A python package for multi-variate time series prediction

# fireTS

import numpy as np
from sklearn.linear_model import LinearRegression
from fireTS.models import NARX

x = np.random.randn(100, 1)
y = np.random.randn(100)
mdl = NARX(LinearRegression(), auto_order=2, exog_order=[2])
mdl.fit(x, y)
y_forecast = mdl.forecast(x, y, step=10, X_future=np.random.randn(9, 1))


# Introduction

fireTS is a sklean style package for multi-variate time-series prediction. Here is a simple code snippet to showcase the awesome features provided by fireTS package.

from fireTS.models import NARX, DirectAutoRegressor
from sklearn.ensemble import RandomForestRegressor
from xgboost import XGBRegressor
import numpy as np

# Random training data
x = np.random.randn(100, 2)
y = np.random.randn(100)

# Build a non-linear autoregression model with exogenous inputs
# using Random Forest regression as the base model
mdl1 = NARX(
RandomForestRegressor(n_estimators=10),
auto_order=2,
exog_order=[2, 2],
exog_delay=[1, 1])
mdl1.fit(x, y)
ypred1 = mdl1.predict(x, y, step=3)

# Build a general autoregression model and make multi-step prediction directly
# using XGBRegressor as the base model
mdl2 = DirectAutoRegressor(
XGBRegressor(n_estimators=10),
auto_order=2,
exog_order=[2, 2],
exog_delay=[1, 1],
pred_step=3)
mdl2.fit(x, y)
ypred2 = mdl2.predict(x, y)

• sklearn style API. The package provides fit and predict methods, which is very similar to sklearn package.
• Plug-and-go. You are able to plug in any machine learning regression algorithms provided in sklearn package and build a time-series forecasting model.
• Create the lag features for you by specifying the autoregression order auto_order, the exogenous input order exog_order, and the exogenous input delay exog_delay.
• Support multi-step prediction. The package can make multi-step prediction in two different ways: recursive way and direct way. NARX model is to build a one-step-ahead-predictive model, and the model will be used recursively to make multi-step prediction (future exogenous input information is needed). DirectAutoRegressor makes multi-step prediction directly (no future exogenous input information is needed) by specifying the prediction step in the constructor.
• Support grid search to tune the hyper-parameters of the base model (cannot do grid search on the orders and delays of the time series model for now).

I developed this package when writing this paper. It is really handy to generate lag features and leverage various regression algorithms provided by sklearn to build non-linear multi-variate time series models. The API can also be used to build deep neural network models to make time-series prediction. The paper used this package to build LSTM models and make multi-step predictions.

The documentation can be found here. The documentation provides the mathematical equations of each model. It is highly recommended to read the documentation before using the model.

### Nonlinear AutoRegression with eXogenous (NARX) model

fireTS.models.NARX model is trying to train a one-step-ahead-prediction model and make multi-step prediction recursively given the future exogenous inputs.

Given the output time series to predict y(t) and exogenous inputs X(t) The model will generate target and features as follows:

Target Features
y(t + 1) y(t), y(t - 1), ..., y(t - p + 1), X(t - d), X(t - d - 1), ..., X(t - d - q + 1)

where p is the autogression order auto_order, q is the exogenous input order exog_order, d is the exogenous delay exog_delay.

NARX model can make any step ahead prediction given the future exogenous inputs. To make multi-step prediction, set the step in the predict method.

### Direct Autoregressor

fireTS.models.DirectAutoRegressor model is trying to train a multi-step-head-prediction model directly. No future exogenous inputs are required to make the multi-step prediction.

Given the output time series to predict y(t) and exogenous inputs X(t) The model will generate target and features as follows:

Target Features
y(t + k) y(t), y(t - 1), ..., y(t - p + 1), X(t - d), X(t - d - 1), ..., X(t - d - q + 1)

where p is the autogression order auto_order, q is the exogenous input order exog_order, d is the exogenous delay exog_delay, k is the prediction step pred_step.

Direct autoregressor does not require future exogenous input information to make multi-step prediction. Its predict method cannot specify prediction step.

## Installation

NOTE: Only python3 is supported.

It is highly recommended to use pip to install fireTS, follow this link to install pip.

After pip is installed,

pip install fireTS


To get the latest development version,

git clone https://github.com/jxx123/fireTS.git
cd fireTS
pip install -e .


## Quick Start

• Use RandomForestRegressor as base model to build a NARX model
from fireTS.models import NARX
from sklearn.ensemble import RandomForestRegressor
import numpy as np

x = np.random.randn(100, 1)
y = np.random.randn(100)
mdl = NARX(RandomForestRegressor(), auto_order=2, exog_order=[2], exog_delay=[1])
mdl.fit(x, y)
ypred = mdl.predict(x, y, step=3)

• Use RandomForestRegressor as base model to build a DirectAutoRegressor model
from fireTS.models import DirectAutoRegressor
from sklearn.ensemble import RandomForestRegressor
import numpy as np

x = np.random.randn(100, 1)
y = np.random.randn(100)
mdl = DirectAutoRegressor(RandomForestRegressor(),
auto_order=2,
exog_order=[2],
exog_delay=[1],
pred_step=3)
mdl.fit(x, y)
ypred = mdl.predict(x, y)

• Usage of grid search
from fireTS.models import NARX
from sklearn.ensemble import RandomForestRegressor
import numpy as np

x = np.random.randn(100, 1)
y = np.random.randn(100)

# DirectAutoRegressor can do grid search as well
mdl = NARX(RandomForestRegressor(), auto_order=2, exog_order=[2], exog_delay=[1])

# Grid search
para_grid = {'n_estimators': [10, 30, 100]}
mdl.grid_search(x, y, para_grid, verbose=2)

# Best hyper-parameters are set after grid search, print the model to see the difference
print(mdl)

# Fit the model and make the prediction
mdl.fit(x, y)
ypred = mdl.predict(x, y, step=3)


The examples folder provides more realistic examples. The example1 and example2 use the data simulated by simglucose pakage to fit time series model and make multi-step prediction.

## FAQ

• What is the difference between predict and forecast?
• For example, given a target time series y(0), y(1), ..., y(9) to predict and the exogenous input time series x(0), x(1), ..., x(9), build a NARX model NARX(RandomForestRegressor(), auto_order=1, exog_order=[1], exog_delay=[0]). The model can be represented by a function y(t + 1) = f(y(t), x(t)) + e(t).
• predict(x, y, step=2) outputs a time series that has the same length as original y, and it means the 2-step-ahead prediction at each step, i.e. nan, nan, y_hat(2), y_hat(3), ..., y_hat(9). Note that y_hat(2) is the 2-step-ahead prediction standing at time 0. y_hat(3) is the 2-step-ahead prediction standing at time 1, and so on. Another very important note is that predicted value y_hat(2) = f(y_hat(1), x(1)) = f(f(y(0), x(0)), x(1)). The prediction uses a perfect future information x(1) (since you are currently at time 0).
• When forecast(x, y, step=2) was called, the output is of length 2, meaning the predicted y in the future 2 steps, i.e. y_hat(10), y_hat(11). Here, both y_hat(10), y_hat(11) are the predicted values standing at time 9. However, forecast will NOT use any perfect future information of the exogenous input x by default. In fact, the default future exogenous inputs x are assume to be zeros across the whole prediction horizon. You can provide your own future exogenous input values through the optional argument X_future (call forcast(x, y, step=2, X_future=your_X_future)).

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