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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', 'exchange_rate_nips', 'electricity_nips', 'traffic_nips', 'solar_nips', 'wiki-rolling_nips', 'taxi_30min', '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.

In [4]:
dataset = get_dataset("m4_hourly", regenerate=True)
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 contains 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
/var/lib/jenkins/workspace/workspace/gluon-ts-gpu-py3/conda/gpu/py3/lib/python3.6/site-packages/ipykernel_launcher.py:2: DeprecationWarning: gluonts.trainer is deprecated. Use gluonts.mx.trainer instead.

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 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.

In [13]:
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, 135.24it/s, epoch=1/5, avg_epoch_loss=5.49]
100%|██████████| 100/100 [00:00<00:00, 130.60it/s, epoch=2/5, avg_epoch_loss=4.96]
100%|██████████| 100/100 [00:00<00:00, 138.61it/s, epoch=3/5, avg_epoch_loss=4.74]
100%|██████████| 100/100 [00:00<00:00, 148.84it/s, epoch=4/5, avg_epoch_loss=4.63]
100%|██████████| 100/100 [00:00<00:00, 146.31it/s, epoch=5/5, avg_epoch_loss=4.79]

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_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:
 [666.5513  590.41876 524.1139  511.3859  584.1948  581.6775  480.09094
 514.0254  523.0961  565.44525 508.04153 680.1175  722.0301  892.41205
 844.0529  908.2834  840.58624 881.22955 855.60974 856.68524 852.1015
 811.8563  775.5197  742.9308  617.4853  568.00256 565.5584  493.7319
 501.26712 538.0488  466.72763 474.52353 516.41223 510.40564 591.6196
 689.69946 755.5346  913.06866 867.9945  829.79486 885.0982  900.13983
 939.3446  804.88635 822.67596 820.78986 725.59546 774.0968 ]
0.5-quantile (median) of the future window:
 [679.72925 574.8424  543.5332  517.2768  568.8477  587.0067  490.69595
 520.70856 520.577   548.95593 502.48468 690.5282  747.1778  899.25104
 840.8809  916.9106  856.9634  891.3923  852.7305  859.80634 866.1713
 791.73425 765.3167  732.37744 620.6388  571.9892  571.505   502.44003
 510.7481  558.8913  458.3605  467.92773 514.9628  507.7992  586.7277
 672.06683 744.31665 885.4744  871.7752  851.55023 884.22943 902.2909
 938.2722  770.57043 804.908   835.9331  742.48584 781.6003 ]

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 [00:00<00:00, 3208.88it/s]

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

In [28]:
print(json.dumps(agg_metrics, indent=4))
{
    "MSE": 10672067.402448904,
    "abs_error": 10191933.334890366,
    "abs_target_sum": 145558863.59960938,
    "abs_target_mean": 7324.822041043146,
    "seasonal_error": 336.9046924038305,
    "MASE": 3.5314557137716376,
    "MAPE": 0.2551973010752877,
    "sMAPE": 0.18779968819859505,
    "OWA": NaN,
    "MSIS": 62.07984730893943,
    "QuantileLoss[0.1]": 4669320.322200584,
    "Coverage[0.1]": 0.11820652173913043,
    "QuantileLoss[0.5]": 10191933.19418192,
    "Coverage[0.5]": 0.5558071658615137,
    "QuantileLoss[0.9]": 7140841.54174671,
    "Coverage[0.9]": 0.8861714975845411,
    "RMSE": 3266.8130345106842,
    "NRMSE": 0.44599213690186107,
    "ND": 0.07001932471062323,
    "wQuantileLoss[0.1]": 0.0320785708731867,
    "wQuantileLoss[0.5]": 0.07001932374394595,
    "wQuantileLoss[0.9]": 0.049058101754552816,
    "mean_wQuantileLoss": 0.050385332123895156,
    "MAE_Coverage": 0.029280730005367694
}

