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1. Synthetic Panel Data

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generate_series

 generate_series (n_series:int, freq:str='D', min_length:int=50,
                  max_length:int=500, n_temporal_features:int=0,
                  n_static_features:int=0, equal_ends:bool=False,
                  seed:int=0)

*Generate Synthetic Panel Series.

Generates n_series of frequency freq of different lengths in the interval [min_length, max_length]. If n_temporal_features > 0, then each serie gets temporal features with random values. If n_static_features > 0, then a static dataframe is returned along the temporal dataframe. If equal_ends == True then all series end at the same date.

Parameters:
n_series: int, number of series for synthetic panel.
min_length: int, minimal length of synthetic panel’s series.
max_length: int, minimal length of synthetic panel’s series.
n_temporal_features: int, default=0, number of temporal exogenous variables for synthetic panel’s series.
n_static_features: int, default=0, number of static exogenous variables for synthetic panel’s series.
equal_ends: bool, if True, series finish in the same date stamp ds.
freq: str, frequency of the data, panda’s available frequencies.

Returns:
freq: pandas.DataFrame, synthetic panel with columns [unique_id, ds, y] and exogenous.*

synthetic_panel = generate_series(n_series=2)
synthetic_panel.groupby('unique_id').head(4)

temporal_df, static_df = generate_series(n_series=1000, n_static_features=2,
                                         n_temporal_features=4, equal_ends=False)
static_df.head(2)

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2. AirPassengers Data

The classic Box & Jenkins airline data. Monthly totals of international airline passengers, 1949 to 1960.

It has been used as a reference on several forecasting libraries, since it is a series that shows clear trends and seasonalities it offers a nice opportunity to quickly showcase a model’s predictions performance.

AirPassengersDF.head(12)

#We are going to plot the ARIMA predictions, and the prediction intervals.
fig, ax = plt.subplots(1, 1, figsize = (20, 7))
plot_df = AirPassengersDF.set_index('ds')

plot_df[['y']].plot(ax=ax, linewidth=2)
ax.set_title('AirPassengers Forecast', fontsize=22)
ax.set_ylabel('Monthly Passengers', fontsize=20)
ax.set_xlabel('Timestamp [t]', fontsize=20)
ax.legend(prop={'size': 15})
ax.grid()

import numpy as np
import pandas as pd

n_static_features = 3
n_series = 5

static_features = np.random.uniform(low=0.0, high=1.0, 
                        size=(n_series, n_static_features))
static_df = pd.DataFrame.from_records(static_features, 
                   columns = [f'static_{i}'for i in  range(n_static_features)])
static_df['unique_id'] = np.arange(n_series)

static_df

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3. Panel AirPassengers Data

Extension to classic Box & Jenkins airline data. Monthly totals of international airline passengers, 1949 to 1960.

It includes two series with static, temporal and future exogenous variables, that can help to explore the performance of models like NBEATSx and TFT.

fig, ax = plt.subplots(1, 1, figsize = (20, 7))
plot_df = AirPassengersPanel.set_index('ds')

plot_df.groupby('unique_id')['y'].plot(legend=True)
ax.set_title('AirPassengers Panel Data', fontsize=22)
ax.set_ylabel('Monthly Passengers', fontsize=20)
ax.set_xlabel('Timestamp [t]', fontsize=20)
ax.legend(title='unique_id', prop={'size': 15})
ax.grid()

fig, ax = plt.subplots(1, 1, figsize = (20, 7))
plot_df = AirPassengersPanel[AirPassengersPanel.unique_id=='Airline1'].set_index('ds')

plot_df[['y', 'trend', 'y_[lag12]']].plot(ax=ax, linewidth=2)
ax.set_title('Box-Cox AirPassengers Data', fontsize=22)
ax.set_ylabel('Monthly Passengers', fontsize=20)
ax.set_xlabel('Timestamp [t]', fontsize=20)
ax.legend(prop={'size': 15})
ax.grid()

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4. Time Features

We have developed a utility that generates normalized calendar features for use as absolute positional embeddings in Transformer-based models. These embeddings capture seasonal patterns in time series data and can be easily incorporated into the model architecture. Additionally, the features can be used as exogenous variables in other models to inform them of calendar patterns in the data.

