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Table Of Contents

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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)
In [1]:
# Third-party imports
%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

GluonTS datasets

GluonTS comes with a number of publicly available datasets.

In [2]:
from gluonts.dataset.repository.datasets import get_dataset, dataset_recipes
from gluonts.dataset.util import to_pandas
In [3]:
print(f"Available datasets: {list(dataset_recipes.keys())}")
Available datasets: ['constant', 'exchange_rate', 'solar-energy', 'electricity', 'traffic', 'm4_hourly', 'm4_daily', 'm4_weekly', 'm4_monthly', 'm4_quarterly', 'm4_yearly']

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.

In [4]:
dataset = get_dataset("m4_hourly", regenerate=True)
INFO:root:downloading and processing m4_hourly
saving time-series into /var/lib/jenkins/.mxnet/gluon-ts/datasets/m4_hourly/train/data.json
saving time-series into /var/lib/jenkins/.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 containts metadata of the dataset such as the frequency of the time series, a recommended prediction horizon, associated features, etc.
In [5]:
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()
../../_images/examples_basic_forecasting_tutorial_tutorial_8_0.png
In [6]:
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()
../../_images/examples_basic_forecasting_tutorial_tutorial_9_0.png
In [7]:
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):

In [8]:
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:

In [9]:
from gluonts.dataset.common import ListDataset
In [10]:
# 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.

In [11]:
from gluonts.model.simple_feedforward import SimpleFeedForwardEstimator
from gluonts.trainer import Trainer
In [12]:
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 specifing 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.

In [13]:
predictor = estimator.train(dataset.train)
INFO:root:Start model training
INFO:root:Number of parameters in SimpleFeedForwardTrainingNetwork: 483
INFO:root:Epoch[0] Learning rate is 0.001
100%|██████████| 100/100 [00:00<00:00, 127.86it/s, avg_epoch_loss=5.43]
INFO:root:Epoch[0] Elapsed time 0.785 seconds
INFO:root:Epoch[0] Evaluation metric 'epoch_loss'=5.427100
INFO:root:Epoch[1] Learning rate is 0.001
100%|██████████| 100/100 [00:00<00:00, 190.76it/s, avg_epoch_loss=4.87]
INFO:root:Epoch[1] Elapsed time 0.525 seconds
INFO:root:Epoch[1] Evaluation metric 'epoch_loss'=4.874734
INFO:root:Epoch[2] Learning rate is 0.001
100%|██████████| 100/100 [00:00<00:00, 190.83it/s, avg_epoch_loss=4.7]
INFO:root:Epoch[2] Elapsed time 0.525 seconds
INFO:root:Epoch[2] Evaluation metric 'epoch_loss'=4.697516
INFO:root:Epoch[3] Learning rate is 0.001
100%|██████████| 100/100 [00:00<00:00, 192.05it/s, avg_epoch_loss=4.82]
INFO:root:Epoch[3] Elapsed time 0.522 seconds
INFO:root:Epoch[3] Evaluation metric 'epoch_loss'=4.824960
INFO:root:Epoch[4] Learning rate is 0.001
100%|██████████| 100/100 [00:00<00:00, 189.68it/s, avg_epoch_loss=4.74]
INFO:root:Epoch[4] Elapsed time 0.528 seconds
INFO:root:Epoch[4] Evaluation metric 'epoch_loss'=4.743535
INFO:root:Loading parameters from best epoch (2)
INFO:root:Final loss: 4.697515823841095 (occurred at epoch 2)
INFO:root:End model training

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)
In [14]:
from gluonts.evaluation.backtest import make_evaluation_predictions
In [15]:
forecast_it, ts_it = make_evaluation_predictions(
    dataset=dataset.test,  # test dataset
    predictor=predictor,  # predictor
    num_eval_samples=100,  # number of sample paths we want for evaluation
)

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

In [16]:
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.

