9.2825 \tabularnewline
71 & 0.1816 & 0.1157 & 0.1556 & 31.3601 & 81.1825 & 9.0101 \tabularnewline
72 & 0.1587 & 0.1737 & 0.1571 & 92.5379 & 82.1288 & 9.0625 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105880&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]0.1657[/C][C]-0.2647[/C][C]0[/C][C]197.1271[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]62[/C][C]0.1678[/C][C]-0.0649[/C][C]0.1648[/C][C]11.5599[/C][C]104.3435[/C][C]10.2149[/C][/ROW]
[ROW][C]63[/C][C]0.1336[/C][C]-0.1185[/C][C]0.1494[/C][C]60.8397[/C][C]89.8422[/C][C]9.4785[/C][/ROW]
[ROW][C]64[/C][C]0.173[/C][C]-0.0748[/C][C]0.1307[/C][C]14.4399[/C][C]70.9917[/C][C]8.4257[/C][/ROW]
[ROW][C]65[/C][C]0.1717[/C][C]-0.1797[/C][C]0.1405[/C][C]84.6397[/C][C]73.7213[/C][C]8.5861[/C][/ROW]
[ROW][C]66[/C][C]0.1485[/C][C]0.0473[/C][C]0.125[/C][C]7.8401[/C][C]62.7411[/C][C]7.9209[/C][/ROW]
[ROW][C]67[/C][C]0.2266[/C][C]0.0052[/C][C]0.1079[/C][C]0.04[/C][C]53.7838[/C][C]7.3337[/C][/ROW]
[ROW][C]68[/C][C]0.3095[/C][C]0.4085[/C][C]0.1454[/C][C]134.5602[/C][C]63.8808[/C][C]7.9925[/C][/ROW]
[ROW][C]69[/C][C]0.1604[/C][C]0.3139[/C][C]0.1642[/C][C]295.8405[/C][C]89.6541[/C][C]9.4686[/C][/ROW]
[ROW][C]70[/C][C]0.1404[/C][C]0.1182[/C][C]0.1596[/C][C]54.7602[/C][C]86.1647[/C][C]9.2825[/C][/ROW]
[ROW][C]71[/C][C]0.1816[/C][C]0.1157[/C][C]0.1556[/C][C]31.3601[/C][C]81.1825[/C][C]9.0101[/C][/ROW]
[ROW][C]72[/C][C]0.1587[/C][C]0.1737[/C][C]0.1571[/C][C]92.5379[/C][C]82.1288[/C][C]9.0625[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105880&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105880&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	0.1657	-0.2647	0	197.1271	0	0
62	0.1678	-0.0649	0.1648	11.5599	104.3435	10.2149
63	0.1336	-0.1185	0.1494	60.8397	89.8422	9.4785
64	0.173	-0.0748	0.1307	14.4399	70.9917	8.4257
65	0.1717	-0.1797	0.1405	84.6397	73.7213	8.5861
66	0.1485	0.0473	0.125	7.8401	62.7411	7.9209
67	0.2266	0.0052	0.1079	0.04	53.7838	7.3337
68	0.3095	0.4085	0.1454	134.5602	63.8808	7.9925
69	0.1604	0.3139	0.1642	295.8405	89.6541	9.4686
70	0.1404	0.1182	0.1596	54.7602	86.1647	9.2825
71	0.1816	0.1157	0.1556	31.3601	81.1825	9.0101
72	0.1587	0.1737	0.1571	92.5379	82.1288	9.0625

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 = 0 ; par7 = 1 ; par8 = 0 ; par9 = 1 ; par10 = FALSE ;

Parameters (R input):

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