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Quick Start Tutorial

The GluonTS toolkit contains components and tools for building time series models using MXNet. The models that are currently included are forecasting models but the components also support other time series use cases, such as classification or anomaly detection.

The toolkit is not intended as a forecasting solution for businesses or end users but it rather targets scientists and engineers who want to tweak algorithms or build and experiment with their own models.

GluonTS contains:

• Components for building new models (likelihoods, feature processing pipelines, calendar features etc.)

• Data loading and processing

• A number of pre-built models

• Plotting and evaluation facilities

• Artificial and real datasets (only external datasets with blessed license)

%matplotlib inline
import mxnet as mx
from mxnet import gluon
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import json

Datasets

Provided datasets

GluonTS comes with a number of publicly available datasets.

from gluonts.dataset.repository.datasets import get_dataset, dataset_recipes
from gluonts.dataset.util import to_pandas

print(f"Available datasets: {list(dataset_recipes.keys())}")

Available datasets: ['constant', 'exchange_rate', 'solar-energy', 'electricity', 'traffic', 'exchange_rate_nips', 'electricity_nips', 'traffic_nips', 'solar_nips', 'wiki-rolling_nips', 'taxi_30min', 'm3_monthly', 'm3_quarterly', 'm3_yearly', 'm3_other', 'm4_hourly', 'm4_daily', 'm4_weekly', 'm4_monthly', 'm4_quarterly', 'm4_yearly', 'm5']

To download one of the built-in datasets, simply call get_dataset with one of the above names. GluonTS can re-use the saved dataset so that it does not need to be downloaded again: simply set regenerate=False.

dataset = get_dataset("m4_hourly", regenerate=True)

saving time-series into /home/runner/.mxnet/gluon-ts/datasets/m4_hourly/train/data.json
saving time-series into /home/runner/.mxnet/gluon-ts/datasets/m4_hourly/test/data.json

In general, the datasets provided by GluonTS are objects that consists of three main members:

• dataset.train is an iterable collection of data entries used for training. Each entry corresponds to one time series

• dataset.test is an iterable collection of data entries used for inference. The test dataset is an extended version of the train dataset that contains a window in the end of each time series that was not seen during training. This window has length equal to the recommended prediction length.

• dataset.metadata contains metadata of the dataset such as the frequency of the time series, a recommended prediction horizon, associated features, etc.

entry = next(iter(dataset.train))
train_series = to_pandas(entry)
train_series.plot()
plt.grid(which="both")
plt.legend(["train series"], loc="upper left")
plt.show()

entry = next(iter(dataset.test))
test_series = to_pandas(entry)
test_series.plot()
plt.axvline(train_series.index[-1], color='r') # end of train dataset
plt.grid(which="both")
plt.legend(["test series", "end of train series"], loc="upper left")
plt.show()

print(f"Length of forecasting window in test dataset: {len(test_series) - len(train_series)}")
print(f"Recommended prediction horizon: {dataset.metadata.prediction_length}")
print(f"Frequency of the time series: {dataset.metadata.freq}")

Length of forecasting window in test dataset: 48
Recommended prediction horizon: 48
Frequency of the time series: H

Custom datasets

At this point, it is important to emphasize that GluonTS does not require this specific format for a custom dataset that a user may have. The only requirements for a custom dataset are to be iterable and have a “target” and a “start” field. To make this more clear, assume the common case where a dataset is in the form of a numpy.array and the index of the time series in a pandas.Timestamp (possibly different for each time series):

N = 10  # number of time series
T = 100  # number of timesteps
prediction_length = 24
freq = "1H"
custom_dataset = np.random.normal(size=(N, T))
start = pd.Timestamp("01-01-2019", freq=freq)  # can be different for each time series

Now, you can split your dataset and bring it in a GluonTS appropriate format with just two lines of code:

from gluonts.dataset.common import ListDataset

# train dataset: cut the last window of length "prediction_length", add "target" and "start" fields
train_ds = ListDataset(
    [{'target': x, 'start': start} for x in custom_dataset[:, :-prediction_length]],
    freq=freq
)
# test dataset: use the whole dataset, add "target" and "start" fields
test_ds = ListDataset(
    [{'target': x, 'start': start} for x in custom_dataset],
    freq=freq
)

Training an existing model (Estimator)

GluonTS comes with a number of pre-built models. All the user needs to do is configure some hyperparameters. The existing models focus on (but are not limited to) probabilistic forecasting. Probabilistic forecasts are predictions in the form of a probability distribution, rather than simply a single point estimate.

We will begin with GulonTS’s pre-built feedforward neural network estimator, a simple but powerful forecasting model. We will use this model to demonstrate the process of training a model, producing forecasts, and evaluating the results.

GluonTS’s built-in feedforward neural network (SimpleFeedForwardEstimator) accepts an input window of length context_length and predicts the distribution of the values of the subsequent prediction_length values. In GluonTS parlance, the feedforward neural network model is an example of Estimator. In GluonTS, Estimator objects represent a forecasting model as well as details such as its coefficients, weights, etc.

