# pyFTS.benchmarks package — pyFTS 1.6 documentation

# pyFTS.benchmarks package

## Module contents

pyFTS module for benchmarking the FTS models

## Submodules

## pyFTS.benchmarks.benchmarks module

Benchmarks methods for FTS methods

`pyFTS.benchmarks.benchmarks.``SelecaoSimples_MenorRMSE`(original, parameters, modelo)

`pyFTS.benchmarks.benchmarks.``common_process_interval_jobs`(conn, data, job)

`pyFTS.benchmarks.benchmarks.``common_process_point_jobs`(conn, data, job)

`pyFTS.benchmarks.benchmarks.``common_process_probabilistic_jobs`(conn, data, job)

`pyFTS.benchmarks.benchmarks.``common_process_time_jobs`(conn, data, job)

`pyFTS.benchmarks.benchmarks.``compareModelsPlot`(original, models_fo, models_ho)

`pyFTS.benchmarks.benchmarks.``compareModelsTable`(original, models_fo, models_ho)

`pyFTS.benchmarks.benchmarks.``distributed_model_train_test_time`(models, data, windowsize, train=0.8, **kwargs)

  Assess the train and test times for a given list of configured models and save the results on a database.

  Parameters

    - models – A list of FTS models already configured, but not yet trained,

    - data – time series data, including train and test data

    - windowsize – Train/test data windows

    - train – Percent of data window that will be used to train the models

    - kwargs –

  Returns

`pyFTS.benchmarks.benchmarks.``get_benchmark_interval_methods`()

  Return all non FTS methods for point_to_interval forecasting

`pyFTS.benchmarks.benchmarks.``get_benchmark_point_methods`()

  Return all non FTS methods for point forecasting

`pyFTS.benchmarks.benchmarks.``get_benchmark_probabilistic_methods`()

  Return all FTS methods for probabilistic forecasting

`pyFTS.benchmarks.benchmarks.``get_interval_methods`()

  Return all FTS methods for point_to_interval forecasting

`pyFTS.benchmarks.benchmarks.``get_point_methods`()

  Return all FTS methods for point forecasting

`pyFTS.benchmarks.benchmarks.``get_point_multivariate_methods`()

  Return all multivariate FTS methods por point forecasting

`pyFTS.benchmarks.benchmarks.``get_probabilistic_methods`()

  Return all FTS methods for probabilistic forecasting

`pyFTS.benchmarks.benchmarks.``multivariate_sliding_window_benchmarks2`(data, windowsize, train=0.8, **kwargs)

`pyFTS.benchmarks.benchmarks.``mv_run_interval2`(mfts, train_data, test_data, window_key=None, **kwargs)

`pyFTS.benchmarks.benchmarks.``mv_run_point2`(mfts, train_data, test_data, window_key=None, **kwargs)

`pyFTS.benchmarks.benchmarks.``mv_run_probabilistic2`(mfts, train_data, test_data, window_key=None, **kwargs)

`pyFTS.benchmarks.benchmarks.``pftsExploreOrderAndPartitions`(data, save=False, file=None)

`pyFTS.benchmarks.benchmarks.``plotCompared`(original, forecasts, labels, title)

`pyFTS.benchmarks.benchmarks.``plot_compared_series`(original, models, colors, typeonlegend=False, save=False, file=None, tam=[20, 5], points=True, intervals=True, linewidth=1.5)

  Plot the forecasts of several one step ahead models, by point or by interval

  Parameters

    - original – Original time series data (list)

    - models – List of models to compare

    - colors – List of models colors

    - typeonlegend – Add the type of forecast (point / interval) on legend

    - save – Save the picture on file

    - file – Filename to save the picture

    - tam – Size of the picture

    - points – True to plot the point forecasts, False otherwise

    - intervals – True to plot the interval forecasts, False otherwise

    - linewidth –

  Returns

`pyFTS.benchmarks.benchmarks.``plot_point`(axis, points, order, label, color='red', ls='-', linewidth=1)

`pyFTS.benchmarks.benchmarks.``print_distribution_statistics`(original, models, steps, resolution)

  Run probabilistic benchmarks on given models and data and print the results

  Parameters

    - data – test data

    - models – a list of FTS models to benchmark

  Returns

`pyFTS.benchmarks.benchmarks.``print_interval_statistics`(original, models)

  Run interval benchmarks on given models and data and print the results

  Parameters

    - data – test data

    - models – a list of FTS models to benchmark

  Returns

`pyFTS.benchmarks.benchmarks.``print_point_statistics`(data, models, externalmodels=None, externalforecasts=None, indexers=None)

  Run point benchmarks on given models and data and print the results

  Parameters

    - data – test data

    - models – a list of FTS models to benchmark

    - externalmodels – a list with benchmark models (façades for other methods)

