verticapy.machine_learning.vertica.tsa.MA¶

class verticapy.machine_learning.vertica.tsa.MA(name: str = None, overwrite_model: bool = False, q: int = 1, penalty: Literal[None, 'none', 'l2'] = 'none', C: Annotated[int | float | Decimal, 'Python Numbers'] = 1.0, missing: Literal['drop', 'error', 'zero', 'linear_interpolation'] = 'linear_interpolation')¶

Creates a inDB Moving Average model.

Added in version 11.0.0.

Note

The MA model may be faster and more accurate than ARIMA(0, 0, q) or ARMA(0, q) because the underlying algorithm of MA is quite different.

Parameters¶

name: str, optional

Name of the model. The model is stored in the database.

overwrite_model: bool, optional

If set to True, training a model with the same name as an existing model overwrites the existing model.

q: int, optional

Integer in the range [1, 67), the number of lags to consider in the computation.

penalty: str, optional

Method of regularization.

none:
No regularization.
l2:
L2 regularization.

C: PythonNumber, optional

The regularization parameter value. The value must be zero or non-negative.

missing: str, optional

Method for handling missing values, one of the following strings:

‘drop’:
Missing values are ignored.
‘error’:
Missing values raise an error.
‘zero’:
Missing values are set to zero.
‘linear_interpolation’:
Missing values are replaced by a linearly interpolated value based on the nearest valid entries before and after the missing value. In cases where the first or last values in a dataset are missing, the function errors.

Attributes¶

Many attributes are created during the fitting phase.

theta_: numpy.array: The theta coefficient of the Moving Average process. It signifies the impact and contribution of the lagged error terms in determining the current value within the time series model.
mu_: float: Represents the mean or average of the series. It is a constant term that reflects the expected value of the time series in the absence of any temporal dependencies or influences from past error terms.
mean_: float: The mean of the time series values.
mse_: float: The mean squared error (MSE) of the model, based on one-step forward forecasting, may not always be relevant. Utilizing a full forecasting approach is recommended to compute a more meaningful and comprehensive metric.
n_: int: The number of rows used to fit the model.

Note

All attributes can be accessed using the get_attributes() method.

Note

Several other attributes can be accessed by using the get_vertica_attributes() method.

Examples¶

The following examples provide a basic understanding of usage. For more detailed examples, please refer to the Machine Learning or the Examples section on the website.

Initialization¶

We import verticapy:

import verticapy as vp

Hint

By assigning an alias to verticapy, we mitigate the risk of code collisions with other libraries. This precaution is necessary because verticapy uses commonly known function names like “average” and “median”, which can potentially lead to naming conflicts. The use of an alias ensures that the functions from verticapy are used as intended without interfering with functions from other libraries.

For this example, we will generate a dummy time-series dataset that has some noise variation centered around a mean value.

# Initialization
N = 30 # Number of rows
temp = [23] * N
noisy_temp = [x + random.uniform(-5, 5) for x in temp]

# Building the vDataFrame
data = vp.vDataFrame(
    {
        "day": [i for i in range(1, N + 1)],
        "temp": noisy_temp,
    }
)

	123 day Integer	123 temp Numeric(19)
1	1	25.99776868256501
2	2	23.78509620789828
3	3	26.987101573945598
4	4	21.083253940016643
5	5	20.086225167143944
6	6	26.68675571707755
7	7	25.121102270162815
8	8	25.66505511256704
9	9	26.20872552468033
10	10	20.59732455277258
11	11	27.009308124075822
12	12	19.51075948939808
13	13	18.179989341221436
14	14	18.103543469447445
15	15	23.370681706296967
16	16	27.636906267910163
17	17	23.926083966340908
18	18	27.277480863553272
19	19	18.080295390297355
20	20	20.66355338354831
21	21	25.470466078666668
22	22	22.200767496639735
23	23	23.257428899548415
24	24	23.198625671701933
25	25	26.367332215581534
26	26	20.641455054989436
27	27	25.481105635616593
28	28	24.511424622975156
29	29	27.68434950257479
30	30	24.339209990522313

Rows: 1-30 | Columns: 2

Note

VerticaPy offers a wide range of sample datasets that are ideal for training and testing purposes. You can explore the full list of available datasets in the Datasets, which provides detailed information on each dataset and how to use them effectively. These datasets are invaluable resources for honing your data analysis and machine learning skills within the VerticaPy environment.

