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R Software Module

rwasp_arimaforecasting.wasp

Title produced by software

ARIMA Forecasting

Date of computation

Fri, 24 Dec 2010 12:12:29 +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/t12931926035cy0zn0f1ayyg12.htm/, Retrieved Tue, 30 Apr 2024 06:52:29 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=114815, Retrieved Tue, 30 Apr 2024 06:52:29 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

144

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

-     [Kendall tau Correlation Matrix] [] [2010-12-05 17:44:33] [b98453cac15ba1066b407e146608df68]
- RMPD  [Kendall tau Correlation Matrix] [WS 10 - Pearson c...] [2010-12-10 16:13:49] [033eb2749a430605d9b2be7c4aac4a0c]
-         [Kendall tau Correlation Matrix] [] [2010-12-13 18:15:16] [d7b28a0391ab3b2ddc9f9fba95a43f33]
- RMPD        [ARIMA Forecasting] [] [2010-12-24 12:12:29] [a75ee4dff32cc2c5ca1525a5910b53eb] [Current]
-   PD          [ARIMA Forecasting] [ARIMA forecast mo...] [2011-12-15 18:32:05] [63813c3109753b730d344072266dee79] 
-   PD          [ARIMA Forecasting] [ARIMA forecast mo...] [2011-12-15 18:32:05] [63813c3109753b730d344072266dee79] 
-   PD          [ARIMA Forecasting] [] [2011-12-15 19:24:16] [63813c3109753b730d344072266dee79] 
-    D          [ARIMA Forecasting] [ARIMA forecast] [2011-12-16 12:54:24] [63813c3109753b730d344072266dee79] 

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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	3 seconds
R Server	'George Udny Yule' @ 72.249.76.132
R Framework error message	Warning: there are blank lines in the 'Data' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values.

\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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
R Framework error message & Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values. \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114815&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[ROW][C]R Framework error message[/C][C]Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114815&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114815&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	3 seconds
R Server	'George Udny Yule' @ 72.249.76.132
R Framework error message	Warning: there are blank lines in the 'Data' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values.

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	4.767	-	-	-	-	-	-	-
49	5.019	-	-	-	-	-	-	-
50	4.343	-	-	-	-	-	-	-
51	4.853	-	-	-	-	-	-	-
52	4.154	-	-	-	-	-	-	-
53	4.035	-	-	-	-	-	-	-
54	3.996	-	-	-	-	-	-	-
55	4.734	-	-	-	-	-	-	-
56	3.778	-	-	-	-	-	-	-
57	3.887	-	-	-	-	-	-	-
58	3.953	-	-	-	-	-	-	-
59	3.987	-	-	-	-	-	-	-
60	4.436	-	-	-	-	-	-	-
61	4.803	4.9454	4.4101	5.4807	0.301	0.9689	0.3938	0.9689
62	4.672	4.4181	3.8381	4.9981	0.1955	0.0967	0.6002	0.4759
63	4.56	4.9071	4.3196	5.4946	0.1234	0.7836	0.5716	0.942
64	4.289	4.2371	3.6483	4.8259	0.4314	0.1412	0.6089	0.2539
65	3.961	4.1148	3.5257	4.7038	0.3044	0.2811	0.6047	0.1426
66	3.943	4.022	3.4329	4.611	0.3964	0.5804	0.5344	0.0842
67	3.932	4.2913	3.7023	4.8804	0.1159	0.8768	0.0704	0.3152
68	3.816	3.8762	3.2871	4.4653	0.4206	0.4264	0.6281	0.0313
69	3.834	3.8835	3.2944	4.4725	0.4347	0.5888	0.4953	0.033
70	4.13	4.1103	3.5212	4.6994	0.4739	0.8211	0.6997	0.1393
71	4.467	4.0628	3.4738	4.6519	0.0894	0.4116	0.5996	0.1072
72	4.447	4.6919	4.1029	5.2809	0.2075	0.7729	0.8028	0.8028