    - externalforecasts –

    - indexers –

  Returns

`pyFTS.benchmarks.benchmarks.``process_interval_jobs`(dataset, tag, job, conn)

  Extract information from an dictionary with interval benchmark results and save it on a database

  Parameters

    - dataset – the benchmark dataset name

    - tag – alias for the benchmark group being executed

    - job – a dictionary with the benchmark results

    - conn – a connection to a Sqlite database

  Returns

`pyFTS.benchmarks.benchmarks.``process_interval_jobs2`(dataset, tag, job, conn)

`pyFTS.benchmarks.benchmarks.``process_point_jobs`(dataset, tag, job, conn)

  Extract information from a dictionary with point benchmark results and save it on a database

  Parameters

    - dataset – the benchmark dataset name

    - tag – alias for the benchmark group being executed

    - job – a dictionary with the benchmark results

    - conn – a connection to a Sqlite database

  Returns

`pyFTS.benchmarks.benchmarks.``process_point_jobs2`(dataset, tag, job, conn)

  Extract information from a dictionary with point benchmark results and save it on a database

  Parameters

    - dataset – the benchmark dataset name

    - tag – alias for the benchmark group being executed

    - job – a dictionary with the benchmark results

    - conn – a connection to a Sqlite database

  Returns

`pyFTS.benchmarks.benchmarks.``process_probabilistic_jobs`(dataset, tag, job, conn)

  Extract information from an dictionary with probabilistic benchmark results and save it on a database

  Parameters

    - dataset – the benchmark dataset name

    - tag – alias for the benchmark group being executed

    - job – a dictionary with the benchmark results

    - conn – a connection to a Sqlite database

  Returns

`pyFTS.benchmarks.benchmarks.``process_probabilistic_jobs2`(dataset, tag, job, conn)

  Extract information from an dictionary with probabilistic benchmark results and save it on a database

  Parameters

    - dataset – the benchmark dataset name

    - tag – alias for the benchmark group being executed

    - job – a dictionary with the benchmark results

    - conn – a connection to a Sqlite database

  Returns

`pyFTS.benchmarks.benchmarks.``run_interval`(mfts, partitioner, train_data, test_data, window_key=None, **kwargs)

  Run the interval forecasting benchmarks

  Parameters

    - mfts – FTS model

    - partitioner – Universe of Discourse partitioner

    - train_data – data used to train the model

    - test_data – ata used to test the model

    - window_key – id of the sliding window

    - transformation – data transformation

    - indexer – seasonal indexer

  Returns

    a dictionary with the benchmark results

`pyFTS.benchmarks.benchmarks.``run_interval2`(fts_method, order, partitioner_method, partitions, transformation, train_data, test_data, window_key=None, **kwargs)

`pyFTS.benchmarks.benchmarks.``run_point`(mfts, partitioner, train_data, test_data, window_key=None, **kwargs)

  Run the point forecasting benchmarks

  Parameters

    - mfts – FTS model

    - partitioner – Universe of Discourse partitioner

    - train_data – data used to train the model

    - test_data – ata used to test the model

    - window_key – id of the sliding window

    - transformation – data transformation

    - indexer – seasonal indexer

  Returns

    a dictionary with the benchmark results

`pyFTS.benchmarks.benchmarks.``run_point2`(fts_method, order, partitioner_method, partitions, transformation, train_data, test_data, window_key=None, **kwargs)

`pyFTS.benchmarks.benchmarks.``run_probabilistic`(mfts, partitioner, train_data, test_data, window_key=None, **kwargs)

  Run the probabilistic forecasting benchmarks

  Parameters

    - mfts – FTS model

    - partitioner – Universe of Discourse partitioner

    - train_data – data used to train the model

    - test_data – ata used to test the model

    - steps –

    - resolution –

    - window_key – id of the sliding window

    - transformation – data transformation

    - indexer – seasonal indexer

  Returns

    a dictionary with the benchmark results

`pyFTS.benchmarks.benchmarks.``run_probabilistic2`(fts_method, order, partitioner_method, partitions, transformation, train_data, test_data, window_key=None, **kwargs)

`pyFTS.benchmarks.benchmarks.``simpleSearch_RMSE`(train, test, model, partitions, orders, save=False, file=None, tam=[10, 15], plotforecasts=False, elev=30, azim=144, intervals=False, parameters=None, partitioner=<class 'pyFTS.partitioners.Grid.GridPartitioner'>, transformation=None, indexer=None)

`pyFTS.benchmarks.benchmarks.``sliding_window_benchmarks`(data, windowsize, train=0.8, **kwargs)

  Sliding window benchmarks for FTS forecasters.

