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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_arimaforecasting.wasp
Title produced by softwareARIMA Forecasting
Date of computationTue, 03 Dec 2013 09:13:20 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Dec/03/t13860800351m7uj0ym8e16weo.htm/, Retrieved Fri, 29 Mar 2024 13:21:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=230320, Retrieved Fri, 29 Mar 2024 13:21:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact63
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [ARIMA Backward Selection] [] [2013-12-03 13:47:50] [fcc5c79267206050edde2804b94bb45f]
- RMP     [ARIMA Forecasting] [] [2013-12-03 14:13:20] [42d3493b68e44bd1b6f64c892e56509b] [Current]
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Dataseries X:
46
62
66
59
58
61
41
27
58
70
49
59
44
36
72
45
56
54
53
35
61
52
47
51
52
63
74
45
51
64
36
30
55
64
39
40
63
45
59
55
40
64
27
28
45
57
45
69
60
56
58
50
51
53
37
22
55
70
62
58
39
49
58
47
42
62
39
40
72
70
54
65




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\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' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230320&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230320&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230320&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Univariate ARIMA Extrapolation Forecast
timeY[t]F[t]95% LB95% UBp-value(H0: Y[t] = F[t])P(F[t]>Y[t-1])P(F[t]>Y[t-s])P(F[t]>Y[48])
3640-------
3763-------
3845-------
3959-------
4055-------
4140-------
4264-------
4327-------
4428-------
4545-------
4657-------
4745-------
4869-------
496051.2532.897769.60230.1750.0290.10480.029
505651.533.147769.85230.31540.1820.75620.0308
515867.7549.397786.10230.14890.89520.8250.4469
52505132.647769.35230.45750.22740.33460.0273
535151.2532.897769.60230.48940.55310.88520.029
545360.7542.397779.10230.20390.85110.36430.1891
553739.2520.897757.60230.40510.0710.90467e-04
56223011.647748.35230.19640.22740.58460
575554.7536.397773.10230.48930.99980.85110.064
587060.7542.397779.10230.16160.73040.65560.1891
59624526.647763.35230.03470.00380.50.0052
605854.7536.397773.10230.36430.21940.0640.064
613951.2532.897769.60230.09540.23550.1750.029
624951.533.147769.85230.39470.90910.31540.0308
635867.7549.397786.10230.14890.97740.85110.4469
64475132.647769.35230.33460.22740.54250.0273
654251.2532.897769.60230.16160.6750.51060.029
666260.7542.397779.10230.44690.97740.79610.1891
673939.2520.897757.60230.48940.00760.59497e-04
68403011.647748.35230.14280.16820.80360
697254.7536.397773.10230.03270.94240.48930.064
707060.7542.397779.10230.16160.11480.16160.1891
71544526.647763.35230.16820.00380.03470.0052
726554.7536.397773.10230.13680.53190.36430.064