We can plot the data to visually inspect it for the presence of any trends:

data["temp"].plot(ts = "day")

It is obvious there is no trend in our example, but we can confirm it by the mkt() (Mann Kendall test) test:

from verticapy.machine_learning.model_selection.statistical_tests import mkt

mkt(data, column = "temp", ts = "day")

	value
Mann Kendall Test Statistic	0.03568206200700313
S	3.0
STDS	56.0505724026675
p_value	0.9715358738879936
Monotonic Trend	❌
Trend	no trend

Rows: 1-6 | Columns: 2

The above report confirms that there is no trend in our data and hence it is stationary. Note the high p-value which is also indicative of the absemce of trend. Once we have established that the data is statioanry, we can then apply MovingAverage model on it.

Model Initialization¶

First we import the MA model:

from verticapy.machine_learning.vertica.tsa import MA

Then we can create the model:

model = MA(q = 2)

Hint

In verticapy 1.0.x and higher, you do not need to specify the model name, as the name is automatically assigned. If you need to re-use the model, you can fetch the model name from the model’s attributes.

Important

The model name is crucial for the model management system and versioning. It’s highly recommended to provide a name if you plan to reuse the model later.

Model Fitting¶

We can now fit the model:

model.fit(data, "day", "temp")


============
coefficients
============
parameter| value  
---------+--------
  alpha  |-0.18935
phi_(t-1)|-1.11907
phi_(t-2)|-0.65551


===============
timeseries_name
===============
temp

==============
timestamp_name
==============
day

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

===========
call_string
===========
moving_average('"public"."_verticapy_tmp_ma_v_demo_7b7740e055a511ef880f0242ac120002_"', '"public"."_verticapy_tmp_view_v_demo_7b838bca55a511ef880f0242ac120002_"', 'temp', 'day'
USING PARAMETERS q=2, missing=linear_interpolation, regularization='none', lambda=1, compute_mse=true);

===============
Additional Info
===============
       Name       |  Value   
------------------+----------
       mean       | 23.63760 
    lag_order     |    2     
      lambda      |  1.00000 
mean_squared_error|4309.56977
rejected_row_count|    0     
accepted_row_count|    30    

Important

To train a model, you can directly use the vDataFrame or the name of the relation stored in the database. The test set is optional and is only used to compute the test metrics. In verticapy, we don’t work using X matrices and y vectors. Instead, we work directly with lists of predictors and the response name.

Model Register¶

In order to register the model for tracking and versioning:

model.register("model_v1")

Please refer to Model Tracking and Versioning for more details on model tracking and versioning.

One important thing in time-series forecasting is that it has two types of forecasting:

One-step ahead forecasting
Full forecasting

Important

The default method is one-step ahead forecasting. To use full forecasting, use ``method = “forecast” ``.

One-step ahead¶

In this type of forecasting, the algorithm utilizes the true value of the previous timestamp (t-1) to predict the immediate next timestamp (t). Subsequently, to forecast additional steps into the future (t+1), it relies on the actual value of the immediately preceding timestamp (t).

A notable drawback of this forecasting method is its tendency to exhibit exaggerated accuracy, particularly when predicting more than one step into the future.

Metrics¶

We can get the entire report using:

model.report(start = 3)

	value
explained_variance	-1.75165648574836
max_error	9.69292628707444
median_absolute_error	3.59637179353554
mean_absolute_error	4.05972507057071
mean_squared_error	25.6051268204896
root_mean_squared_error	5.06015086934072
r2	-1.75998568189474
r2_adj	-1.87038510917053
aic	92.38873347556
bic	94.1470738742354

Rows: 1-10 | Columns: 2

Important

The value for start has to be greater than the q value selected for the MA model.

You can also choose the number of predictions and where to start the forecast. For example, the following code will allow you to generate a report with 10 predictions, starting the forecasting process at index 25.

model.report(start = 25, npredictions = 10)

	value
explained_variance	-1.49289720704668
max_error	5.57379646792889
median_absolute_error	3.59637179353554
mean_absolute_error	3.27891135112869
mean_squared_error	13.3720097557971
root_mean_squared_error	3.65677586895849
r2	-1.57035016751736
r2_adj	-2.42713355668982
aic	26.9658184906331
bic	16.1846943155013

Rows: 1-10 | Columns: 2

Important

Most metrics are computed using a single SQL query, but some of them might require multiple SQL queries. Selecting only the necessary metrics in the report can help optimize performance. E.g. model.report(metrics = ["mse", "r2"]).