  For each data window, a train and test datasets will be splitted. For each train split, number of partitions and partitioning method will be created a partitioner model. And for each partitioner, order, steps ahead and FTS method a foreasting model will be trained.

  Then all trained models are benchmarked on the test data and the metrics are stored on a sqlite3 database (identified by the ‘file’ parameter) for posterior analysis.

  All these process can be distributed on a dispy cluster, setting the atributed ‘distributed’ to true and informing the list of dispy nodes on ‘nodes’ parameter.

  The number of experiments is determined by ‘windowsize’ and ‘inc’ parameters.

  Parameters

    - data – test data

    - windowsize – size of sliding window

    - train – percentual of sliding window data used to train the models

    - kwargs – dict, optional arguments

    - benchmark_methods – a list with Non FTS models to benchmark. The default is None.

    - benchmark_methods_parameters – a list with Non FTS models parameters. The default is None.

    - benchmark_models – A boolean value indicating if external FTS methods will be used on benchmark. The default is False.

    - build_methods – A boolean value indicating if the default FTS methods will be used on benchmark. The default is True.

    - dataset – the dataset name to identify the current set of benchmarks results on database.

    - distributed – A boolean value indicating if the forecasting procedure will be distributed in a dispy cluster. . The default is False

    - file – file path to save the results. The default is benchmarks.db.

    - inc – a float on interval [0,1] indicating the percentage of the windowsize to move the window

    - methods – a list with FTS class names. The default depends on the forecasting type and contains the list of all FTS methods.

    - models – a list with prebuilt FTS objects. The default is None.

    - nodes – a list with the dispy cluster nodes addresses. The default is [127.0.0.1].

    - orders – a list with orders of the models (for high order models). The default is [1,2,3].

    - partitions – a list with the numbers of partitions on the Universe of Discourse. The default is [10].

    - partitioners_models – a list with prebuilt Universe of Discourse partitioners objects. The default is None.

    - partitioners_methods – a list with Universe of Discourse partitioners class names. The default is [partitioners.Grid.GridPartitioner].

    - progress – If true a progress bar will be displayed during the benchmarks. The default is False.

    - start – in the multi step forecasting, the index of the data where to start forecasting. The default is 0.

    - steps_ahead – a list with the forecasting horizons, i. e., the number of steps ahead to forecast. The default is 1.

    - tag – a name to identify the current set of benchmarks results on database.

    - type – the forecasting type, one of these values: point(default), interval or distribution. The default is point.

    - transformations – a list with data transformations do apply . The default is [None].

`pyFTS.benchmarks.benchmarks.``sliding_window_benchmarks2`(data, windowsize, train=0.8, **kwargs)

`pyFTS.benchmarks.benchmarks.``train_test_time`(data, windowsize, train=0.8, **kwargs)

## pyFTS.benchmarks.Measures module

pyFTS module for common benchmark metrics

`pyFTS.benchmarks.Measures.``TheilsInequality`(targets, forecasts)

  Theil’s Inequality Coefficient

  Parameters

    - targets –

    - forecasts –

  Returns

`pyFTS.benchmarks.Measures.``UStatistic`(targets, forecasts)

  Theil’s U Statistic

  Parameters

    - targets –

    - forecasts –

  Returns

`pyFTS.benchmarks.Measures.``acf`(data, k)

  Autocorrelation function estimative

  Parameters

    - data –

    - k –

  Returns

`pyFTS.benchmarks.Measures.``brier_score`(targets, densities)

  Brier Score for probabilistic forecasts. Brier (1950). “Verification of Forecasts Expressed in Terms of Probability”. Monthly Weather Review. 78: 1–3.

  Parameters

    - targets – a list with the target values

    - densities – a list with pyFTS.probabil objectsistic.ProbabilityDistribution

  Returns

    float

`pyFTS.benchmarks.Measures.``coverage`(targets, forecasts)

  Percent of target values that fall inside forecasted interval

`pyFTS.benchmarks.Measures.``crps`(targets, densities)

  Continuous Ranked Probability Score

  Parameters

    - targets – a list with the target values

    - densities – a list with pyFTS.probabil objectsistic.ProbabilityDistribution

  Returns

    float

`pyFTS.benchmarks.Measures.``get_distribution_ahead_statistics`(data, distributions)

  Get CRPS statistic and time for a forecasting model

  Parameters

    - data – test data

    - model – FTS model with probabilistic forecasting capability

    - kwargs –

  Returns

    a list with the CRPS and execution time

`pyFTS.benchmarks.Measures.``get_distribution_statistics`(data, model, **kwargs)

  Get CRPS statistic and time for a forecasting model

  Parameters

    - data – test data

    - model – FTS model with probabilistic forecasting capability

    - kwargs –

  Returns

    a list with the CRPS and execution time

`pyFTS.benchmarks.Measures.``get_interval_ahead_statistics`(data, intervals, **kwargs)

  Condensate all measures for point interval forecasters

  Parameters

    - data – test data

    - intervals – predicted intervals for each datapoint

    - kwargs –

  Returns

    a list with the sharpness, resolution, coverage, .05 pinball mean, .25 pinball mean, .75 pinball mean and .95 pinball mean.