\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[48]) \tabularnewline
36 & 40 & - & - & - & - & - & - & - \tabularnewline
37 & 63 & - & - & - & - & - & - & - \tabularnewline
38 & 45 & - & - & - & - & - & - & - \tabularnewline
39 & 59 & - & - & - & - & - & - & - \tabularnewline
40 & 55 & - & - & - & - & - & - & - \tabularnewline
41 & 40 & - & - & - & - & - & - & - \tabularnewline
42 & 64 & - & - & - & - & - & - & - \tabularnewline
43 & 27 & - & - & - & - & - & - & - \tabularnewline
44 & 28 & - & - & - & - & - & - & - \tabularnewline
45 & 45 & - & - & - & - & - & - & - \tabularnewline
46 & 57 & - & - & - & - & - & - & - \tabularnewline
47 & 45 & - & - & - & - & - & - & - \tabularnewline
48 & 69 & - & - & - & - & - & - & - \tabularnewline
49 & 60 & 51.25 & 32.8977 & 69.6023 & 0.175 & 0.029 & 0.1048 & 0.029 \tabularnewline
50 & 56 & 51.5 & 33.1477 & 69.8523 & 0.3154 & 0.182 & 0.7562 & 0.0308 \tabularnewline
51 & 58 & 67.75 & 49.3977 & 86.1023 & 0.1489 & 0.8952 & 0.825 & 0.4469 \tabularnewline
52 & 50 & 51 & 32.6477 & 69.3523 & 0.4575 & 0.2274 & 0.3346 & 0.0273 \tabularnewline
53 & 51 & 51.25 & 32.8977 & 69.6023 & 0.4894 & 0.5531 & 0.8852 & 0.029 \tabularnewline
54 & 53 & 60.75 & 42.3977 & 79.1023 & 0.2039 & 0.8511 & 0.3643 & 0.1891 \tabularnewline
55 & 37 & 39.25 & 20.8977 & 57.6023 & 0.4051 & 0.071 & 0.9046 & 7e-04 \tabularnewline
56 & 22 & 30 & 11.6477 & 48.3523 & 0.1964 & 0.2274 & 0.5846 & 0 \tabularnewline
57 & 55 & 54.75 & 36.3977 & 73.1023 & 0.4893 & 0.9998 & 0.8511 & 0.064 \tabularnewline
58 & 70 & 60.75 & 42.3977 & 79.1023 & 0.1616 & 0.7304 & 0.6556 & 0.1891 \tabularnewline
59 & 62 & 45 & 26.6477 & 63.3523 & 0.0347 & 0.0038 & 0.5 & 0.0052 \tabularnewline
60 & 58 & 54.75 & 36.3977 & 73.1023 & 0.3643 & 0.2194 & 0.064 & 0.064 \tabularnewline
61 & 39 & 51.25 & 32.8977 & 69.6023 & 0.0954 & 0.2355 & 0.175 & 0.029 \tabularnewline
62 & 49 & 51.5 & 33.1477 & 69.8523 & 0.3947 & 0.9091 & 0.3154 & 0.0308 \tabularnewline
63 & 58 & 67.75 & 49.3977 & 86.1023 & 0.1489 & 0.9774 & 0.8511 & 0.4469 \tabularnewline
64 & 47 & 51 & 32.6477 & 69.3523 & 0.3346 & 0.2274 & 0.5425 & 0.0273 \tabularnewline
65 & 42 & 51.25 & 32.8977 & 69.6023 & 0.1616 & 0.675 & 0.5106 & 0.029 \tabularnewline
66 & 62 & 60.75 & 42.3977 & 79.1023 & 0.4469 & 0.9774 & 0.7961 & 0.1891 \tabularnewline
67 & 39 & 39.25 & 20.8977 & 57.6023 & 0.4894 & 0.0076 & 0.5949 & 7e-04 \tabularnewline
68 & 40 & 30 & 11.6477 & 48.3523 & 0.1428 & 0.1682 & 0.8036 & 0 \tabularnewline
69 & 72 & 54.75 & 36.3977 & 73.1023 & 0.0327 & 0.9424 & 0.4893 & 0.064 \tabularnewline
70 & 70 & 60.75 & 42.3977 & 79.1023 & 0.1616 & 0.1148 & 0.1616 & 0.1891 \tabularnewline
71 & 54 & 45 & 26.6477 & 63.3523 & 0.1682 & 0.0038 & 0.0347 & 0.0052 \tabularnewline