References
- Haoyi Zhou, Shanghang Zhang, Jieqi Peng, Shuai Zhang, Jianxin Li, Hui Xiong, Wancai Zhang. “Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting”

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augment_calendar_df

 augment_calendar_df (df, freq='H')

*> * Q - [month] > * M - [month] > * W - [Day of month, week of year] > * D - [Day of week, day of month, day of year] > * B - [Day of week, day of month, day of year] > * H - [Hour of day, day of week, day of month, day of year] > * T - [Minute of hour*, hour of day, day of week, day of month, day of year] > * S - [Second of minute, minute of hour, hour of day, day of week, day of month, day of year] minute returns a number from 0-3 corresponding to the 15 minute period it falls into.

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time_features_from_frequency_str

 time_features_from_frequency_str (freq_str:str)

Returns a list of time features that will be appropriate for the given frequency string. Parameters ———- freq_str Frequency string of the form [multiple][granularity] such as “12H”, “5min”, “1D” etc.

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WeekOfYear

 WeekOfYear ()

Week of year encoded as value between [-0.5, 0.5]

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MonthOfYear

 MonthOfYear ()

Month of year encoded as value between [-0.5, 0.5]

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DayOfYear

 DayOfYear ()

Day of year encoded as value between [-0.5, 0.5]

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DayOfMonth

 DayOfMonth ()

Day of month encoded as value between [-0.5, 0.5]

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DayOfWeek

 DayOfWeek ()

Hour of day encoded as value between [-0.5, 0.5]

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HourOfDay

 HourOfDay ()

Hour of day encoded as value between [-0.5, 0.5]

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MinuteOfHour

 MinuteOfHour ()

Minute of hour encoded as value between [-0.5, 0.5]

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SecondOfMinute

 SecondOfMinute ()

Minute of hour encoded as value between [-0.5, 0.5]

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TimeFeature

 TimeFeature ()

Initialize self. See help(type(self)) for accurate signature.

AirPassengerPanelCalendar, calendar_cols = augment_calendar_df(df=AirPassengersPanel, freq='M')
AirPassengerPanelCalendar.head()

plot_df = AirPassengerPanelCalendar[AirPassengerPanelCalendar.unique_id=='Airline1'].set_index('ds')
plt.plot(plot_df['month'])
plt.grid()
plt.xlabel('Datestamp')
plt.ylabel('Normalized Month')
plt.show()
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get_indexer_raise_missing

 get_indexer_raise_missing (idx:pandas.core.indexes.base.Index,
                            vals:List[str])

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5. Prediction Intervals

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PredictionIntervals

 PredictionIntervals (n_windows:int=2,
                      method:str='conformal_distribution')

Class for storing prediction intervals metadata information.

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add_conformal_distribution_intervals

 add_conformal_distribution_intervals (model_fcsts:<built-
                                       infunctionarray>, cs_df:~DFType,
                                       model:str, cs_n_windows:int,
                                       n_series:int, horizon:int, level:Op
                                       tional[List[Union[int,float]]]=None
                                       , quantiles:Optional[List[float]]=N
                                       one)

Adds conformal intervals to a fcst_df based on conformal scores cs_df. level should be already sorted. This strategy creates forecasts paths based on errors and calculate quantiles using those paths.

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add_conformal_error_intervals

 add_conformal_error_intervals (model_fcsts:<built-infunctionarray>,
                                cs_df:~DFType, model:str,
                                cs_n_windows:int, n_series:int,
                                horizon:int, level:Optional[List[Union[int
                                ,float]]]=None,
                                quantiles:Optional[List[float]]=None)

Adds conformal intervals to a fcst_df based on conformal scores cs_df. level should be already sorted. This startegy creates prediction intervals based on the absolute errors.

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get_prediction_interval_method

 get_prediction_interval_method (method:str)
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quantiles_to_level

 quantiles_to_level (quantiles:List[float])

Converts a list of quantiles to a list of levels.

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level_to_quantiles

 level_to_quantiles (level:List[Union[int,float]])

Converts a list of levels to a list of quantiles.