`pyFTS.benchmarks.Measures.``get_interval_statistics`(data, model, **kwargs)

  Condensate all measures for point interval forecasters

  Parameters

    - data – test data

    - model – FTS model with interval forecasting capability

    - kwargs –

  Returns

    a list with the sharpness, resolution, coverage, .05 pinball mean, .25 pinball mean, .75 pinball mean and .95 pinball mean.

`pyFTS.benchmarks.Measures.``get_point_ahead_statistics`(data, forecasts, **kwargs)

  Condensate all measures for point forecasters

  Parameters

    - data – test data

    - model – FTS model with point forecasting capability

    - kwargs –

  Returns

    a list with the RMSE, SMAPE and U Statistic

`pyFTS.benchmarks.Measures.``get_point_statistics`(data, model, **kwargs)

  Condensate all measures for point forecasters

  Parameters

    - data – test data

    - model – FTS model with point forecasting capability

    - kwargs –

  Returns

    a list with the RMSE, SMAPE and U Statistic

`pyFTS.benchmarks.Measures.``logarithm_score`(targets, densities)

  Logarithm Score for probabilistic forecasts. Good IJ (1952). “Rational Decisions.”Journal of the Royal Statistical Society B,14(1),107–114. URLhttps://www.jstor.org/stable/2984087.

  Parameters

    - targets – a list with the target values

    - densities – a list with pyFTS.probabil objectsistic.ProbabilityDistribution

  Returns

    float

`pyFTS.benchmarks.Measures.``mape`(targets, forecasts)

  Mean Average Percentual Error

  Parameters

    - targets –

    - forecasts –

  Returns

`pyFTS.benchmarks.Measures.``mape_interval`(targets, forecasts)

`pyFTS.benchmarks.Measures.``pinball`(tau, target, forecast)

  Pinball loss function. Measure the distance of forecast to the tau-quantile of the target

  Parameters

    - tau – quantile value in the range (0,1)

    - target –

    - forecast –

  Returns

    float, distance of forecast to the tau-quantile of the target

`pyFTS.benchmarks.Measures.``pinball_mean`(tau, targets, forecasts)

  Mean pinball loss value of the forecast for a given tau-quantile of the targets

  Parameters

    - tau – quantile value in the range (0,1)

    - targets – list of target values

    - forecasts – list of prediction intervals

  Returns

    float, the pinball loss mean for tau quantile

`pyFTS.benchmarks.Measures.``resolution`(forecasts)

  Resolution - Standard deviation of the intervals

`pyFTS.benchmarks.Measures.``rmse`(targets, forecasts)

  Root Mean Squared Error

  Parameters

    - targets –

    - forecasts –

  Returns

`pyFTS.benchmarks.Measures.``rmse_interval`(targets, forecasts)

  Root Mean Squared Error

  Parameters

    - targets –

    - forecasts –

  Returns

`pyFTS.benchmarks.Measures.``sharpness`(forecasts)

  Sharpness - Mean size of the intervals

`pyFTS.benchmarks.Measures.``smape`(targets, forecasts, type=2)

  Symmetric Mean Average Percentual Error

  Parameters

    - targets –

    - forecasts –

    - type –

  Returns

`pyFTS.benchmarks.Measures.``winkler_mean`(tau, targets, forecasts)

  Mean Winkler score value of the forecast for a given tau-quantile of the targets

  Parameters

    - tau – quantile value in the range (0,1)

    - targets – list of target values

    - forecasts – list of prediction intervals

  Returns

    float, the Winkler score mean for tau quantile

`pyFTS.benchmarks.Measures.``winkler_score`(tau, target, forecast)

  18. 12. Winkler, A Decision-Theoretic Approach to Interval Estimation, J. Am. Stat. Assoc. 67 (337) (1972) 187–191. doi:10.2307/2284720.