In [17]:
# first entry of the time series list
ts_entry = tss[0]
In [18]:
# first 5 values of the time series (convert from pandas to numpy)
np.array(ts_entry[:5]).reshape(-1,)
Out[18]:
array([605., 586., 586., 559., 511.], dtype=float32)
In [19]:
# first entry of dataset.test
dataset_test_entry = next(iter(dataset.test))
In [20]:
# first 5 values
dataset_test_entry['target'][:5]
Out[20]:
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.

In [21]:
# first entry of the forecast list
forecast_entry = forecasts[0]
In [22]:
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.

In [23]:
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:
 [637.3781  624.776   547.43164 520.3194  516.33496 468.351   454.59518
 501.57535 559.55426 608.1965  615.90186 699.252   698.84436 809.0959
 843.1813  882.49493 878.32886 878.6906  832.3315  839.98315 891.08
 779.14514 806.9432  752.55835 599.97595 581.4701  545.7095  505.30313
 526.18756 488.3147  450.25894 494.8213  479.23184 551.00354 606.2315
 682.97406 781.12665 821.1357  886.40045 806.3649  870.32    868.37164
 870.56354 825.7976  846.09686 822.9115  726.62    685.7912 ]
0.5-quantile (median) of the future window:
 [649.7218  615.1258  568.0607  519.00037 507.9442  470.75555 471.04538
 514.5377  559.0283  594.2491  613.7288  694.7169  735.4618  825.48944
 844.4672  896.12787 901.16406 884.9443  836.5291  838.05725 911.79254
 764.72894 803.6277  725.53033 606.8058  588.4905  551.68604 508.66315
 550.5681  501.4631  440.2583  493.7902  475.35876 554.8016  594.0473
 673.058   751.5446  826.5322  876.07526 835.73486 849.27374 872.17017
 869.69574 803.0832  819.75757 826.82434 722.3834  690.05505]

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”.

In [24]:
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()
In [25]:
plot_prob_forecasts(ts_entry, forecast_entry)
../../_images/examples_basic_forecasting_tutorial_tutorial_38_0.png

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).

In [26]:
from gluonts.evaluation import Evaluator
In [27]:
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 [00:01<00:00, 220.77it/s]

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

In [28]:
print(json.dumps(agg_metrics, indent=4))
{
    "MSE": 6987964.148162645,
    "abs_error": 8595155.117189407,
    "abs_target_sum": 145558863.59960938,
    "abs_target_mean": 7324.822041043146,
    "seasonal_error": 336.9046924038305,
    "MASE": 3.3432178165504647,
    "sMAPE": 0.19009264561053982,
    "MSIS": 41.02699583950569,
    "QuantileLoss[0.1]": 6025018.132624531,
    "Coverage[0.1]": 0.08549718196457326,
    "QuantileLoss[0.5]": 8595155.219514847,
    "Coverage[0.5]": 0.5425221417069243,
    "QuantileLoss[0.9]": 8265220.6777450545,
    "Coverage[0.9]": 0.8981481481481481,
    "RMSE": 2643.475770299899,
    "NRMSE": 0.36089283200161343,
    "ND": 0.05904934199563559,
    "wQuantileLoss[0.1]": 0.04139231362232688,
    "wQuantileLoss[0.5]": 0.05904934269861882,
    "wQuantileLoss[0.9]": 0.05678266835388536,
    "mean_wQuantileLoss": 0.052408108224943684,
    "MAE_Coverage": 0.019625603864734293
}

Individual metrics are aggregated only across time-steps.