\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 & 4.767 & - & - & - & - & - & - & - \tabularnewline
49 & 5.019 & - & - & - & - & - & - & - \tabularnewline
50 & 4.343 & - & - & - & - & - & - & - \tabularnewline
51 & 4.853 & - & - & - & - & - & - & - \tabularnewline
52 & 4.154 & - & - & - & - & - & - & - \tabularnewline
53 & 4.035 & - & - & - & - & - & - & - \tabularnewline
54 & 3.996 & - & - & - & - & - & - & - \tabularnewline
55 & 4.734 & - & - & - & - & - & - & - \tabularnewline
56 & 3.778 & - & - & - & - & - & - & - \tabularnewline
57 & 3.887 & - & - & - & - & - & - & - \tabularnewline
58 & 3.953 & - & - & - & - & - & - & - \tabularnewline
59 & 3.987 & - & - & - & - & - & - & - \tabularnewline
60 & 4.436 & - & - & - & - & - & - & - \tabularnewline
61 & 4.803 & 4.9454 & 4.4101 & 5.4807 & 0.301 & 0.9689 & 0.3938 & 0.9689 \tabularnewline
62 & 4.672 & 4.4181 & 3.8381 & 4.9981 & 0.1955 & 0.0967 & 0.6002 & 0.4759 \tabularnewline
63 & 4.56 & 4.9071 & 4.3196 & 5.4946 & 0.1234 & 0.7836 & 0.5716 & 0.942 \tabularnewline
64 & 4.289 & 4.2371 & 3.6483 & 4.8259 & 0.4314 & 0.1412 & 0.6089 & 0.2539 \tabularnewline
65 & 3.961 & 4.1148 & 3.5257 & 4.7038 & 0.3044 & 0.2811 & 0.6047 & 0.1426 \tabularnewline
66 & 3.943 & 4.022 & 3.4329 & 4.611 & 0.3964 & 0.5804 & 0.5344 & 0.0842 \tabularnewline
67 & 3.932 & 4.2913 & 3.7023 & 4.8804 & 0.1159 & 0.8768 & 0.0704 & 0.3152 \tabularnewline
68 & 3.816 & 3.8762 & 3.2871 & 4.4653 & 0.4206 & 0.4264 & 0.6281 & 0.0313 \tabularnewline
69 & 3.834 & 3.8835 & 3.2944 & 4.4725 & 0.4347 & 0.5888 & 0.4953 & 0.033 \tabularnewline
70 & 4.13 & 4.1103 & 3.5212 & 4.6994 & 0.4739 & 0.8211 & 0.6997 & 0.1393 \tabularnewline
71 & 4.467 & 4.0628 & 3.4738 & 4.6519 & 0.0894 & 0.4116 & 0.5996 & 0.1072 \tabularnewline
72 & 4.447 & 4.6919 & 4.1029 & 5.2809 & 0.2075 & 0.7729 & 0.8028 & 0.8028 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114815&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]4.767[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]49[/C][C]5.019[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]50[/C][C]4.343[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]51[/C][C]4.853[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]52[/C][C]4.154[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]53[/C][C]4.035[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]54[/C][C]3.996[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]55[/C][C]4.734[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]56[/C][C]3.778[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]57[/C][C]3.887[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]58[/C][C]3.953[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]59[/C][C]3.987[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]60[/C][C]4.436[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]61[/C][C]4.803[/C][C]4.9454[/C][C]4.4101[/C][C]5.4807[/C][C]0.301[/C][C]0.9689[/C][C]0.3938[/C][C]0.9689[/C][/ROW]
