Time Series

Time series models are a type of regression on a dataset with a timestamp label.

The following example creates a time series model to predict the number of forest fires in Brazil with the amazon dataset.

from vastorbit.datasets import load_amazon

amazon = load_amazon().groupby("date", "SUM(number) AS number")
amazon.head(100)

	📅 date Date 100%	123 number Bigint 100%
1	1998-05-01	0
2	1998-10-01	23495
3	2000-01-01	778
4	2001-06-01	8433
5	2017-01-01	2408
6	2009-04-01	1078
7	2003-08-01	43736
8	2004-11-01	30763
9	2004-12-01	17524
10	2012-04-01	2193
11	2013-07-01	7310
12	2005-05-01	3210
13	2005-06-01	5811
14	1998-03-01	0
15	1999-01-01	1081
16	1999-07-01	8756
17	1999-12-01	4376
18	2001-08-01	31887
19	2001-11-01	15639
20	2016-06-01	6339
21	2016-12-01	8613
22	2007-04-01	415
23	2008-09-01	39445
24	2009-05-01	2593
25	2009-08-01	17559
26	2009-12-01	9494
27	2010-02-01	2386
28	2003-06-01	6506
29	2004-03-01	2040
30	2011-02-01	973
31	2011-12-01	9828
32	2012-01-01	2491
33	2015-05-01	2384
34	2006-01-01	3255
35	1998-12-01	4448
36	2017-07-01	22911
37	2017-08-01	49485
38	2017-09-01	110988
39	2017-10-01	42720
40	2009-02-01	1140
41	2002-10-01	47722
42	2011-03-01	937
43	2011-07-01	8524
44	2012-11-01	13586
45	2013-11-01	12150
46	2015-03-01	2202
47	2015-04-01	2573
48	2015-10-01	49979
49	2015-11-01	27529
50	1998-01-01	0
51	2001-12-01	6201
52	2007-02-01	1751
53	2009-06-01	2962
54	2010-01-01	2851
55	2002-02-01	1570
56	2002-06-01	10839
57	2003-11-01	23572
58	2004-09-01	83500
59	2011-06-01	4578
60	2012-05-01	3240
61	2012-07-01	13507
62	2012-12-01	6823
63	2013-09-01	31585
64	2006-12-01	5027
65	2016-02-01	4147
66	2017-04-01	1559
67	2017-05-01	2506
68	2008-02-01	1275
69	2009-09-01	29430
70	2009-10-01	24202
71	2003-01-01	5091
72	2003-07-01	11804
73	2004-05-01	3535
74	2013-02-01	1587
75	2014-06-01	6483
76	2014-12-01	10938
77	2006-02-01	1666
78	2016-04-01	3972
79	2008-06-01	1287
80	2008-11-01	12778
81	2010-03-01	2417
82	2010-06-01	3642
83	2010-12-01	6856
84	2002-05-01	3818
85	2003-10-01	43295
86	2005-07-01	15663
87	2006-04-01	792
88	2000-02-01	561
89	2000-04-01	537
90	2000-05-01	2097
91	2000-06-01	6275
92	2001-03-01	1268
93	2016-03-01	3796
94	2008-07-01	4507
95	2008-12-01	4995
96	2010-10-01	31485
97	2004-06-01	14262
98	2011-04-01	1152
99	2013-03-01	1969
100	2005-02-01	2153

The feature date tells us that we should be working with a time series model. To do predictions on time series, we use previous values called lags.

To help visualize the seasonality of forest fires, we’ll draw some autocorrelation plots.

amazon.acf(
    ts = "date",
    column = "number",
    p = 24,
)

amazon.pacf(
    ts = "date",
    column = "number",
    p = 8,
)

Forest fires follow a predictable, seasonal pattern, so it should be easy to predict future forest fires with past data.

vastorbit offers several models, including a multiple time series model. For this example, let’s use a ARIMA model.

from vastorbit.machine_learning.vast import ARIMA

model = ARIMA(order = (12, 0, 0))
model.fit(
    amazon,
    y = "number",
    ts = "date",
)

Just like with other regression models, we’ll evaluate our model with the report() method.

model.report(npredictions = 50, start = 50)

	value
explained_variance	0.8603952980284197
max_error	31495.699489466093
median_absolute_error	2584.3152
mean_absolute_error	5443.646700206962
mean_squared_error	78073484.64492206
root_mean_squared_error	8835.920135725653
r2	0.8500646923570399
r2_adj	0.8469410401144781
aic	913.0835845138098
bic	916.4820986097724

We can also draw our model using one-step ahead and dynamic forecasting.

model.plot(amazon, npredictions = 40,)

In the next lesson, we’ll go over Regression