In [29]:
item_metrics.head()
Out[29]:
item_id MSE abs_error abs_target_sum abs_target_mean seasonal_error MASE sMAPE MSIS QuantileLoss[0.1] Coverage[0.1] QuantileLoss[0.5] Coverage[0.5] QuantileLoss[0.9] Coverage[0.9]
0 NaN 2023.726237 1697.030762 31644.0 659.250000 42.371302 0.834405 0.053232 7.449056 1263.126416 0.000000 1697.030853 0.812500 1766.884937 1.000000
1 NaN 170014.625000 18240.031250 124149.0 2586.437500 165.107988 2.301528 0.141956 8.154324 2817.462842 0.041667 18240.031128 0.979167 9812.729199 1.000000
2 NaN 36724.294271 6477.572266 65030.0 1354.791667 78.889053 1.710623 0.094186 11.529441 3935.374902 0.000000 6477.572449 0.229167 2387.036133 0.854167
3 NaN 202065.791667 17380.332031 235783.0 4912.145833 258.982249 1.398128 0.071996 8.154208 10505.408350 0.000000 17380.332275 0.479167 9767.824316 1.000000
4 NaN 70907.125000 9372.942383 131088.0 2731.000000 200.494083 0.973942 0.066239 7.347368 5552.993652 0.000000 9372.942139 0.833333 8588.804102 1.000000
In [30]:
item_metrics.plot(x='MSIS', y='MASE', kind='scatter')
plt.grid(which="both")
plt.show()
../../_images/examples_basic_forecasting_tutorial_tutorial_46_0.png

Create your own forecast model

For creating your own forecast model you need to:

  • Define the training and prediction network
  • Define a new estimator that specifies any data processing and uses the networks

The training and prediction networks can be arbitrarily complex but they should follow some basic rules:

  • Both should have a hybrid_forward method that defines what should happen when the network is called
  • The trainng network’s hybrid_forward should return a loss based on the prediction and the true values
  • The prediction network’s hybrid_forward should return the predictions

For example, we can create a simple training network that defines a neural network which takes as an input the past values of the time series and outputs a future predicted window of length prediction_length. It uses the L1 loss in the hybrid_forward method to evaluate the error among the predictions and the true values of the time series. The corresponding prediction network should be identical to the training network in terms of architecture (we achieve this by inheriting the training network class), and its hybrid_forward method outputs directly the predictions.

Note that this simple model does only point forecasts by construction, i.e., we train it to outputs directly the future values of the time series and not any probabilistic view of the future (to achieve this we should train a network to learn a probability distribution and then sample from it to create sample paths).

In [31]:
class MyTrainNetwork(gluon.HybridBlock):
    def __init__(self, prediction_length, **kwargs):
        super().__init__(**kwargs)
        self.prediction_length = prediction_length

        with self.name_scope():
            # Set up a 3 layer neural network that directly predicts the target values
            self.nn = mx.gluon.nn.HybridSequential()
            self.nn.add(mx.gluon.nn.Dense(units=40, activation='relu'))
            self.nn.add(mx.gluon.nn.Dense(units=40, activation='relu'))
            self.nn.add(mx.gluon.nn.Dense(units=self.prediction_length, activation='softrelu'))

    def hybrid_forward(self, F, past_target, future_target):
        prediction = self.nn(past_target)
        # calculate L1 loss with the future_target to learn the median
        return (prediction - future_target).abs().mean(axis=-1)


class MyPredNetwork(MyTrainNetwork):
    # The prediction network only receives past_target and returns predictions
    def hybrid_forward(self, F, past_target):
        prediction = self.nn(past_target)
        return prediction.expand_dims(axis=1)

Now, we need to construct the estimator which should also follow some rules:

  • It should include a create_transformation method that defines all the possible feature transformations and how the data is split during training
  • It should include a create_training_network method that returns the training network configured with any necessary hyperparameters
  • It should include a create_predictor method that creates the prediction network, and returns a Predictor object

A Predictor defines the predict method of a given predictor. Roughly, this method takes the test dataset, it passes it through the prediction network and yields the predictions. You can think of the Predictor object as a wrapper of the prediction network that defines its predict method.

Earlier, we used the make_evaluation_predictions to evaluate our predictor. Internally, the make_evaluation_predictions function invokes the predict method of the predictor to get the forecasts.