In general, each estimator (pre-built or custom) is configured by a number of hyperparameters that can be either common (but not binding) among all estimators (e.g., the prediction_length) or specific for the particular estimator (e.g., number of layers for a neural network or the stride in a CNN).

Finally, each estimator is configured by a Trainer, which defines how the model will be trained i.e., the number of epochs, the learning rate, etc.

from gluonts.model.simple_feedforward import SimpleFeedForwardEstimator
from gluonts.mx.trainer import Trainer

estimator = SimpleFeedForwardEstimator(
    num_hidden_dimensions=[10],
    prediction_length=dataset.metadata.prediction_length,
    context_length=100,
    freq=dataset.metadata.freq,
    trainer=Trainer(
        ctx="cpu",
        epochs=5,
        learning_rate=1e-3,
        num_batches_per_epoch=100
    )
)

After specifying our estimator with all the necessary hyperparameters we can train it using our training dataset dataset.train by invoking the train method of the estimator. The training algorithm returns a fitted model (or a Predictor in GluonTS parlance) that can be used to construct forecasts.

predictor = estimator.train(dataset.train)

  0%|          | 0/100 [00:00<?, ?it/s]

learning rate from ``lr_scheduler`` has been overwritten by ``learning_rate`` in optimizer.

100%|██████████| 100/100 [00:00<00:00, 104.53it/s, epoch=1/5, avg_epoch_loss=5.57]
100%|██████████| 100/100 [00:00<00:00, 115.73it/s, epoch=2/5, avg_epoch_loss=4.89]
100%|██████████| 100/100 [00:00<00:00, 112.88it/s, epoch=3/5, avg_epoch_loss=4.83]
100%|██████████| 100/100 [00:00<00:00, 112.68it/s, epoch=4/5, avg_epoch_loss=4.82]
100%|██████████| 100/100 [00:00<00:00, 114.48it/s, epoch=5/5, avg_epoch_loss=4.63]

Visualize and evaluate forecasts

With a predictor in hand, we can now predict the last window of the dataset.test and evaluate our model’s performance.

GluonTS comes with the make_evaluation_predictions function that automates the process of prediction and model evaluation. Roughly, this function performs the following steps:

• Removes the final window of length prediction_length of the dataset.test that we want to predict

• The estimator uses the remaining data to predict (in the form of sample paths) the “future” window that was just removed

• The module outputs the forecast sample paths and the dataset.test (as python generator objects)

from gluonts.evaluation import make_evaluation_predictions

forecast_it, ts_it = make_evaluation_predictions(
    dataset=dataset.test,  # test dataset
    predictor=predictor,  # predictor
    num_samples=100,  # number of sample paths we want for evaluation
)

First, we can convert these generators to lists to ease the subsequent computations.

forecasts = list(forecast_it)
tss = list(ts_it)

We can examine the first element of these lists (that corresponds to the first time series of the dataset). Let’s start with the list containing the time series, i.e., tss. We expect the first entry of tss to contain the (target of the) first time series of dataset.test.

# first entry of the time series list
ts_entry = tss[0]

# first 5 values of the time series (convert from pandas to numpy)
np.array(ts_entry[:5]).reshape(-1,)

array([605., 586., 586., 559., 511.], dtype=float32)

# first entry of dataset.test
dataset_test_entry = next(iter(dataset.test))

# first 5 values
dataset_test_entry['target'][:5]

array([605., 586., 586., 559., 511.], dtype=float32)

The entries in the forecast list are a bit more complex. They are objects that contain all the sample paths in the form of numpy.ndarray with dimension (num_samples, prediction_length), the start date of the forecast, the frequency of the time series, etc. We can access all these information by simply invoking the corresponding attribute of the forecast object.

# first entry of the forecast list
forecast_entry = forecasts[0]

print(f"Number of sample paths: {forecast_entry.num_samples}")
print(f"Dimension of samples: {forecast_entry.samples.shape}")
print(f"Start date of the forecast window: {forecast_entry.start_date}")
print(f"Frequency of the time series: {forecast_entry.freq}")

Number of sample paths: 100
Dimension of samples: (100, 48)
Start date of the forecast window: 1750-01-30 04:00:00
Frequency of the time series: H

We can also do calculations to summarize the sample paths, such computing the mean or a quantile for each of the 48 time steps in the forecast window.

print(f"Mean of the future window:\n {forecast_entry.mean}")
print(f"0.5-quantile (median) of the future window:\n {forecast_entry.quantile(0.5)}")