72 & 65 & 54.75 & 36.3977 & 73.1023 & 0.1368 & 0.5319 & 0.3643 & 0.064 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230320&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[48])[/C][/ROW]
[ROW][C]36[/C][C]40[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]37[/C][C]63[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]38[/C][C]45[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]39[/C][C]59[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]40[/C][C]55[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]41[/C][C]40[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]42[/C][C]64[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]43[/C][C]27[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]44[/C][C]28[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]45[/C][C]45[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]46[/C][C]57[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]47[/C][C]45[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/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]51.25[/C][C]32.8977[/C][C]69.6023[/C][C]0.175[/C][C]0.029[/C][C]0.1048[/C][C]0.029[/C][/ROW]
[ROW][C]50[/C][C]56[/C][C]51.5[/C][C]33.1477[/C][C]69.8523[/C][C]0.3154[/C][C]0.182[/C][C]0.7562[/C][C]0.0308[/C][/ROW]
[ROW][C]51[/C][C]58[/C][C]67.75[/C][C]49.3977[/C][C]86.1023[/C][C]0.1489[/C][C]0.8952[/C][C]0.825[/C][C]0.4469[/C][/ROW]
[ROW][C]52[/C][C]50[/C][C]51[/C][C]32.6477[/C][C]69.3523[/C][C]0.4575[/C][C]0.2274[/C][C]0.3346[/C][C]0.0273[/C][/ROW]
[ROW][C]53[/C][C]51[/C][C]51.25[/C][C]32.8977[/C][C]69.6023[/C][C]0.4894[/C][C]0.5531[/C][C]0.8852[/C][C]0.029[/C][/ROW]
[ROW][C]54[/C][C]53[/C][C]60.75[/C][C]42.3977[/C][C]79.1023[/C][C]0.2039[/C][C]0.8511[/C][C]0.3643[/C][C]0.1891[/C][/ROW]
[ROW][C]55[/C][C]37[/C][C]39.25[/C][C]20.8977[/C][C]57.6023[/C][C]0.4051[/C][C]0.071[/C][C]0.9046[/C][C]7e-04[/C][/ROW]
[ROW][C]56[/C][C]22[/C][C]30[/C][C]11.6477[/C][C]48.3523[/C][C]0.1964[/C][C]0.2274[/C][C]0.5846[/C][C]0[/C][/ROW]
[ROW][C]57[/C][C]55[/C][C]54.75[/C][C]36.3977[/C][C]73.1023[/C][C]0.4893[/C][C]0.9998[/C][C]0.8511[/C][C]0.064[/C][/ROW]
[ROW][C]58[/C][C]70[/C][C]60.75[/C][C]42.3977[/C][C]79.1023[/C][C]0.1616[/C][C]0.7304[/C][C]0.6556[/C][C]0.1891[/C][/ROW]
[ROW][C]59[/C][C]62[/C][C]45[/C][C]26.6477[/C][C]63.3523[/C][C]0.0347[/C][C]0.0038[/C][C]0.5[/C][C]0.0052[/C][/ROW]
[ROW][C]60[/C][C]58[/C][C]54.75[/C][C]36.3977[/C][C]73.1023[/C][C]0.3643[/C][C]0.2194[/C][C]0.064[/C][C]0.064[/C][/ROW]
[ROW][C]61[/C][C]39[/C][C]51.25[/C][C]32.8977[/C][C]69.6023[/C][C]0.0954[/C][C]0.2355[/C][C]0.175[/C][C]0.029[/C][/ROW]
[ROW][C]62[/C][C]49[/C][C]51.5[/C][C]33.1477[/C][C]69.8523[/C][C]0.3947[/C][C]0.9091[/C][C]0.3154[/C][C]0.0308[/C][/ROW]
[ROW][C]63[/C][C]58[/C][C]67.75[/C][C]49.3977[/C][C]86.1023[/C][C]0.1489[/C][C]0.9774[/C][C]0.8511[/C][C]0.4469[/C][/ROW]
