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verticapy.machine_learning.vertica.tsa.AR.report

AR.report(metrics: str | Literal[None, 'anova', 'details'] | list[Literal['aic', 'bic', 'r2', 'rsquared', 'mae', 'mean_absolute_error', 'mse', 'mean_squared_error', 'msle', 'mean_squared_log_error', 'max', 'max_error', 'median', 'median_absolute_error', 'var', 'explained_variance']] | None = None, start: int | None = None, npredictions: int | None = None, method: Literal['auto', 'forecast'] = 'auto') → float | TableSample

Computes a regression report using multiple metrics to evaluate the model (r2, mse, max error…).

Parameters

metrics: str | list, optional

The metrics used to compute the regression report.

• None:

  Computes the model different metrics.

• anova:

  Computes the model ANOVA table.

• details:

  Computes the model details.

It can also be a list of the metrics used to compute the final report.

• aic:

  Akaike’s Information Criterion

  \[AIC = 2k - 2\ln(\hat{L})\]

• bic:

  Bayesian Information Criterion

  \[BIC = -2\ln(\hat{L}) + k \ln(n)\]

• max:

  Max Error.

  \[ME = \max_{i=1}^{n} \left| y_i - \hat{y}_i \right|\]

• mae:

  Mean Absolute Error.

  \[MAE = \frac{1}{n} \sum_{i=1}^{n} \left| y_i - \hat{y}_i \right|\]

• median:

  Median Absolute Error.

  \[MedAE = \text{median}_{i=1}^{n} \left| y_i - \hat{y}_i \right|\]

• mse:

  Mean Squared Error.

  \[MsE = \frac{1}{n} \sum_{i=1}^{n} \left( y_i - \hat{y}_i \right)^2\]

• msle:

  Mean Squared Log Error.

  \[MSLE = \frac{1}{n} \sum_{i=1}^{n} (\log(1 + y_i) - \log(1 + \hat{y}_i))^2\]

• r2:

  R squared coefficient.

  \[R^2 = 1 - \frac{\sum_{i=1}^{n} (y_i - \hat{y}_i)^2}{\sum_{i=1}^{n} (y_i - \bar{y})^2}\]

• r2a:

  R2 adjusted

  \[\text{Adjusted } R^2 = 1 - \frac{(1 - R^2)(n - 1)}{n - k - 1}\]

• qe:

  quantile error, the quantile must be included in the name. Example: qe50.1% will return the quantile error using q=0.501.

• rmse:

  Root-mean-squared error

  \[RMSE = \sqrt{\frac{1}{n} \sum_{i=1}^{n} (y_i - \hat{y}_i)^2}\]

• var:

  Explained Variance

  \[\text{Explained Variance} = 1 - \frac{Var(y - \hat{y})}{Var(y)}\]

start: int, optional

The behavior of the start parameter and its range of accepted values depends on whether you provide a timeseries-column (ts):

• No provided timeseries-column:

  start must be an integer greater or equal to 0, where zero indicates to start prediction at the end of the in-sample data. If start is a positive value, the function predicts the values between the end of the in-sample data and the start index, and then uses the predicted values as time series inputs for the subsequent npredictions.

• timeseries-column provided:

  start must be an integer greater or equal to 1 and identifies the index (row) of the timeseries-column at which to begin prediction. If the start index is greater than the number of rows, N, in the input data, the function predicts the values between N and start and uses the predicted values as time series inputs for the subsequent npredictions.

Default:

• No provided timeseries-column:

  prediction begins from the end of the in-sample data.

• timeseries-column provided:

  prediction begins from the end of the provided input data.

npredictions: int, optional

integer greater or equal to 1, the number of predicted timesteps.

method: str, optional

Forecasting method. One of the following:

• auto:

  the model initially utilizes the true values at each step for forecasting. However, when it reaches a point where it can no longer rely on true values, it transitions to using its own predictions for further forecasting. This method is often referred to as “one step ahead” forecasting.

• forecast:

  the model initiates forecasting from an initial value and entirely disregards any subsequent true values. This approach involves forecasting based solely on the model’s own predictions and does not consider actual observations after the start point.

Returns

TableSample

report.