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 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 3293.359049 2093.649414 31644.0 659.250000 42.371302 1.029416 0.067667 0.064355 NaN 13.758485 946.534595 0.020833 2093.649567 0.791667 1493.040466 1.000000
1 1.0 190619.020833 19443.568359 124149.0 2586.437500 165.107988 2.453390 0.165516 0.150670 NaN 13.689049 3788.782544 0.250000 19443.567627 0.958333 8718.069971 1.000000
2 2.0 31945.205729 6701.100586 65030.0 1354.791667 78.889053 1.769653 0.094789 0.100001 NaN 13.076949 3338.587573 0.000000 6701.100586 0.166667 2366.554858 0.791667
3 3.0 216843.083333 18185.765625 235783.0 4912.145833 258.982249 1.462919 0.078546 0.077411 NaN 14.393600 9636.913428 0.083333 18185.766602 0.437500 8100.886426 0.979167
4 4.0 91357.750000 10644.054688 131088.0 2731.000000 200.494083 1.106023 0.081128 0.076562 NaN 13.098720 4268.313916 0.083333 10644.055054 0.729167 7297.340918 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 training 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
from gluonts.dataset.field_names import 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)
  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, 146.94it/s, epoch=1/5, avg_epoch_loss=2.46e+3]
100%|██████████| 100/100 [00:00<00:00, 164.98it/s, epoch=2/5, avg_epoch_loss=1.46e+3]
100%|██████████| 100/100 [00:00<00:00, 159.64it/s, epoch=3/5, avg_epoch_loss=1.52e+3]
100%|██████████| 100/100 [00:00<00:00, 162.49it/s, epoch=4/5, avg_epoch_loss=1.27e+3]
100%|██████████| 100/100 [00:00<00:00, 165.63it/s, epoch=5/5, avg_epoch_loss=1.22e+3]
In [36]:
forecast_it, ts_it = make_evaluation_predictions(
    dataset=dataset.test,
    predictor=predictor,
    num_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 [00:00<00:00, 5010.77it/s]
In [40]:
print(json.dumps(agg_metrics, indent=4))
{
    "MSE": 84415284.47261478,
    "abs_error": 27677848.865325928,
    "abs_target_sum": 145558863.59960938,
    "abs_target_mean": 7324.822041043146,
    "seasonal_error": 336.9046924038305,
    "MASE": 14.501348258411864,
    "MAPE": 0.697928451068643,
    "sMAPE": 0.31331464812117377,
    "OWA": NaN,
    "MSIS": 580.0539294491899,
    "QuantileLoss[0.1]": 44986401.38542252,
    "Coverage[0.1]": 0.7438607085346217,
    "QuantileLoss[0.5]": 27677848.740650177,
    "Coverage[0.5]": 0.7438607085346217,
    "QuantileLoss[0.9]": 10369296.09587784,
    "Coverage[0.9]": 0.7438607085346217,
    "RMSE": 9187.779082706265,
    "NRMSE": 1.2543347853674014,
    "ND": 0.19014883862696083,
    "wQuantileLoss[0.1]": 0.309059855737588,
    "wQuantileLoss[0.5]": 0.19014883777042935,
    "wQuantileLoss[0.9]": 0.07123781980327075,
    "mean_wQuantileLoss": 0.19014883777042935,
    "MAE_Coverage": 0.34795356951154055
}
In [41]:
item_metrics.head(10)
Out[41]:
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 2.177683e+04 5843.476562 31644.0 659.250000 42.371302 2.873150 0.197772 0.174579 NaN 114.925990 9443.185504 0.791667 5843.476349 0.791667 2243.767194 0.791667
1 1.0 7.930107e+05 37184.296875 124149.0 2586.437500 165.107988 4.691916 0.328085 0.267688 NaN 187.676634 66167.074146 0.916667 37184.295532 0.916667 8201.516919 0.916667
2 2.0 6.388186e+04 9609.374023 65030.0 1354.791667 78.889053 2.537682 0.153313 0.150272 NaN 101.507263 8909.700696 0.458333 9609.374084 0.458333 10309.047473 0.458333
3 3.0 1.006690e+06 40632.660156 235783.0 4912.145833 258.982249 3.268617 0.178525 0.161573 NaN 130.744673 62882.628760 0.770833 40632.659424 0.770833 18382.690088 0.770833
4 4.0 3.566465e+05 21656.921875 131088.0 2731.000000 200.494083 2.250370 0.183116 0.160000 NaN 90.014801 33673.493359 0.729167 21656.921875 0.729167 9640.350391 0.729167
5 5.0 1.755999e+06 52445.710938 303379.0 6320.395833 212.875740 5.132661 0.181342 0.160801 NaN 205.306441 88598.513770 0.812500 52445.713379 0.812500 16292.912988 0.812500
6 6.0 5.884259e+07 286851.718750 1985325.0 41360.937500 1947.687870 3.068293 0.153507 0.139263 NaN 122.731721 421069.880859 0.645833 286851.716797 0.645833 152633.552734 0.645833
7 7.0 3.465019e+07 239306.796875 1540706.0 32098.041667 1624.044379 3.069841 0.162561 0.149701 NaN 122.793648 351118.396094 0.729167 239306.792969 0.729167 127495.189844 0.729167
8 8.0 7.525102e+07 354413.562500 1640860.0 34184.583333 1850.988166 3.989013 0.223141 0.193621 NaN 159.560526 619663.202734 0.854167 354413.560547 0.854167 89163.918359 0.854167
9 9.0 6.885606e+03 3194.729492 21408.0 446.000000 10.526627 6.322715 0.151074 0.137751 NaN 252.908618 4997.515082 0.708333 3194.729706 0.708333 1391.944330 0.708333
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