  Parameters

    - tau –

    - target –

    - forecast –

  Returns

## pyFTS.benchmarks.ResidualAnalysis module

Residual Analysis methods

`pyFTS.benchmarks.ResidualAnalysis.``compare_residuals`(data, models, alpha=0.05)

  Compare residual’s statistics of several models

  Parameters

    - data – test data

    - models –

  Returns

    a Pandas dataframe with the Box-Ljung statistic for each model

`pyFTS.benchmarks.ResidualAnalysis.``ljung_box_test`(residuals, lags=[1, 2, 3], alpha=0.5)

`pyFTS.benchmarks.ResidualAnalysis.``plot_residuals_by_model`(targets, models, tam=[8, 8], save=False, file=None)

`pyFTS.benchmarks.ResidualAnalysis.``residuals`(targets, forecasts, order=1)

  First order residuals

`pyFTS.benchmarks.ResidualAnalysis.``single_plot_residuals`(res, order, tam=[10, 7], save=False, file=None)

## pyFTS.benchmarks.Tests module

`pyFTS.benchmarks.Tests.``BoxLjungStatistic`(data, h)

  Q Statistic for Ljung–Box test

  Parameters

    - data –

    - h –

  Returns

`pyFTS.benchmarks.Tests.``BoxPierceStatistic`(data, h)

  Q Statistic for Box-Pierce test

  Parameters

    - data –

    - h –

  Returns

`pyFTS.benchmarks.Tests.``format_experiment_table`(df, exclude=[], replace={}, csv=True, std=False)

`pyFTS.benchmarks.Tests.``post_hoc_tests`(post_hoc, control_method, alpha=0.05, method='finner')

  Finner paired post-hoc test with NSFTS as control method.

  $H_0$: There is no significant difference between the means

  $H_1$: There is a significant difference between the means

  Parameters

    - post_hoc –

    - control_method –

    - alpha –

    - method –

  Returns

`pyFTS.benchmarks.Tests.``test_mean_equality`(tests, alpha=0.05, method='friedman')

  Test for the equality of the means, with alpha confidence level.

  H_0: There’s no significant difference between the means H_1: There is at least one significant difference between the means

  Parameters

    - tests –

    - alpha –

    - method –

  Returns

## pyFTS.benchmarks.Util module

Facilities for pyFTS Benchmark module

`pyFTS.benchmarks.Util.``analytic_tabular_dataframe`(dataframe)

`pyFTS.benchmarks.Util.``analytical_data_columns`(experiments)

`pyFTS.benchmarks.Util.``base_dataframe_columns`()

`pyFTS.benchmarks.Util.``cast_dataframe_to_synthetic`(infile, outfile, experiments, type)

`pyFTS.benchmarks.Util.``cast_dataframe_to_synthetic_interval`(df, data_columns)

`pyFTS.benchmarks.Util.``cast_dataframe_to_synthetic_point`(df, data_columns)

`pyFTS.benchmarks.Util.``cast_dataframe_to_synthetic_probabilistic`(df, data_columns)

`pyFTS.benchmarks.Util.``check_ignore_list`(b, ignore)

`pyFTS.benchmarks.Util.``check_replace_list`(m, replace)

`pyFTS.benchmarks.Util.``create_benchmark_tables`(conn)

  Create a sqlite3 table designed to store benchmark results.

  Parameters

    conn – a sqlite3 database connection

`pyFTS.benchmarks.Util.``extract_measure`(dataframe, measure, data_columns)

`pyFTS.benchmarks.Util.``find_best`(dataframe, criteria, ascending)

`pyFTS.benchmarks.Util.``get_dataframe_from_bd`(file, filter)

  Query the sqlite benchmark database and return a pandas dataframe with the results

  Parameters

    - file – the url of the benchmark database

    - filter – sql conditions to filter

  Returns

    pandas dataframe with the query results

`pyFTS.benchmarks.Util.``insert_benchmark`(data, conn)

  Insert benchmark data on database

  Parameters

    data – a tuple with the benchmark data with format:

  ID: integer incremental primary key Date: Date/hour of benchmark execution Dataset: Identify on which dataset the dataset was performed Tag: a user defined word that indentify a benchmark set Type: forecasting type (point, interval, distribution) Model: FTS model Transformation: The name of data transformation, if one was used Order: the order of the FTS method Scheme: UoD partitioning scheme Partitions: Number of partitions Size: Number of rules of the FTS model Steps: prediction horizon, i. e., the number of steps ahead Measure: accuracy measure Value: the measure value

  Parameters

    conn – a sqlite3 database connection

  Returns

`pyFTS.benchmarks.Util.``interval_dataframe_analytic_columns`(experiments)

`pyFTS.benchmarks.Util.``interval_dataframe_synthetic_columns`()

`pyFTS.benchmarks.Util.``open_benchmark_db`(name)

  Open a connection with a Sqlite database designed to store benchmark results.