You can utilize the score() function to calculate various regression metrics, with the explained variance being the default.

model.score(start = 25, npredictions = 10)
Out[5]: -1.57035016751736

Important

If you do not specify a starting point and the number of predictions, the forecast will begin at one-fourth of the dataset, which can result in an inaccurate score, especially for large datasets. It’s important to choose these parameters carefully.

Prediction¶

Prediction is straight-forward:

model.predict()

	123 prediction Float(22)
1	26.8860856340679
2	27.5434357195859
3	29.9485570910623
4	33.0709474389758
5	38.1416913309188
6	45.862949456756
7	57.8274747750378
8	76.2779371940548
9	104.768099191753
10	148.744950154913

Rows: 1-10 | Column: prediction | Type: Float(22)

Hint

You can control the number of prediction steps by changing the npredictions parameter: model.predict(npredictions = 30).

Note

Predictions can be made automatically by using the training set, in which case you don’t need to specify the predictors. Alternatively, you can pass only the vDataFrame to the predict() function, but in this case, it’s essential that the column names of the vDataFrame match the predictors and response name in the model.

If you would like to have the ‘time-stamps’ (ts) in the output then you can switch the output_estimated_ts the parameter.

model.predict(output_estimated_ts = True)

	123 day Float(22)	123 prediction Float(22)
1	31.0	26.8860856340679
2	32.0	27.5434357195859
3	33.0	29.9485570910623
4	34.0	33.0709474389758
5	35.0	38.1416913309188
6	36.0	45.862949456756
7	37.0	57.8274747750378
8	38.0	76.2779371940548
9	39.0	104.768099191753
10	40.0	148.744950154913

Rows: 1-10 | Columns: 2

Important

The output_estimated_ts parameter provides an estimation of ‘ts’ assuming that ‘ts’ is regularly spaced.

If you don’t provide any input, the function will begin forecasting after the last known value. If you want to forecast starting from a specific value within the input dataset or another dataset, you can use the following syntax.

model.predict(
    data,
    "day",
    "temp",
    start = 25,
    npredictions = 10,
    output_estimated_ts = True,
)

	123 day Float(22)	123 prediction Float(22)
1	26.0	26.2152515229183
2	27.0	21.8847338420811
3	28.0	23.5472536822833
4	29.0	25.6345564492153
5	30.0	28.54963449065
6	31.0	26.8860856340679
7	32.0	27.5434357195859
8	33.0	29.9485570910623
9	34.0	33.0709474389758
10	35.0	38.1416913309188

Rows: 1-10 | Columns: 2

Plots¶

We can conveniently plot the predictions on a line plot to observe the efficacy of our model:

model.plot(data, "day", "temp", npredictions = 15, start=25)

Note

You can control the number of prediction steps by changing the npredictions parameter: model.plot(npredictions = 30).

Please refer to Machine Learning - Time Series Plots for more examples.

Model Register¶

In order to register the model for tracking and versioning:

model.register("model_v1")

Please refer to Model Tracking and Versioning for more details on model tracking and versioning.

Full forecasting¶

In this forecasting approach, the algorithm relies solely on a chosen true value for initiation. Subsequently, all predictions are established based on a series of previously predicted values.

This methodology aligns the accuracy of predictions more closely with reality. In practical forecasting scenarios, the goal is to predict all future steps, and this technique ensures a progressive sequence of predictions.

Metrics¶

We can get the report using:

model.report(start = 25, method = "forecast")

By selecting start = 25, we will measure the accuracy from 40th time-stamp and continue the assessment until the last available time-stamp.

	value
explained_variance	-2.1500796531772
max_error	14.623695842718
median_absolute_error	5.64505003835683
mean_absolute_error	6.89645304383813
mean_squared_error	63.9490635387499
root_mean_squared_error	7.99681583749119
r2	-11.2922050747192
r2_adj	-15.3896067662923
aic	34.7904344213513
bic	24.0093102462194

Rows: 1-10 | Columns: 2

Notice that the accuracy using method = forecast is poorer than the one-step ahead forecasting.