[ROW][C]62[/C][C]4.672[/C][C]4.4181[/C][C]3.8381[/C][C]4.9981[/C][C]0.1955[/C][C]0.0967[/C][C]0.6002[/C][C]0.4759[/C][/ROW]
[ROW][C]63[/C][C]4.56[/C][C]4.9071[/C][C]4.3196[/C][C]5.4946[/C][C]0.1234[/C][C]0.7836[/C][C]0.5716[/C][C]0.942[/C][/ROW]
[ROW][C]64[/C][C]4.289[/C][C]4.2371[/C][C]3.6483[/C][C]4.8259[/C][C]0.4314[/C][C]0.1412[/C][C]0.6089[/C][C]0.2539[/C][/ROW]
[ROW][C]65[/C][C]3.961[/C][C]4.1148[/C][C]3.5257[/C][C]4.7038[/C][C]0.3044[/C][C]0.2811[/C][C]0.6047[/C][C]0.1426[/C][/ROW]
[ROW][C]66[/C][C]3.943[/C][C]4.022[/C][C]3.4329[/C][C]4.611[/C][C]0.3964[/C][C]0.5804[/C][C]0.5344[/C][C]0.0842[/C][/ROW]
[ROW][C]67[/C][C]3.932[/C][C]4.2913[/C][C]3.7023[/C][C]4.8804[/C][C]0.1159[/C][C]0.8768[/C][C]0.0704[/C][C]0.3152[/C][/ROW]
[ROW][C]68[/C][C]3.816[/C][C]3.8762[/C][C]3.2871[/C][C]4.4653[/C][C]0.4206[/C][C]0.4264[/C][C]0.6281[/C][C]0.0313[/C][/ROW]
[ROW][C]69[/C][C]3.834[/C][C]3.8835[/C][C]3.2944[/C][C]4.4725[/C][C]0.4347[/C][C]0.5888[/C][C]0.4953[/C][C]0.033[/C][/ROW]
[ROW][C]70[/C][C]4.13[/C][C]4.1103[/C][C]3.5212[/C][C]4.6994[/C][C]0.4739[/C][C]0.8211[/C][C]0.6997[/C][C]0.1393[/C][/ROW]
[ROW][C]71[/C][C]4.467[/C][C]4.0628[/C][C]3.4738[/C][C]4.6519[/C][C]0.0894[/C][C]0.4116[/C][C]0.5996[/C][C]0.1072[/C][/ROW]
[ROW][C]72[/C][C]4.447[/C][C]4.6919[/C][C]4.1029[/C][C]5.2809[/C][C]0.2075[/C][C]0.7729[/C][C]0.8028[/C][C]0.8028[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114815&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114815&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	4.767	-	-	-	-	-	-	-
49	5.019	-	-	-	-	-	-	-
50	4.343	-	-	-	-	-	-	-
51	4.853	-	-	-	-	-	-	-
52	4.154	-	-	-	-	-	-	-
53	4.035	-	-	-	-	-	-	-
54	3.996	-	-	-	-	-	-	-
55	4.734	-	-	-	-	-	-	-
56	3.778	-	-	-	-	-	-	-
57	3.887	-	-	-	-	-	-	-
58	3.953	-	-	-	-	-	-	-
59	3.987	-	-	-	-	-	-	-
60	4.436	-	-	-	-	-	-	-
61	4.803	4.9454	4.4101	5.4807	0.301	0.9689	0.3938	0.9689
62	4.672	4.4181	3.8381	4.9981	0.1955	0.0967	0.6002	0.4759
63	4.56	4.9071	4.3196	5.4946	0.1234	0.7836	0.5716	0.942
64	4.289	4.2371	3.6483	4.8259	0.4314	0.1412	0.6089	0.2539
65	3.961	4.1148	3.5257	4.7038	0.3044	0.2811	0.6047	0.1426
66	3.943	4.022	3.4329	4.611	0.3964	0.5804	0.5344	0.0842
67	3.932	4.2913	3.7023	4.8804	0.1159	0.8768	0.0704	0.3152
68	3.816	3.8762	3.2871	4.4653	0.4206	0.4264	0.6281	0.0313
69	3.834	3.8835	3.2944	4.4725	0.4347	0.5888	0.4953	0.033
70	4.13	4.1103	3.5212	4.6994	0.4739	0.8211	0.6997	0.1393
71	4.467	4.0628	3.4738	4.6519	0.0894	0.4116	0.5996	0.1072
72	4.447	4.6919	4.1029	5.2809	0.2075	0.7729	0.8028	0.8028