  Parameters

    name – database filenem

  Returns

    a sqlite3 database connection

`pyFTS.benchmarks.Util.``plot_dataframe_interval`(file_synthetic, file_analytic, experiments, tam, save=False, file=None, sort_columns=['COVAVG', 'SHARPAVG', 'COVSTD', 'SHARPSTD'], sort_ascend=[True, False, True, True], save_best=False, ignore=None, replace=None)

`pyFTS.benchmarks.Util.``plot_dataframe_interval_pinball`(file_synthetic, file_analytic, experiments, tam, save=False, file=None, sort_columns=['COVAVG', 'SHARPAVG', 'COVSTD', 'SHARPSTD'], sort_ascend=[True, False, True, True], save_best=False, ignore=None, replace=None)

`pyFTS.benchmarks.Util.``plot_dataframe_point`(file_synthetic, file_analytic, experiments, tam, save=False, file=None, sort_columns=['UAVG', 'RMSEAVG', 'USTD', 'RMSESTD'], sort_ascend=[1, 1, 1, 1], save_best=False, ignore=None, replace=None)

`pyFTS.benchmarks.Util.``plot_dataframe_probabilistic`(file_synthetic, file_analytic, experiments, tam, save=False, file=None, sort_columns=['CRPS1AVG', 'CRPS2AVG', 'CRPS1STD', 'CRPS2STD'], sort_ascend=[True, True, True, True], save_best=False, ignore=None, replace=None)

`pyFTS.benchmarks.Util.``point_dataframe_analytic_columns`(experiments)

`pyFTS.benchmarks.Util.``point_dataframe_synthetic_columns`()

`pyFTS.benchmarks.Util.``probabilistic_dataframe_analytic_columns`(experiments)

`pyFTS.benchmarks.Util.``probabilistic_dataframe_synthetic_columns`()

`pyFTS.benchmarks.Util.``process_common_data`(dataset, tag, type, job)

  Wraps benchmark information on a tuple for sqlite database

  Parameters

    - dataset – benchmark dataset

    - tag – benchmark set alias

    - type – forecasting type

    - job – a dictionary with benchmark data

  Returns

    tuple for sqlite database

`pyFTS.benchmarks.Util.``process_common_data2`(dataset, tag, type, job)

  Wraps benchmark information on a tuple for sqlite database

  Parameters

    - dataset – benchmark dataset

    - tag – benchmark set alias

    - type – forecasting type

    - job – a dictionary with benchmark data

  Returns

    tuple for sqlite database

`pyFTS.benchmarks.Util.``save_dataframe_interval`(coverage, experiments, file, objs, resolution, save, sharpness, synthetic, times, q05, q25, q75, q95, steps, method)

`pyFTS.benchmarks.Util.``save_dataframe_point`(experiments, file, objs, rmse, save, synthetic, smape, times, u, steps, method)

  Create a dataframe to store the benchmark results

  Parameters

    - experiments – dictionary with the execution results

    - file –

    - objs –

    - rmse –

    - save –

    - synthetic –

    - smape –

    - times –

    - u –

  Returns

`pyFTS.benchmarks.Util.``save_dataframe_probabilistic`(experiments, file, objs, crps, times, save, synthetic, steps, method)

  Save benchmark results for m-step ahead probabilistic forecasters :param experiments: :param file: :param objs: :param crps_interval: :param crps_distr: :param times: :param times2: :param save: :param synthetic: :return:

`pyFTS.benchmarks.Util.``scale`(data, params)

`pyFTS.benchmarks.Util.``scale_params`(data)

`pyFTS.benchmarks.Util.``simple_synthetic_dataframe`(file, tag, measure, sql=None)

  Read experiments results from sqlite3 database in ‘file’, make a synthesis of the results of the metric ‘measure’ with the same ‘tag’, returning a Pandas DataFrame with the mean results.

  Parameters

    - file – sqlite3 database file name

    - tag – common tag of the experiments

    - measure – metric to synthetize

  Returns

    Pandas DataFrame with the mean results

`pyFTS.benchmarks.Util.``stats`(measure, data)

`pyFTS.benchmarks.Util.``tabular_dataframe_columns`()

`pyFTS.benchmarks.Util.``unified_scaled_interval`(experiments, tam, save=False, file=None, sort_columns=['COVAVG', 'SHARPAVG', 'COVSTD', 'SHARPSTD'], sort_ascend=[True, False, True, True], save_best=False, ignore=None, replace=None)

`pyFTS.benchmarks.Util.``unified_scaled_interval_pinball`(experiments, tam, save=False, file=None, sort_columns=['COVAVG', 'SHARPAVG', 'COVSTD', 'SHARPSTD'], sort_ascend=[True, False, True, True], save_best=False, ignore=None, replace=None)

`pyFTS.benchmarks.Util.``unified_scaled_point`(experiments, tam, save=False, file=None, sort_columns=['UAVG', 'RMSEAVG', 'USTD', 'RMSESTD'], sort_ascend=[1, 1, 1, 1], save_best=False, ignore=None, replace=None)

