2. Arima

By presenting a good adjustment for different types of problems, the model Arima is undoubtedly one of the models of series temporal most used in practice.

Example:

Adjustment of the Arima(p,d,q) model for the AMBV3 dataset.

AMBV3
84.06
83.85
83.56
83.47
83.27
82.81
82.20
82.06
81.62
80.77
81.30
81.92
82.75
82.77
82.84
82.82
82.72
82.29
81.18
80.11
80.27
80.21
79.92
79.96
80.19
80.17
80.17
79.85
81.00
80.44
79.96
79.85
79.82
80.11
80.20
80.31
81.18
80.81
81.15
81.32
81.21
81.40
81.10
81.40
82.27
82.15
81.78
81.69
81.34
81.88

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We will upload the data to the system.

Configuring as shown in the figure below to we will carry out the analysis

Then click Calculate to get the results. You can also generate the analyses and download them in Word format.

The results are:

Coefficients

	Values ​​
ar1	1.2991770
ar2	-0.3315352
ma1	-1.1432995
ma2	0.1433067

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Accuracy Measurements

	Values ​​
MAPE	0.4195899
MAD	0.3415169
MSD	0.1980571

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Results

Data	Fit	Residuals
84.06	83.97594	0.08405996
83.85	84.05419	-0.20419184
83.56	83.80930	-0.24929614
83.47	83.50654	-0.03654120
83.27	83.45321	-0.18320532
82.81	83.23766	-0.42766339
82.20	82.73172	-0.53171661
82.06	82.10190	-0.04189500
81.62	82.04797	-0.42797245
80.77	81.56606	-0.79605654
81.30	80.66053	0.63947339
81.92	81.43665	0.48334558
82.75	82.09832	0.65168277
82.77	82.94994	-0.17994385
82.84	82.81778	0.02222283
82.82	82.87305	-0.05304950
82.72	82.83318	-0.11317707
82.29	82.71394	-0.42393938
81.18	82.22084	-1.04083993
80.11	80.99494	-0.88494483
80.27	79.94805	0.32195173
80.21	80.34001	-0.13001000
79.92	80.26963	-0.34962719
79.96	79.94210	0.01789635
80.19	80.03927	0.15073363
80.17	80.30572	-0.13571517
80.17	80.24290	-0.07290330
79.85	80.23729	-0.38728594
81.00	79.87258	1.12742243
80.44	81.25721	-0.81721024
79.96	80.41750	-0.45750058
79.85	79.92551	-0.07551215
79.82	79.88654	-0.06654408
80.11	79.88400	0.22600473
80.20	80.22997	-0.02997067
80.31	80.28719	0.02280863
81.18	80.39805	0.78194752
80.81	81.38372	-0.57371613
81.15	80.80714	0.34286168
81.32	81.24309	0.07691003
81.21	81.38832	-0.17831860
81.40	81.22568	0.17431784
81.10	81.45735	-0.35734615
81.40	81.08071	0.31929431
82.27	81.47966	0.79033756
82.15	82.44500	-0.29499787
81.78	82.15185	-0.37185024
81.69	81.72017	-0.03016952
81.34	81.67519	-0.33518824
81.88	81.29572	0.58427699

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Forecast

	Forecast	C.I. Min. 80%	C.I. Supp. 80%	C.I. Min. 95%	I.C. Supp. 95%
51	81.98464	81.4055	82.56379	81.09892	82.87037
52	82.02483	81.1348	82.91485	80.66365	83.38600
53	82.04233	80.9153	83.16937	80.31868	83.76599
54	82.05176	80.7357	83.36782	80.03902	84.06450
55	82.05820	80.5864	83.53000	79.80728	84.30913

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