Examples

We import verticapy:

import verticapy as vp

For this example, we will use the airline passengers dataset.

import verticapy.datasets as vpd

data = vpd.load_airline_passengers()

	📅 date Date	123 passengers Integer
1	1949-06-01	135
2	1950-05-01	125
3	1950-09-01	158
4	1950-11-01	114
5	1951-02-01	150
6	1951-04-01	163
7	1951-05-01	172
8	1951-07-01	199
9	1951-11-01	146
10	1952-02-01	180
11	1952-07-01	230
12	1953-02-01	196
13	1953-03-01	236
14	1953-07-01	264
15	1953-10-01	211
16	1954-10-01	229
17	1955-02-01	233
18	1955-09-01	312
19	1955-12-01	278
20	1956-01-01	284
21	1956-02-01	277
22	1956-09-01	355
23	1957-05-01	355
24	1957-09-01	404
25	1958-05-01	363
26	1958-10-01	359
27	1959-02-01	342
28	1959-04-01	396
29	1959-08-01	559
30	1959-10-01	407
31	1959-11-01	362
32	1960-05-01	472
33	1960-09-01	508
34	1960-10-01	461
35	1960-12-01	432
36	1949-03-01	132
37	1949-05-01	121
38	1949-07-01	148
39	1949-08-01	148
40	1949-10-01	119
41	1950-02-01	126
42	1950-03-01	141
43	1950-04-01	135
44	1950-08-01	170
45	1950-12-01	140
46	1951-06-01	178
47	1951-08-01	199
48	1951-10-01	162
49	1952-01-01	171
50	1952-03-01	193
51	1952-04-01	181
52	1952-08-01	242
53	1953-04-01	235
54	1953-05-01	229
55	1953-09-01	237
56	1953-11-01	180
57	1954-01-01	204
58	1954-04-01	227
59	1954-06-01	264
60	1954-07-01	302
61	1954-08-01	293
62	1954-09-01	259
63	1954-11-01	203
64	1955-03-01	267
65	1955-05-01	270
66	1955-10-01	274
67	1955-11-01	237
68	1956-05-01	318
69	1956-06-01	374
70	1956-07-01	413
71	1956-08-01	405
72	1956-11-01	271
73	1957-03-01	356
74	1957-04-01	348
75	1957-07-01	465
76	1957-11-01	305
77	1958-01-01	340
78	1958-03-01	362
79	1958-06-01	435
80	1958-07-01	491
81	1958-08-01	505
82	1959-05-01	420
83	1960-01-01	417
84	1949-02-01	118
85	1949-04-01	129
86	1949-11-01	104
87	1950-07-01	170
88	1950-10-01	133
89	1951-01-01	145
90	1951-03-01	178
91	1951-09-01	184
92	1951-12-01	166
93	1952-06-01	218
94	1952-09-01	209
95	1952-10-01	191
96	1952-12-01	194
97	1953-08-01	272
98	1953-12-01	201
99	1954-03-01	235
100	1954-05-01	234

Rows: 1-100 | Columns: 2

First we import the model:

from verticapy.machine_learning.vertica.tsa import ARIMA

Then we can create the model:

model = ARIMA(order = (12, 1, 2))

We can now fit the model:

model.fit(data, "date", "passengers")


============
coefficients
============
parameter| value  
---------+--------
  phi_1  |-0.02408
  phi_2  |-0.03398
  phi_3  |-0.02702
  phi_4  |-0.12197
  phi_5  |-0.01651
  phi_6  |-0.21558
  phi_7  |-0.00477
  phi_8  |-0.15146
  phi_9  | 0.04249
 phi_10  |-0.16296
 phi_11  | 0.04043
 phi_12  | 0.86090
 theta_1 | 0.06580
 theta_2 |-0.06794


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

===============
timeseries_name
===============
"passengers"

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

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

===========
call_string
===========
ARIMA('"public"."_verticapy_tmp_arima_v_mldb_8ea6f55e979d11efa8720242ac120002_"', '"public"."_verticapy_tmp_view_v_mldb_8ecc7374979d11efa8720242ac120002_"', '"passengers"', 'date' USING PARAMETERS p=12, d=1, q=2, missing='linear_interpolation', init_method='Zero', epsilon=1e-06, max_iterations=100);

===============
Additional Info
===============
       Name       |  Value  
------------------+---------
        p         |   12    
        d         |    1    
        q         |    2    
       mean       | 2.23776 
      lambda      | 1.00000 
mean_squared_error|178.86952
rejected_row_count|    0    
accepted_row_count|   144   

We can get the entire report using:

model.report()

	value
explained_variance	0.982735881765428
max_error	48.4615393398698
median_absolute_error	8.8869044124404
mean_absolute_error	10.7142254584427
mean_squared_error	186.453227831831
root_mean_squared_error	13.6547877256232
r2	0.982701333744078
r2_adj	0.982538138779399
aic	568.833961391237
bic	574.007747655009

Rows: 1-10 | Columns: 2

Important

For this example, a specific model is utilized, and it may not correspond exactly to the model you are working with. To see a comprehensive example specific to your class of interest, please refer to that particular class.

Examples: ARIMA; ARMA; AR; MA;