`pyFTS.benchmarks.Util.``unified_scaled_probabilistic`(experiments, tam, save=False, file=None, sort_columns=['CRPSAVG', 'CRPSSTD'], sort_ascend=[True, True], save_best=False, ignore=None, replace=None)

## pyFTS.benchmarks.arima module

class `pyFTS.benchmarks.arima.``ARIMA`(**kwargs)

  Bases: `pyFTS.common.fts.FTS`

  Façade for statsmodels.tsa.arima_model

  `ar`(data)
  `forecast`(ndata, **kwargs)

    Point forecast one step ahead

    Parameters

      - data – time series data with the minimal length equal to the max_lag of the model

      - kwargs – model specific parameters

    Returns

      a list with the forecasted values

  `forecast_ahead_distribution`(data, steps, **kwargs)

    Probabilistic forecast from 1 to H steps ahead, where H is given by the steps parameter

    Parameters

      - data – time series data with the minimal length equal to the max_lag of the model

      - steps – the number of steps ahead to forecast

      - start_at – in the multi step forecasting, the index of the data where to start forecasting (default: 0)

    Returns

      a list with the forecasted Probability Distributions

  `forecast_ahead_interval`(ndata, steps, **kwargs)

    Interval forecast from 1 to H steps ahead, where H is given by the steps parameter

    Parameters

      - data – time series data with the minimal length equal to the max_lag of the model

      - steps – the number of steps ahead to forecast

      - start_at – in the multi step forecasting, the index of the data where to start forecasting (default: 0)

    Returns

      a list with the forecasted intervals

  `forecast_distribution`(data, **kwargs)

    Probabilistic forecast one step ahead

    Parameters

      - data – time series data with the minimal length equal to the max_lag of the model

      - kwargs – model specific parameters

    Returns

      a list with probabilistic.ProbabilityDistribution objects representing the forecasted Probability Distributions

  `forecast_interval`(data, **kwargs)

    Interval forecast one step ahead

    Parameters

      - data – time series data with the minimal length equal to the max_lag of the model

      - kwargs – model specific parameters

    Returns

      a list with the prediction intervals

  `ma`(data)
  `train`(data, **kwargs)

    Method specific parameter fitting

    Parameters

      - data – training time series data

      - kwargs – Method specific parameters

## pyFTS.benchmarks.knn module

class `pyFTS.benchmarks.knn.``KNearestNeighbors`(**kwargs)

  Bases: `pyFTS.common.fts.FTS`

  A façade for sklearn.neighbors

  `forecast`(data, **kwargs)

    Point forecast one step ahead

    Parameters

      - data – time series data with the minimal length equal to the max_lag of the model

      - kwargs – model specific parameters

    Returns

      a list with the forecasted values

  `forecast_ahead_distribution`(data, steps, **kwargs)

    Probabilistic forecast from 1 to H steps ahead, where H is given by the steps parameter

    Parameters

      - data – time series data with the minimal length equal to the max_lag of the model

      - steps – the number of steps ahead to forecast

      - start_at – in the multi step forecasting, the index of the data where to start forecasting (default: 0)

    Returns

      a list with the forecasted Probability Distributions

  `forecast_ahead_interval`(data, steps, **kwargs)

    Interval forecast from 1 to H steps ahead, where H is given by the steps parameter

    Parameters

      - data – time series data with the minimal length equal to the max_lag of the model

      - steps – the number of steps ahead to forecast

      - start_at – in the multi step forecasting, the index of the data where to start forecasting (default: 0)

    Returns

      a list with the forecasted intervals

  `forecast_distribution`(data, **kwargs)

    Probabilistic forecast one step ahead

    Parameters

      - data – time series data with the minimal length equal to the max_lag of the model

      - kwargs – model specific parameters

    Returns

      a list with probabilistic.ProbabilityDistribution objects representing the forecasted Probability Distributions

  `forecast_interval`(data, **kwargs)

    Interval forecast one step ahead

    Parameters

      - data – time series data with the minimal length equal to the max_lag of the model

      - kwargs – model specific parameters

    Returns

      a list with the prediction intervals

  `knn`(sample)
  `train`(data, **kwargs)

    Method specific parameter fitting

    Parameters

      - data – training time series data

      - kwargs – Method specific parameters

## pyFTS.benchmarks.naive module

class `pyFTS.benchmarks.naive.``Naive`(**kwargs)

  Bases: `pyFTS.common.fts.FTS`

  Naïve Forecasting method

  `forecast`(data, **kwargs)

    Point forecast one step ahead

    Parameters

      - data – time series data with the minimal length equal to the max_lag of the model

