tsa.md

Time series analysis (TSA)

EWM optimization

The calc_optimized_ewm tries to find the alpha that minimises a metric between a series and the exponentially weighted average (EWM) of parameter alpha. The optimisation is done with differential evolution. The EWM is calculated on the input series shifted by an input paramater called shift. This ensures that the EWM can only look at values that are in the past with a margin of shift. For example if you want the EWM to predict today's values with data that only goes up to yesterday then you would set shift to be equal to 1 (which also happens to be the default value).

>>> import pandas as pd
>>> from sklearn import metrics
>>> import xam

>>> series = pd.Series([1, 2, 3, 1, 2, 3, 1, 2, 3])
>>> shift = 3
>>> metric = metrics.mean_squared_error
>>> ewm = xam.tsa.calc_optimized_ewm(series, shift=shift, metric=metric, seed=42)
>>> ewm
0       NaN
1       NaN
2       NaN
3    1.0000
4    1.9999
5    2.9999
6    1.0002
7    1.9999
8    2.9999
dtype: float64

Exponential smoothing

>>> import datetime as dt
>>> from math import sqrt
>>> import numpy as np
>>> import pandas as pd
>>> from sklearn import metrics
>>> import xam

>>> df = pd.read_csv('datasets/airline-passengers.csv')
>>> series = pd.Series(
...     data=df['passengers'].tolist(),
...     index=pd.DatetimeIndex([dt.datetime.strptime(m, '%Y-%m') for m in df['month']]),
...     dtype=np.float
... )

>>> # Determine how long a season lasts (in this case twelve months)
>>> season_length = 12

>>> # Train/test split
>>> train_test_split_index = 12 # Forecast the last year
>>> train = series[:-train_test_split_index]
>>> test = series[-train_test_split_index:]

>>> # Learning coefficients
>>> alpha = 0.1
>>> beta = 0.2
>>> gamma = 0.6

>>> pred = xam.tsa.SimpleExponentialSmoothingForecaster(alpha).fit(train).predict(test.index)
>>> print('RMSE: {:.3f}'.format(sqrt(metrics.mean_squared_error(test, pred))))
RMSE: 99.293

>>> pred = xam.tsa.DoubleExponentialSmoothingForecaster(alpha, beta).fit(train).predict(test.index)
>>> print('RMSE: {:.3f}'.format(sqrt(metrics.mean_squared_error(test, pred))))
RMSE: 73.265

>>> pred = xam.tsa.TripleExponentialSmoothingForecaster(
...     alpha,
...     beta,
...     gamma,
...     season_length=season_length,
...     multiplicative=True
... ).fit(train).predict(test.index)
>>> print('RMSE: {:.3f}'.format(sqrt(metrics.mean_squared_error(test, pred))))
RMSE: 17.543

Frequency average forecasting

>>> import datetime as dt
>>> import pandas as pd
>>> import xam

>>> df = pd.read_csv('datasets/bike-station.csv')
>>> series = pd.Series(
...     data=df['bikes'].tolist(),
...     index=pd.to_datetime(df['moment'], format='%Y-%m-%d %H:%M:%S')
... )

>>> forecaster = xam.tsa.FrequencyAverageForecaster(lambda d: f'{d.weekday()}-{d.hour}')
>>> forecaster.fit(series[:-10]).predict(series.index[-10:])
moment
2016-10-05 09:28:48    8.622535
2016-10-05 09:32:34    8.622535
2016-10-05 09:40:55    8.622535
2016-10-05 09:42:34    8.622535
2016-10-05 09:45:06    8.622535
2016-10-05 09:46:29    8.622535
2016-10-05 09:50:54    8.622535
2016-10-05 09:53:00    8.622535
2016-10-05 09:54:04    8.622535
2016-10-05 09:57:18    8.622535
dtype: float64