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 verticapy.datasets import load_amazon

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

	📅 date Date 100%	123 number Integer 100%
1	1998-01-01	0
2	1998-05-01	0
3	1998-10-01	23495
4	1998-12-01	4448
5	1999-03-01	667
6	1999-04-01	717
7	2000-01-01	778
8	2000-03-01	848
9	2000-09-01	23291
10	2000-10-01	27336
11	2000-12-01	4465
12	2001-01-01	547
13	2001-12-01	6201
14	2002-03-01	1679
15	2002-04-01	1682
16	2002-05-01	3818
17	2002-08-01	57151
18	2002-10-01	47722
19	2002-11-01	28179
20	2002-12-01	11944
21	2003-03-01	2749
22	2003-06-01	6506
23	2003-09-01	76325
24	2003-10-01	43295
25	2004-02-01	1255
26	2004-03-01	2040
27	2004-10-01	40331
28	2005-01-01	4990
29	2005-02-01	2153
30	2005-03-01	1706
31	2005-08-01	51981
32	2005-11-01	21752
33	2006-05-01	808
34	2007-01-01	3055
35	2007-02-01	1751
36	2007-03-01	2136
37	2007-05-01	1286
38	2007-07-01	7808
39	2007-09-01	94526
40	2008-04-01	1253
41	2008-06-01	1287
42	2008-09-01	39445
43	2008-12-01	4995
44	2009-02-01	1140
45	2009-08-01	17559
46	2009-09-01	29430
47	2010-04-01	2200
48	2010-09-01	85408
49	2011-01-01	1416
50	2011-11-01	12221
51	2012-02-01	1436
52	2012-03-01	2058
53	2012-05-01	3240
54	2012-06-01	5890
55	2012-10-01	34213
56	2012-12-01	6823
57	2013-04-01	1372
58	2013-09-01	31585
59	2013-12-01	12006
60	2014-01-01	2633
61	2014-05-01	3189
62	2014-07-01	10801
63	2014-12-01	10938
64	2015-04-01	2573
65	2015-05-01	2384
66	2015-06-01	5810
67	2015-09-01	72083
68	2015-11-01	27529
69	2016-01-01	5979
70	2016-02-01	4147
71	2016-05-01	3568
72	2016-07-01	19141
73	2016-10-01	30210
74	2017-01-01	2408
75	2017-06-01	7506
76	2017-07-01	22911
77	2017-11-01	17585
78	1998-04-01	0
79	1998-08-01	35549
80	1998-09-01	41968
81	1998-11-01	6804
82	1999-02-01	1284
83	1999-05-01	1812
84	1999-08-01	39486
85	1999-09-01	36913
86	2000-02-01	561
87	2000-04-01	537
88	2000-06-01	6275
89	2000-11-01	8399
90	2001-04-01	1081
91	2001-05-01	2090
92	2001-07-01	6490
93	2001-10-01	31038
94	2002-06-01	10839
95	2002-09-01	55803
96	2003-07-01	11804
97	2003-08-01	43736
98	2003-11-01	23572
99	2003-12-01	15342
100	2004-01-01	2705

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.

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

from verticapy.machine_learning.vertica import ARIMA

model = ARIMA(order = (12, 0, 1))

model.fit(
    amazon,
    y = "number",
    ts = "date",
)



============
coefficients
============
parameter| value  
---------+--------
  phi_1  | 0.31880
  phi_2  |-0.10672
  phi_3  |-0.07836
  phi_4  |-0.03784
  phi_5  |-0.00728
  phi_6  | 0.05855
  phi_7  |-0.05685
  phi_8  | 0.02299
  phi_9  |-0.02943
 phi_10  |-0.03170
 phi_11  | 0.08016
 phi_12  | 0.67982
 theta_1 | 0.37215


==============
regularization
==============
none

===============
timeseries_name
===============
"number"

==============
timestamp_name
==============
date

==============
missing_method
==============
linear_interpolation

===========
call_string
===========
ARIMA('"public"."_verticapy_tmp_arima_v_mldb_01927f5497bf11efa8720242ac120002_"', '"public"."_verticapy_tmp_view_v_mldb_01e38a5c97bf11efa8720242ac120002_"', '"number"', 'date' USING PARAMETERS p=12, d=0, q=1, missing='linear_interpolation', init_method='Zero', epsilon=1e-06, max_iterations=100);

===============
Additional Info
===============
       Name       |     Value     
------------------+---------------
        p         |      12       
        d         |       0       
        q         |       1       
       mean       |  15288.86611  
      lambda      |    1.00000    
mean_squared_error|110069159.22574
rejected_row_count|       0       
accepted_row_count|      239      

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

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

	value
explained_variance	0.886197750335032
max_error	27071.0112210089
median_absolute_error	2512.26144236847
mean_absolute_error	4999.39474659287
mean_squared_error	61686598.2683679
root_mean_squared_error	7854.08163112454
r2	0.881534696051036
r2_adj	0.879066668885433
aic	901.304394780616
bic	904.702908876578

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