      - kwargs – model specific parameters

    Returns

      a list with the forecasted values

## pyFTS.benchmarks.quantreg module

class `pyFTS.benchmarks.quantreg.``QuantileRegression`(**kwargs)

  Bases: `pyFTS.common.fts.FTS`

  Façade for statsmodels.regression.quantile_regression

  `forecast`(ndata, **kwargs)

    Point forecast one step ahead

    Parameters

      - data – time series data with the minimal length equal to the max_lag of the model

      - kwargs – model specific parameters

    Returns

      a list with the forecasted values

  `forecast_ahead_distribution`(ndata, steps, **kwargs)

    Probabilistic forecast from 1 to H steps ahead, where H is given by the steps parameter

    Parameters

      - data – time series data with the minimal length equal to the max_lag of the model

      - steps – the number of steps ahead to forecast

      - start_at – in the multi step forecasting, the index of the data where to start forecasting (default: 0)

    Returns

      a list with the forecasted Probability Distributions

  `forecast_ahead_interval`(ndata, steps, **kwargs)

    Interval forecast from 1 to H steps ahead, where H is given by the steps parameter

    Parameters

      - data – time series data with the minimal length equal to the max_lag of the model

      - steps – the number of steps ahead to forecast

      - start_at – in the multi step forecasting, the index of the data where to start forecasting (default: 0)

    Returns

      a list with the forecasted intervals

  `forecast_distribution`(ndata, **kwargs)

    Probabilistic forecast one step ahead

    Parameters

      - data – time series data with the minimal length equal to the max_lag of the model

      - kwargs – model specific parameters

    Returns

      a list with probabilistic.ProbabilityDistribution objects representing the forecasted Probability Distributions

  `forecast_interval`(ndata, **kwargs)

    Interval forecast one step ahead

    Parameters

      - data – time series data with the minimal length equal to the max_lag of the model

      - kwargs – model specific parameters

    Returns

      a list with the prediction intervals

  `interval_to_interval`(data, lo_params, up_params)
  `linearmodel`(data, params)
  `point_to_interval`(data, lo_params, up_params)
  `train`(data, **kwargs)

    Method specific parameter fitting

    Parameters

      - data – training time series data

      - kwargs – Method specific parameters

## pyFTS.benchmarks.gaussianproc module

## pyFTS.benchmarks.BSTS module

class `pyFTS.benchmarks.BSTS.``ARIMA`(**kwargs)

  Bases: `pyFTS.common.fts.FTS`

  Façade for statsmodels.tsa.arima_model

  `forecast`(ndata, **kwargs)

    Point forecast one step ahead

    Parameters

      - data – time series data with the minimal length equal to the max_lag of the model

      - kwargs – model specific parameters

    Returns

      a list with the forecasted values

  `forecast_ahead`(data, steps, **kwargs)

    Point forecast from 1 to H steps ahead, where H is given by the steps parameter

    Parameters

      - data – time series data with the minimal length equal to the max_lag of the model

      - steps – the number of steps ahead to forecast (default: 1)

      - start_at – in the multi step forecasting, the index of the data where to start forecasting (default: 0)

    Returns

      a list with the forecasted values

  `forecast_ahead_distribution`(data, steps, **kwargs)

    Probabilistic forecast from 1 to H steps ahead, where H is given by the steps parameter

    Parameters

      - data – time series data with the minimal length equal to the max_lag of the model

      - steps – the number of steps ahead to forecast

      - start_at – in the multi step forecasting, the index of the data where to start forecasting (default: 0)

    Returns

      a list with the forecasted Probability Distributions

  `forecast_ahead_interval`(ndata, steps, **kwargs)

    Interval forecast from 1 to H steps ahead, where H is given by the steps parameter

    Parameters

      - data – time series data with the minimal length equal to the max_lag of the model

      - steps – the number of steps ahead to forecast

      - start_at – in the multi step forecasting, the index of the data where to start forecasting (default: 0)

    Returns

      a list with the forecasted intervals

  `forecast_distribution`(data, **kwargs)

    Probabilistic forecast one step ahead

    Parameters

      - data – time series data with the minimal length equal to the max_lag of the model

      - kwargs – model specific parameters

    Returns

      a list with probabilistic.ProbabilityDistribution objects representing the forecasted Probability Distributions

  `forecast_interval`(data, **kwargs)

    Interval forecast one step ahead

    Parameters

      - data – time series data with the minimal length equal to the max_lag of the model

      - kwargs – model specific parameters

    Returns

      a list with the prediction intervals

  `inference`(steps)
  `train`(data, **kwargs)

    Method specific parameter fitting

    Parameters

      - data – training time series data

      - kwargs – Method specific parameters