Univariate ARIMA Extrapolation Forecast Performance
time	% S.E.	PE	MAPE	Sq.E	MSE	RMSE
61	0.0552	-0.0288	0	0.0203	0	0
62	0.067	0.0575	0.0431	0.0645	0.0424	0.2058
63	0.0611	-0.0707	0.0523	0.1205	0.0684	0.2616
64	0.0709	0.0123	0.0423	0.0027	0.052	0.228
65	0.073	-0.0374	0.0413	0.0237	0.0463	0.2152
66	0.0747	-0.0196	0.0377	0.0062	0.0396	0.1991
67	0.07	-0.0837	0.0443	0.1291	0.0524	0.229
68	0.0775	-0.0155	0.0407	0.0036	0.0463	0.2152
69	0.0774	-0.0127	0.0376	0.0024	0.0414	0.2036
70	0.0731	0.0048	0.0343	4e-04	0.0373	0.1932
71	0.074	0.0995	0.0402	0.1633	0.0488	0.2209
72	0.064	-0.0522	0.0412	0.06	0.0497	0.223

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
61 & 0.0552 & -0.0288 & 0 & 0.0203 & 0 & 0 \tabularnewline
62 & 0.067 & 0.0575 & 0.0431 & 0.0645 & 0.0424 & 0.2058 \tabularnewline
63 & 0.0611 & -0.0707 & 0.0523 & 0.1205 & 0.0684 & 0.2616 \tabularnewline
64 & 0.0709 & 0.0123 & 0.0423 & 0.0027 & 0.052 & 0.228 \tabularnewline
65 & 0.073 & -0.0374 & 0.0413 & 0.0237 & 0.0463 & 0.2152 \tabularnewline
66 & 0.0747 & -0.0196 & 0.0377 & 0.0062 & 0.0396 & 0.1991 \tabularnewline
67 & 0.07 & -0.0837 & 0.0443 & 0.1291 & 0.0524 & 0.229 \tabularnewline
68 & 0.0775 & -0.0155 & 0.0407 & 0.0036 & 0.0463 & 0.2152 \tabularnewline
69 & 0.0774 & -0.0127 & 0.0376 & 0.0024 & 0.0414 & 0.2036 \tabularnewline
70 & 0.0731 & 0.0048 & 0.0343 & 4e-04 & 0.0373 & 0.1932 \tabularnewline
71 & 0.074 & 0.0995 & 0.0402 & 0.1633 & 0.0488 & 0.2209 \tabularnewline
72 & 0.064 & -0.0522 & 0.0412 & 0.06 & 0.0497 & 0.223 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114815&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]0.0552[/C][C]-0.0288[/C][C]0[/C][C]0.0203[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]62[/C][C]0.067[/C][C]0.0575[/C][C]0.0431[/C][C]0.0645[/C][C]0.0424[/C][C]0.2058[/C][/ROW]
[ROW][C]63[/C][C]0.0611[/C][C]-0.0707[/C][C]0.0523[/C][C]0.1205[/C][C]0.0684[/C][C]0.2616[/C][/ROW]
[ROW][C]64[/C][C]0.0709[/C][C]0.0123[/C][C]0.0423[/C][C]0.0027[/C][C]0.052[/C][C]0.228[/C][/ROW]
[ROW][C]65[/C][C]0.073[/C][C]-0.0374[/C][C]0.0413[/C][C]0.0237[/C][C]0.0463[/C][C]0.2152[/C][/ROW]
[ROW][C]66[/C][C]0.0747[/C][C]-0.0196[/C][C]0.0377[/C][C]0.0062[/C][C]0.0396[/C][C]0.1991[/C][/ROW]
[ROW][C]67[/C][C]0.07[/C][C]-0.0837[/C][C]0.0443[/C][C]0.1291[/C][C]0.0524[/C][C]0.229[/C][/ROW]
[ROW][C]68[/C][C]0.0775[/C][C]-0.0155[/C][C]0.0407[/C][C]0.0036[/C][C]0.0463[/C][C]0.2152[/C][/ROW]
[ROW][C]69[/C][C]0.0774[/C][C]-0.0127[/C][C]0.0376[/C][C]0.0024[/C][C]0.0414[/C][C]0.2036[/C][/ROW]
[ROW][C]70[/C][C]0.0731[/C][C]0.0048[/C][C]0.0343[/C][C]4e-04[/C][C]0.0373[/C][C]0.1932[/C][/ROW]
[ROW][C]71[/C][C]0.074[/C][C]0.0995[/C][C]0.0402[/C][C]0.1633[/C][C]0.0488[/C][C]0.2209[/C][/ROW]
[ROW][C]72[/C][C]0.064[/C][C]-0.0522[/C][C]0.0412[/C][C]0.06[/C][C]0.0497[/C][C]0.223[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114815&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114815&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	0.0552	-0.0288	0	0.0203	0	0
62	0.067	0.0575	0.0431	0.0645	0.0424	0.2058
63	0.0611	-0.0707	0.0523	0.1205	0.0684	0.2616
64	0.0709	0.0123	0.0423	0.0027	0.052	0.228
65	0.073	-0.0374	0.0413	0.0237	0.0463	0.2152
66	0.0747	-0.0196	0.0377	0.0062	0.0396	0.1991
67	0.07	-0.0837	0.0443	0.1291	0.0524	0.229
68	0.0775	-0.0155	0.0407	0.0036	0.0463	0.2152
69	0.0774	-0.0127	0.0376	0.0024	0.0414	0.2036
70	0.0731	0.0048	0.0343	4e-04	0.0373	0.1932
71	0.074	0.0995	0.0402	0.1633	0.0488	0.2209
72	0.064	-0.0522	0.0412	0.06	0.0497	0.223

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

Parameters (R input):

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