In [32]:
from gluonts.model.estimator import GluonEstimator
from gluonts.model.predictor import Predictor, RepresentableBlockPredictor
from gluonts.core.component import validated
from gluonts.support.util import copy_parameters
from gluonts.transform import ExpectedNumInstanceSampler, Transformation, InstanceSplitter, FieldName
from mxnet.gluon import HybridBlock
In [33]:
class MyEstimator(GluonEstimator):
    @validated()
    def __init__(
        self,
        freq: str,
        context_length: int,
        prediction_length: int,
        trainer: Trainer = Trainer()
    ) -> None:
        super().__init__(trainer=trainer)
        self.context_length = context_length
        self.prediction_length = prediction_length
        self.freq = freq


    def create_transformation(self):
        # Feature transformation that the model uses for input.
        # Here we use a transformation that randomly select training samples from all time series.
        return InstanceSplitter(
                    target_field=FieldName.TARGET,
                    is_pad_field=FieldName.IS_PAD,
                    start_field=FieldName.START,
                    forecast_start_field=FieldName.FORECAST_START,
                    train_sampler=ExpectedNumInstanceSampler(num_instances=1),
                    past_length=self.context_length,
                    future_length=self.prediction_length,
                )

    def create_training_network(self) -> MyTrainNetwork:
        return MyTrainNetwork(
            prediction_length=self.prediction_length
        )

    def create_predictor(
        self, transformation: Transformation, trained_network: HybridBlock
    ) -> Predictor:
        prediction_network = MyPredNetwork(
            prediction_length=self.prediction_length
        )

        copy_parameters(trained_network, prediction_network)

        return RepresentableBlockPredictor(
            input_transform=transformation,
            prediction_net=prediction_network,
            batch_size=self.trainer.batch_size,
            freq=self.freq,
            prediction_length=self.prediction_length,
            ctx=self.trainer.ctx,
        )

Now, we can repeat the same pipeline as in the case we had a pre-built model: train the predictor, create the forecasts and evaluate the results.

In [34]:
estimator = MyEstimator(
    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
                   )
)
In [35]:
predictor = estimator.train(dataset.train)
INFO:root:Start model training
INFO:root:Number of parameters in MyTrainNetwork: 128
INFO:root:Epoch[0] Learning rate is 0.001
100%|██████████| 100/100 [00:00<00:00, 186.96it/s, avg_epoch_loss=2.09e+3]
INFO:root:Epoch[0] Elapsed time 0.536 seconds
INFO:root:Epoch[0] Evaluation metric 'epoch_loss'=2086.043991
INFO:root:Epoch[1] Learning rate is 0.001
100%|██████████| 100/100 [00:00<00:00, 219.31it/s, avg_epoch_loss=1.03e+3]
INFO:root:Epoch[1] Elapsed time 0.457 seconds
INFO:root:Epoch[1] Evaluation metric 'epoch_loss'=1034.880341
INFO:root:Epoch[2] Learning rate is 0.001
100%|██████████| 100/100 [00:00<00:00, 224.02it/s, avg_epoch_loss=586]
INFO:root:Epoch[2] Elapsed time 0.447 seconds
INFO:root:Epoch[2] Evaluation metric 'epoch_loss'=585.546419
INFO:root:Epoch[3] Learning rate is 0.001
100%|██████████| 100/100 [00:00<00:00, 218.54it/s, avg_epoch_loss=616]
INFO:root:Epoch[3] Elapsed time 0.459 seconds
INFO:root:Epoch[3] Evaluation metric 'epoch_loss'=616.042674
INFO:root:Epoch[4] Learning rate is 0.001
100%|██████████| 100/100 [00:00<00:00, 216.28it/s, avg_epoch_loss=473]
INFO:root:Epoch[4] Elapsed time 0.464 seconds
INFO:root:Epoch[4] Evaluation metric 'epoch_loss'=473.012655
INFO:root:Loading parameters from best epoch (4)
INFO:root:Final loss: 473.0126550102234 (occurred at epoch 4)
INFO:root:End model training
In [36]:
forecast_it, ts_it = make_evaluation_predictions(
    dataset=dataset.test,
    predictor=predictor,
    num_eval_samples=100
)
In [37]:
forecasts = list(forecast_it)
tss = list(ts_it)
In [38]:
plot_prob_forecasts(tss[0], forecasts[0])
../../_images/examples_basic_forecasting_tutorial_tutorial_57_0.png

Observe that we cannot actually see any prediction intervals in the predictions. This is expected since the model that we defined does not do probabilistic forecasting but it just gives point estimates. By requiring 100 sample paths (defined in make_evaluation_predictions) in such a network, we get 100 times the same output.