[ROW][C]64[/C][C]47[/C][C]51[/C][C]32.6477[/C][C]69.3523[/C][C]0.3346[/C][C]0.2274[/C][C]0.5425[/C][C]0.0273[/C][/ROW]
[ROW][C]65[/C][C]42[/C][C]51.25[/C][C]32.8977[/C][C]69.6023[/C][C]0.1616[/C][C]0.675[/C][C]0.5106[/C][C]0.029[/C][/ROW]
[ROW][C]66[/C][C]62[/C][C]60.75[/C][C]42.3977[/C][C]79.1023[/C][C]0.4469[/C][C]0.9774[/C][C]0.7961[/C][C]0.1891[/C][/ROW]
[ROW][C]67[/C][C]39[/C][C]39.25[/C][C]20.8977[/C][C]57.6023[/C][C]0.4894[/C][C]0.0076[/C][C]0.5949[/C][C]7e-04[/C][/ROW]
[ROW][C]68[/C][C]40[/C][C]30[/C][C]11.6477[/C][C]48.3523[/C][C]0.1428[/C][C]0.1682[/C][C]0.8036[/C][C]0[/C][/ROW]
[ROW][C]69[/C][C]72[/C][C]54.75[/C][C]36.3977[/C][C]73.1023[/C][C]0.0327[/C][C]0.9424[/C][C]0.4893[/C][C]0.064[/C][/ROW]
[ROW][C]70[/C][C]70[/C][C]60.75[/C][C]42.3977[/C][C]79.1023[/C][C]0.1616[/C][C]0.1148[/C][C]0.1616[/C][C]0.1891[/C][/ROW]
[ROW][C]71[/C][C]54[/C][C]45[/C][C]26.6477[/C][C]63.3523[/C][C]0.1682[/C][C]0.0038[/C][C]0.0347[/C][C]0.0052[/C][/ROW]
[ROW][C]72[/C][C]65[/C][C]54.75[/C][C]36.3977[/C][C]73.1023[/C][C]0.1368[/C][C]0.5319[/C][C]0.3643[/C][C]0.064[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230320&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230320&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
timeY[t]F[t]95% LB95% UBp-value(H0: Y[t] = F[t])P(F[t]>Y[t-1])P(F[t]>Y[t-s])P(F[t]>Y[48])
3640-------
3763-------
3845-------
3959-------
4055-------
4140-------
4264-------
4327-------
4428-------
4545-------
4657-------
4745-------
4869-------
496051.2532.897769.60230.1750.0290.10480.029
505651.533.147769.85230.31540.1820.75620.0308
515867.7549.397786.10230.14890.89520.8250.4469
52505132.647769.35230.45750.22740.33460.0273
535151.2532.897769.60230.48940.55310.88520.029
545360.7542.397779.10230.20390.85110.36430.1891
553739.2520.897757.60230.40510.0710.90467e-04
56223011.647748.35230.19640.22740.58460
575554.7536.397773.10230.48930.99980.85110.064
587060.7542.397779.10230.16160.73040.65560.1891
59624526.647763.35230.03470.00380.50.0052
605854.7536.397773.10230.36430.21940.0640.064
613951.2532.897769.60230.09540.23550.1750.029
624951.533.147769.85230.39470.90910.31540.0308
635867.7549.397786.10230.14890.97740.85110.4469
64475132.647769.35230.33460.22740.54250.0273
654251.2532.897769.60230.16160.6750.51060.029
666260.7542.397779.10230.44690.97740.79610.1891
673939.2520.897757.60230.48940.00760.59497e-04
68403011.647748.35230.14280.16820.80360
697254.7536.397773.10230.03270.94240.48930.064
707060.7542.397779.10230.16160.11480.16160.1891
71544526.647763.35230.16820.00380.03470.0052
726554.7536.397773.10230.13680.53190.36430.064







Univariate ARIMA Extrapolation Forecast Performance
time% S.E.PEMAPEsMAPESq.EMSERMSEScaledEMASE
490.18270.14580.14580.157376.5627000.75370.7537
500.18180.08040.11310.120520.250148.40646.95750.38760.5707
