# BATS and TBATS time series forecasting

Package provides BATS and TBATS time series forecasting methods described in:

De Livera, A.M., Hyndman, R.J., & Snyder, R. D. (2011), Forecasting time series with complex seasonal patterns using exponential smoothing, Journal of the American Statistical Association, 106(496), 1513-1527.

## Installation

From pypi:

`pip install tbats`

Import via:

`from tbats import BATS, TBATS`

## Minimal working example:

```
from tbats import TBATS
import numpy as np
# required on windows for multi-processing,
# see https://docs.python.org/2/library/multiprocessing.html#windows
if __name__ == '__main__':
np.random.seed(2342)
t = np.array(range(0, 160))
y = 5 * np.sin(t * 2 * np.pi / 7) + 2 * np.cos(t * 2 * np.pi / 30.5) + \
((t / 20) ** 1.5 + np.random.normal(size=160) * t / 50) + 10
# Create estimator
estimator = TBATS(seasonal_periods=[14, 30.5])
# Fit model
fitted_model = estimator.fit(y)
# Forecast 14 steps ahead
y_forecasted = fitted_model.forecast(steps=14)
# Summarize fitted model
print(fitted_model.summary())
```

Reading model details

```
# Time series analysis
print(fitted_model.y_hat) # in sample prediction
print(fitted_model.resid) # in sample residuals
print(fitted_model.aic)
# Reading model parameters
print(fitted_model.params.alpha)
print(fitted_model.params.beta)
print(fitted_model.params.x0)
print(fitted_model.params.components.use_box_cox)
print(fitted_model.params.components.seasonal_harmonics)
```

See **examples** directory for more details.

## Troubleshooting

BATS and TBATS tries multitude of models under the hood and **may appear slow when fitting** to long time series. In order to speed it up you can start with constrained model search space. It is recommended to run it without Box-Cox transformation and ARMA errors modelling that are the slowest model elements:

```
# Create estimator
estimator = TBATS(
seasonal_periods=[14, 30.5],
use_arma_errors=False, # shall try only models without ARMA
use_box_cox=False # will not use Box-Cox
)
fitted_model = estimator.fit(y)
```

In some environment configurations parallel computation of models freezes. Reason for this is unclear yet. If **the process appears to be stuck** you can try running it on a single core:

```
estimator = TBATS(
seasonal_periods=[14, 30.5],
n_jobs=1
)
fitted_model = estimator.fit(y)
```

## For Contributors

Building package:

`pip install -e .[dev]`

Unit and integration tests:

`pytest test/`

R forecast package comparison tests. Those DO NOT RUN with default test command, you need R and forecast package installed:

`pytest test_R/`

## Comparison to R implementation

Python implementation is meant to be as much as possible equivalent to R implementation in forecast package.