You can utilize the score() function to calculate various regression metrics, with the explained variance being the default.

model.score(start = 25, npredictions = 30, method = "forecast")
Out[6]: -11.2922050747192

Prediction¶

Prediction is straight-forward:

model.predict(start = 25, npredictions = 15, method = "forecast")

	123 prediction Float(22)
1	26.2152515229183
2	28.122182546842
3	30.156474661332
4	33.6829954615364
5	38.9629058332403
6	47.1831467813304
7	59.8431778009141
8	79.3990456501726
9	109.582140868074
10	156.178101146864
11	228.107404120281
12	339.145201611428
13	510.554268046629
14	775.158813600652
15	1183.62927638196

Rows: 1-15 | Column: prediction | Type: Float(22)

If you want to forecast starting from a specific value within the input dataset or another dataset, you can use the following syntax.

model.predict(
    data,
    "day",
    "temp",
    start = 25,
    npredictions = 20,
    output_estimated_ts = True,
    output_standard_errors = True,
    method = "forecast",
)

	123 day Float(22)	123 prediction Float(22)
1	26.0	26.2152515229183
2	27.0	28.122182546842
3	28.0	30.156474661332
4	29.0	33.6829954615364
5	30.0	38.9629058332403
6	31.0	47.1831467813304
7	32.0	59.8431778009141
8	33.0	79.3990456501726
9	34.0	109.582140868074
10	35.0	156.178101146864
11	36.0	228.107404120281
12	37.0	339.145201611428
13	38.0	510.554268046629
14	39.0	775.158813600652
15	40.0	1183.62927638196
16	41.0	1814.18584862748
17	42.0	2787.57711276634
18	43.0	4290.20289101052
19	44.0	6609.80889944925
20	45.0	10190.5887019083

Rows: 1-20 | Columns: 2

Plots¶

We can conveniently plot the predictions on a line plot to observe the efficacy of our model:

model.plot(
    data,
    "day",
    "temp",
    npredictions = 15,
    start = 25,
    method = "forecast",
)

__init__(name: str = None, overwrite_model: bool = False, q: int = 1, penalty: Literal[None, 'none', 'l2'] = 'none', C: Annotated[int | float | Decimal, 'Python Numbers'] = 1.0, missing: Literal['drop', 'error', 'zero', 'linear_interpolation'] = 'linear_interpolation') → None¶: Must be overridden in the child class

Methods

`__init__`([name, overwrite_model, q, ...])	Must be overridden in the child class
`contour`([nbins, chart])	Draws the model's contour plot.
`deploySQL`([ts, y, start, npredictions, ...])	Returns the SQL code needed to deploy the model.
`does_model_exists`(name[, raise_error, ...])	Checks whether the model is stored in the Vertica database.
`drop`()	Drops the model from the Vertica database.
`export_models`(name, path[, kind])	Exports machine learning models.
`features_importance`([idx, show, chart])	Computes the model's features importance.
`fit`(input_relation, ts, y[, test_relation, ...])	Trains the model.
`get_attributes`([attr_name])	Returns the model attributes.
`get_match_index`(x, col_list[, str_check])	Returns the matching index.
`get_params`()	Returns the parameters of the model.
`get_plotting_lib`([class_name, chart, ...])	Returns the first available library (Plotly, Matplotlib, or Highcharts) to draw a specific graphic.
`get_vertica_attributes`([attr_name])	Returns the model Vertica attributes.
`import_models`(path[, schema, kind])	Imports machine learning models.
`plot`([vdf, ts, y, start, npredictions, ...])	Draws the model.
`predict`([vdf, ts, y, start, npredictions, ...])	Predicts using the input relation.
`register`(registered_name[, raise_error])	Registers the model and adds it to in-DB Model versioning environment with a status of 'under_review'.
`regression_report`([metrics, start, ...])	Computes a regression report using multiple metrics to evaluate the model (`r2`, `mse`, `max error`...).
`report`([metrics, start, npredictions, method])	Computes a regression report using multiple metrics to evaluate the model (`r2`, `mse`, `max error`...).
`score`([metric, start, npredictions, method])	Computes the model score.
`set_params`([parameters])	Sets the parameters of the model.
`summarize`()	Summarizes the model.
`to_binary`(path)	Exports the model to the Vertica Binary format.
`to_pmml`(path)	Exports the model to PMML.
`to_python`([return_proba, ...])	Returns the Python function needed for in-memory scoring without using built-in Vertica functions.
`to_sql`([X, return_proba, ...])	Returns the SQL code needed to deploy the model without using built-in Vertica functions.
`to_tf`(path)	Exports the model to the Frozen Graph format (TensorFlow).

Attributes

object_type