In [39]:
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 [00:01<00:00, 226.24it/s]
In [40]:
print(json.dumps(agg_metrics, indent=4))
{
    "MSE": 7355475.08461168,
    "abs_error": 9318348.60062027,
    "abs_target_sum": 145558863.59960938,
    "abs_target_mean": 7324.822041043146,
    "seasonal_error": 336.9046924038305,
    "MASE": 4.340838009582843,
    "sMAPE": 0.2258314961191691,
    "MSIS": 173.63352012595402,
    "QuantileLoss[0.1]": 10321315.793073274,
    "Coverage[0.1]": 0.46779388083735907,
    "QuantileLoss[0.5]": 9318348.52790451,
    "Coverage[0.5]": 0.46779388083735907,
    "QuantileLoss[0.9]": 8315381.26273575,
    "Coverage[0.9]": 0.46779388083735907,
    "RMSE": 2712.0979120621146,
    "NRMSE": 0.3702612700848467,
    "ND": 0.06401773392689002,
    "wQuantileLoss[0.1]": 0.07090819162661402,
    "wQuantileLoss[0.5]": 0.06401773342732746,
    "wQuantileLoss[0.9]": 0.057127275228040904,
    "mean_wQuantileLoss": 0.06401773342732746,
    "MAE_Coverage": 0.27740203972088034
}
In [41]:
item_metrics.head(10)
Out[41]:
item_id MSE abs_error abs_target_sum abs_target_mean seasonal_error MASE sMAPE MSIS QuantileLoss[0.1] Coverage[0.1] QuantileLoss[0.5] Coverage[0.5] QuantileLoss[0.9] Coverage[0.9]
0 NaN 1.982680e+03 1598.827026 31644.0 659.250000 42.371302 0.786119 0.054123 31.444771 1647.838452 0.520833 1598.827026 0.520833 1549.815601 0.520833
1 NaN 1.432031e+05 15812.218750 124149.0 2586.437500 165.107988 1.995186 0.123362 79.807467 28133.833057 0.958333 15812.218994 0.958333 3490.604932 0.958333
2 NaN 6.666798e+04 9389.882812 65030.0 1354.791667 78.889053 2.479717 0.144288 99.188696 2852.362427 0.229167 9389.882935 0.229167 15927.403442 0.229167
3 NaN 1.418979e+05 14928.930664 235783.0 4912.145833 258.982249 1.200929 0.066899 48.037177 8052.141260 0.250000 14928.930908 0.250000 21805.720557 0.250000
4 NaN 1.401335e+05 14748.746094 131088.0 2731.000000 200.494083 1.532542 0.112007 61.301665 15799.684595 0.583333 14748.745239 0.583333 13697.805884 0.583333
5 NaN 1.332025e+05 13463.467773 303379.0 6320.395833 212.875740 1.317618 0.046059 52.704725 12377.652148 0.458333 13463.467773 0.458333 14549.283398 0.458333
6 NaN 1.588192e+07 146165.593750 1985325.0 41360.937500 1947.687870 1.563452 0.075520 62.538078 68348.130469 0.291667 146165.589844 0.291667 223983.049219 0.291667
7 NaN 5.094711e+06 88214.289062 1540706.0 32098.041667 1624.044379 1.131618 0.060099 45.264712 44521.554297 0.270833 88214.287109 0.270833 131907.019922 0.270833
8 NaN 6.782401e+06 102576.687500 1640860.0 34184.583333 1850.988166 1.154526 0.059383 46.181048 165195.770703 0.854167 102576.681641 0.854167 39957.592578 0.854167
9 NaN 1.857677e+03 1634.504883 21408.0 446.000000 10.526627 3.234862 0.077743 129.394475 988.496429 0.458333 1634.504852 0.458333 2280.513275 0.458333
In [42]:
item_metrics.plot(x='MSIS', y='MASE', kind='scatter')
plt.grid(which="both")
plt.show()
../../_images/examples_basic_forecasting_tutorial_tutorial_62_0.png