510.1382-0.16810.13140.13295.062263.95837.9974-0.83990.6604
520.1836-0.020.10360.104148.21876.944-0.08610.5169
530.1827-0.00490.08380.08420.062538.58756.2119-0.02150.4178
540.1541-0.14620.09420.092860.062342.16666.4936-0.66760.4594
550.2386-0.06080.08950.0885.062536.8666.0717-0.19380.4215
560.3121-0.36360.12370.115563.999940.25786.3449-0.68910.4549
570.1710.00450.11050.10310.062535.79165.98260.02150.4068
580.15410.13210.11270.10785.562840.76876.3850.79680.4458
590.20810.27420.12730.1261289.000463.33527.95831.46440.5384
600.1710.0560.12140.120410.562658.93757.67710.280.5169
610.1827-0.31410.13620.1321150.062265.94718.1208-1.05520.5583
620.1818-0.0510.13010.12626.249961.6837.8539-0.21540.5338
630.1382-0.16810.13270.128195.062263.90837.9943-0.83990.5542
640.1836-0.08510.12970.125215.999960.9147.8047-0.34460.5411
650.1827-0.22020.1350.129585.562362.36397.8971-0.79680.5561
660.15410.02020.12860.12341.562558.98617.68020.10770.5312
670.2386-0.00640.12220.11730.062555.88487.4756-0.02150.5044
680.31210.250.12860.1257100.000258.09067.62170.86140.5222
690.1710.23960.13390.1327297.56369.4948.33631.4860.5681
700.15410.13210.13380.133185.562870.22448.380.79680.5785
710.20810.16670.13520.135281.000270.6938.40790.77530.5871
720.1710.15770.13620.1367105.062872.1258.49260.8830.5994

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & sMAPE & Sq.E & MSE & RMSE & ScaledE & MASE \tabularnewline
49 & 0.1827 & 0.1458 & 0.1458 & 0.1573 & 76.5627 & 0 & 0 & 0.7537 & 0.7537 \tabularnewline
50 & 0.1818 & 0.0804 & 0.1131 & 0.1205 & 20.2501 & 48.4064 & 6.9575 & 0.3876 & 0.5707 \tabularnewline
51 & 0.1382 & -0.1681 & 0.1314 & 0.132 & 95.0622 & 63.9583 & 7.9974 & -0.8399 & 0.6604 \tabularnewline
52 & 0.1836 & -0.02 & 0.1036 & 0.104 & 1 & 48.2187 & 6.944 & -0.0861 & 0.5169 \tabularnewline
53 & 0.1827 & -0.0049 & 0.0838 & 0.0842 & 0.0625 & 38.5875 & 6.2119 & -0.0215 & 0.4178 \tabularnewline
54 & 0.1541 & -0.1462 & 0.0942 & 0.0928 & 60.0623 & 42.1666 & 6.4936 & -0.6676 & 0.4594 \tabularnewline
55 & 0.2386 & -0.0608 & 0.0895 & 0.088 & 5.0625 & 36.866 & 6.0717 & -0.1938 & 0.4215 \tabularnewline
56 & 0.3121 & -0.3636 & 0.1237 & 0.1155 & 63.9999 & 40.2578 & 6.3449 & -0.6891 & 0.4549 \tabularnewline
57 & 0.171 & 0.0045 & 0.1105 & 0.1031 & 0.0625 & 35.7916 & 5.9826 & 0.0215 & 0.4068 \tabularnewline
58 & 0.1541 & 0.1321 & 0.1127 & 0.107 & 85.5628 & 40.7687 & 6.385 & 0.7968 & 0.4458 \tabularnewline
59 & 0.2081 & 0.2742 & 0.1273 & 0.1261 & 289.0004 & 63.3352 & 7.9583 & 1.4644 & 0.5384 \tabularnewline
60 & 0.171 & 0.056 & 0.1214 & 0.1204 & 10.5626 & 58.9375 & 7.6771 & 0.28 & 0.5169 \tabularnewline
61 & 0.1827 & -0.3141 & 0.1362 & 0.1321 & 150.0622 & 65.9471 & 8.1208 & -1.0552 & 0.5583 \tabularnewline
62 & 0.1818 & -0.051 & 0.1301 & 0.1262 & 6.2499 & 61.683 & 7.8539 & -0.2154 & 0.5338 \tabularnewline