Mean of the future window:
 [657.432   567.8759  509.03964 462.90637 533.49255 474.97253 449.83563
 489.14816 520.5916  556.1061  586.52    689.13794 743.9377  755.9347
 846.90674 861.06946 884.1995  844.0505  858.2082  851.92267 804.64655
 809.32513 808.19763 698.4341  628.41486 571.8308  545.1014  489.84125
 533.61194 497.71265 527.5373  463.3403  488.81894 553.01324 617.9387
 693.801   704.50995 802.0996  779.80225 842.65845 859.039   937.10315
 886.0708  741.0214  912.11237 926.66284 805.56836 730.22266]
0.5-quantile (median) of the future window:
 [669.59045 575.02576 531.0032  464.3974  525.8405  476.6602  458.5382
 489.29544 519.2877  542.18964 585.2373  681.03265 763.4545  773.0337
 843.76996 875.1853  872.0016  834.8163  849.573   841.62476 808.5004
 801.8551  802.89844 679.6511  631.09546 573.2768  555.4188  487.28363
 518.59454 508.8435  502.41446 456.2519  490.46066 551.9699  612.1071
 685.0114  684.63007 789.92535 762.7166  859.23254 848.2905  952.18243
 890.4299  755.653   881.6748  933.1342  800.9058  744.48395]

Forecast objects have a plot method that can summarize the forecast paths as the mean, prediction intervals, etc. The prediction intervals are shaded in different colors as a “fan chart”.

def plot_prob_forecasts(ts_entry, forecast_entry):
    plot_length = 150
    prediction_intervals = (50.0, 90.0)
    legend = ["observations", "median prediction"] + [f"{k}% prediction interval" for k in prediction_intervals][::-1]

    fig, ax = plt.subplots(1, 1, figsize=(10, 7))
    ts_entry[-plot_length:].plot(ax=ax)  # plot the time series
    forecast_entry.plot(prediction_intervals=prediction_intervals, color='g')
    plt.grid(which="both")
    plt.legend(legend, loc="upper left")
    plt.show()

plot_prob_forecasts(ts_entry, forecast_entry)

We can also evaluate the quality of our forecasts numerically. In GluonTS, the Evaluator class can compute aggregate performance metrics, as well as metrics per time series (which can be useful for analyzing performance across heterogeneous time series).

from gluonts.evaluation import Evaluator

evaluator = Evaluator(quantiles=[0.1, 0.5, 0.9])
agg_metrics, item_metrics = evaluator(iter(tss), iter(forecasts), num_series=len(dataset.test))

Running evaluation: 100%|██████████| 414/414 [00:00<00:00, 19917.66it/s]

Aggregate metrics aggregate both across time-steps and across time series.

print(json.dumps(agg_metrics, indent=4))

{
    "MSE": 9656613.653655292,
    "abs_error": 8926028.686189651,
    "abs_target_sum": 145558863.59960938,
    "abs_target_mean": 7324.822041043146,
    "seasonal_error": 336.9046924038305,
    "MASE": 3.3882664642129723,
    "MAPE": 0.24571015283273423,
    "sMAPE": 0.1852512300890329,
    "OWA": NaN,
    "MSIS": 63.97941756142848,
    "QuantileLoss[0.1]": 5090296.274248887,
    "Coverage[0.1]": 0.09686996779388084,
    "QuantileLoss[0.5]": 8926028.815477371,
    "Coverage[0.5]": 0.46804549114331717,
    "QuantileLoss[0.9]": 6892946.789128493,
    "Coverage[0.9]": 0.8796296296296295,
    "RMSE": 3107.509236294446,
    "NRMSE": 0.4242436497272087,
    "ND": 0.06132246752587044,
    "wQuantileLoss[0.1]": 0.034970706340843864,
    "wQuantileLoss[0.5]": 0.0613224684140865,
    "wQuantileLoss[0.9]": 0.047355046739640735,
    "mean_absolute_QuantileLoss": 6969757.292951584,
    "mean_wQuantileLoss": 0.047882740498190364,
    "MAE_Coverage": 0.01848497047772416
}

Individual metrics are aggregated only across time-steps.

item_metrics.head()

	item_id	MSE	abs_error	abs_target_sum	abs_target_mean	seasonal_error	MASE	MAPE	sMAPE	OWA	MSIS	QuantileLoss[0.1]	Coverage[0.1]	QuantileLoss[0.5]	Coverage[0.5]	QuantileLoss[0.9]	Coverage[0.9]
0	0.0	2997.847005	1756.685791	31644.0	659.250000	42.371302	0.863736	0.054706	0.052378	NaN	13.179705	972.442920	0.020833	1756.685730	0.666667	1419.121350	1.000000
1	1.0	155417.968750	16964.033203	124149.0	2586.437500	165.107988	2.140522	0.142941	0.131103	NaN	13.879598	3420.709351	0.166667	16964.032104	0.979167	8374.049316	1.000000
2	2.0	29935.947917	6447.917969	65030.0	1354.791667	78.889053	1.702792	0.089015	0.095048	NaN	13.872233	3473.809839	0.000000	6447.917603	0.145833	1539.831445	0.833333
3	3.0	292266.479167	19561.388672	235783.0	4912.145833	258.982249	1.573579	0.080606	0.080400	NaN	14.879645	10134.517090	0.041667	19561.388916	0.416667	8175.906152	0.979167
4	4.0	100070.489583	9540.142578	131088.0	2731.000000	200.494083	0.991316	0.065609	0.061433	NaN	13.176000	4892.513110	0.062500	9540.142822	0.812500	7150.268848	1.000000

item_metrics.plot(x='MSIS', y='MASE', kind='scatter')
plt.grid(which="both")
plt.show()