63 & 0.1382 & -0.1681 & 0.1327 & 0.1281 & 95.0622 & 63.9083 & 7.9943 & -0.8399 & 0.5542 \tabularnewline
64 & 0.1836 & -0.0851 & 0.1297 & 0.1252 & 15.9999 & 60.914 & 7.8047 & -0.3446 & 0.5411 \tabularnewline
65 & 0.1827 & -0.2202 & 0.135 & 0.1295 & 85.5623 & 62.3639 & 7.8971 & -0.7968 & 0.5561 \tabularnewline
66 & 0.1541 & 0.0202 & 0.1286 & 0.1234 & 1.5625 & 58.9861 & 7.6802 & 0.1077 & 0.5312 \tabularnewline
67 & 0.2386 & -0.0064 & 0.1222 & 0.1173 & 0.0625 & 55.8848 & 7.4756 & -0.0215 & 0.5044 \tabularnewline
68 & 0.3121 & 0.25 & 0.1286 & 0.1257 & 100.0002 & 58.0906 & 7.6217 & 0.8614 & 0.5222 \tabularnewline
69 & 0.171 & 0.2396 & 0.1339 & 0.1327 & 297.563 & 69.494 & 8.3363 & 1.486 & 0.5681 \tabularnewline
70 & 0.1541 & 0.1321 & 0.1338 & 0.1331 & 85.5628 & 70.2244 & 8.38 & 0.7968 & 0.5785 \tabularnewline
71 & 0.2081 & 0.1667 & 0.1352 & 0.1352 & 81.0002 & 70.693 & 8.4079 & 0.7753 & 0.5871 \tabularnewline
72 & 0.171 & 0.1577 & 0.1362 & 0.1367 & 105.0628 & 72.125 & 8.4926 & 0.883 & 0.5994 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230320&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]sMAPE[/C][C]Sq.E[/C][C]MSE[/C][C]RMSE[/C][C]ScaledE[/C][C]MASE[/C][/ROW]
[ROW][C]49[/C][C]0.1827[/C][C]0.1458[/C][C]0.1458[/C][C]0.1573[/C][C]76.5627[/C][C]0[/C][C]0[/C][C]0.7537[/C][C]0.7537[/C][/ROW]
[ROW][C]50[/C][C]0.1818[/C][C]0.0804[/C][C]0.1131[/C][C]0.1205[/C][C]20.2501[/C][C]48.4064[/C][C]6.9575[/C][C]0.3876[/C][C]0.5707[/C][/ROW]
[ROW][C]51[/C][C]0.1382[/C][C]-0.1681[/C][C]0.1314[/C][C]0.132[/C][C]95.0622[/C][C]63.9583[/C][C]7.9974[/C][C]-0.8399[/C][C]0.6604[/C][/ROW]
[ROW][C]52[/C][C]0.1836[/C][C]-0.02[/C][C]0.1036[/C][C]0.104[/C][C]1[/C][C]48.2187[/C][C]6.944[/C][C]-0.0861[/C][C]0.5169[/C][/ROW]
[ROW][C]53[/C][C]0.1827[/C][C]-0.0049[/C][C]0.0838[/C][C]0.0842[/C][C]0.0625[/C][C]38.5875[/C][C]6.2119[/C][C]-0.0215[/C][C]0.4178[/C][/ROW]
[ROW][C]54[/C][C]0.1541[/C][C]-0.1462[/C][C]0.0942[/C][C]0.0928[/C][C]60.0623[/C][C]42.1666[/C][C]6.4936[/C][C]-0.6676[/C][C]0.4594[/C][/ROW]
[ROW][C]55[/C][C]0.2386[/C][C]-0.0608[/C][C]0.0895[/C][C]0.088[/C][C]5.0625[/C][C]36.866[/C][C]6.0717[/C][C]-0.1938[/C][C]0.4215[/C][/ROW]
[ROW][C]56[/C][C]0.3121[/C][C]-0.3636[/C][C]0.1237[/C][C]0.1155[/C][C]63.9999[/C][C]40.2578[/C][C]6.3449[/C][C]-0.6891[/C][C]0.4549[/C][/ROW]
[ROW][C]57[/C][C]0.171[/C][C]0.0045[/C][C]0.1105[/C][C]0.1031[/C][C]0.0625[/C][C]35.7916[/C][C]5.9826[/C][C]0.0215[/C][C]0.4068[/C][/ROW]
[ROW][C]58[/C][C]0.1541[/C][C]0.1321[/C][C]0.1127[/C][C]0.107[/C][C]85.5628[/C][C]40.7687[/C][C]6.385[/C][C]0.7968[/C][C]0.4458[/C][/ROW]
[ROW][C]59[/C][C]0.2081[/C][C]0.2742[/C][C]0.1273[/C][C]0.1261[/C][C]289.0004[/C][C]63.3352[/C][C]7.9583[/C][C]1.4644[/C][C]0.5384[/C][/ROW]
[ROW][C]60[/C][C]0.171[/C][C]0.056[/C][C]0.1214[/C][C]0.1204[/C][C]10.5626[/C][C]58.9375[/C][C]7.6771[/C][C]0.28[/C][C]0.5169[/C][/ROW]
[ROW][C]61[/C][C]0.1827[/C][C]-0.3141[/C][C]0.1362[/C][C]0.1321[/C][C]150.0622[/C][C]65.9471[/C][C]8.1208[/C][C]-1.0552[/C][C]0.5583[/C][/ROW]
[ROW][C]62[/C][C]0.1818[/C][C]-0.051[/C][C]0.1301[/C][C]0.1262[/C][C]6.2499[/C][C]61.683[/C][C]7.8539[/C][C]-0.2154[/C][C]0.5338[/C][/ROW]
[ROW][C]63[/C][C]0.1382[/C][C]-0.1681[/C][C]0.1327[/C][C]0.1281[/C][C]95.0622[/C][C]63.9083[/C][C]7.9943[/C][C]-0.8399[/C][C]0.5542[/C][/ROW]
[ROW][C]64[/C][C]0.1836[/C][C]-0.0851[/C][C]0.1297[/C][C]0.1252[/C][C]15.9999[/C][C]60.914[/C][C]7.8047[/C][C]-0.3446[/C][C]0.5411[/C][/ROW]
[ROW][C]65[/C][C]0.1827[/C][C]-0.2202[/C][C]0.135[/C][C]0.1295[/C][C]85.5623[/C][C]62.3639[/C][C]7.8971[/C][C]-0.7968[/C][C]0.5561[/C][/ROW]
[ROW][C]66[/C][C]0.1541[/C][C]0.0202[/C][C]0.1286[/C][C]0.1234[/C][C]1.5625[/C][C]58.9861[/C][C]7.6802[/C][C]0.1077[/C][C]0.5312[/C][/ROW]
[ROW][C]67[/C][C]0.2386[/C][C]-0.0064[/C][C]0.1222[/C][C]0.1173[/C][C]0.0625[/C][C]55.8848[/C][C]7.4756[/C][C]-0.0215[/C][C]0.5044[/C][/ROW]
[ROW][C]68[/C][C]0.3121[/C][C]0.25[/C][C]0.1286[/C][C]0.1257[/C][C]100.0002[/C][C]58.0906[/C][C]7.6217[/C][C]0.8614[/C][C]0.5222[/C][/ROW]
[ROW][C]69[/C][C]0.171[/C][C]0.2396[/C][C]0.1339[/C][C]0.1327[/C][C]297.563[/C][C]69.494[/C][C]8.3363[/C][C]1.486[/C][C]0.5681[/C][/ROW]
[ROW][C]70[/C][C]0.1541[/C][C]0.1321[/C][C]0.1338[/C][C]0.1331[/C][C]85.5628[/C][C]70.2244[/C][C]8.38[/C][C]0.7968[/C][C]0.5785[/C][/ROW]
[ROW][C]71[/C][C]0.2081[/C][C]0.1667[/C][C]0.1352[/C][C]0.1352[/C][C]81.0002[/C][C]70.693[/C][C]8.4079[/C][C]0.7753[/C][C]0.5871[/C][/ROW]
[ROW][C]72[/C][C]0.171[/C][C]0.1577[/C][C]0.1362[/C][C]0.1367[/C][C]105.0628[/C][C]72.125[/C][C]8.4926[/C][C]0.883[/C][C]0.5994[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230320&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230320&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.PEMAPEsMAPESq.EMSERMSEScaledEMASE
490.18270.14580.14580.157376.5627000.75370.7537
500.18180.08040.11310.120520.250148.40646.95750.38760.5707
510.1382-0.16810.13140.13295.062263.95837.9974-0.83990.6604
520.1836-0.020.10360.104148.21876.944-0.08610.5169
530.1827-0.00490.08380.08420.062538.58756.2119-0.02150.4178
540.1541-0.14620.09420.092860.062342.16666.4936-0.66760.4594
550.2386-0.06080.08950.0885.062536.8666.0717-0.19380.4215
560.3121-0.36360.12370.115563.999940.25786.3449-0.68910.4549
570.1710.00450.11050.10310.062535.79165.98260.02150.4068
580.15410.13210.11270.10785.562840.76876.3850.79680.4458
590.20810.27420.12730.1261289.000463.33527.95831.46440.5384
600.1710.0560.12140.120410.562658.93757.67710.280.5169
610.1827-0.31410.13620.1321150.062265.94718.1208-1.05520.5583
620.1818-0.0510.13010.12626.249961.6837.8539-0.21540.5338
630.1382-0.16810.13270.128195.062263.90837.9943-0.83990.5542
640.1836-0.08510.12970.125215.999960.9147.8047-0.34460.5411
650.1827-0.22020.1350.129585.562362.36397.8971-0.79680.5561
660.15410.02020.12860.12341.562558.98617.68020.10770.5312
670.2386-0.00640.12220.11730.062555.88487.4756-0.02150.5044
680.31210.250.12860.1257100.000258.09067.62170.86140.5222
690.1710.23960.13390.1327297.56369.4948.33631.4860.5681
700.15410.13210.13380.133185.562870.22448.380.79680.5785
710.20810.16670.13520.135281.000270.6938.40790.77530.5871
720.1710.15770.13620.1367105.062872.1258.49260.8830.5994



Parameters (Session):
par1 = 24 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = 0 ; par7 = 0 ; par8 = 0 ; par9 = 1 ; par10 = FALSE ;
Parameters (R input):
par1 = 24 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = 0 ; par7 = 0 ; par8 = 0 ; par9 = 1 ; par10 = FALSE ;
R code (references can be found in the software module):
par10 <- 'FALSE'
par9 <- '1'
par8 <- '0'
par7 <- '0'
par6 <- '0'
par5 <- '12'
par4 <- '1'
par3 <- '0'
par2 <- '1'
par1 <- '0'
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.spe <- array(0, dim=fx)
perf.scalederr <- array(0, dim=fx)
perf.mase <- array(0, dim=fx)
perf.mase1 <- array(0, dim=fx)
perf.mape <- array(0, dim=fx)
perf.smape <- array(0, dim=fx)
perf.mape1 <- array(0, dim=fx)
perf.smape1 <- 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)
perf.scaleddenom <- 0
for (i in 2:fx) {
perf.scaleddenom = perf.scaleddenom + abs(x[nx+i] - x[nx+i-1])
}
perf.scaleddenom = perf.scaleddenom / (fx-1)
for (i in 1:fx) {
locSD <- (ub[i] - forecast$pred[i]) / 1.96
perf.scalederr[i] = (x[nx+i] - forecast$pred[i]) / perf.scaleddenom
perf.pe[i] = (x[nx+i] - forecast$pred[i]) / x[nx+i]
perf.spe[i] = 2*(x[nx+i] - forecast$pred[i]) / (x[nx+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.smape[1] = abs(perf.spe[1])
perf.mape1[1] = perf.mape[1]
perf.smape1[1] = perf.smape[1]
perf.mse[1] = perf.se[1]
perf.mase[1] = abs(perf.scalederr[1])
perf.mase1[1] = perf.mase[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.smape[i] = perf.smape[i-1] + abs(perf.spe[i])
perf.smape1[i] = perf.smape[i] / i
perf.mse[i] = perf.mse[i-1] + perf.se[i]
perf.mse1[i] = perf.mse[i] / i
perf.mase[i] = perf.mase[i-1] + abs(perf.scalederr[i])
perf.mase1[i] = perf.mase[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',10,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,'sMAPE',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.element(a,'ScaledE',1,header=TRUE)
a<-table.element(a,'MASE',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.smape1[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.element(a,round(perf.scalederr[i],4))
a<-table.element(a,round(perf.mase1[i],4))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')