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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
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, 136.26it/s, epoch=1/5, avg_epoch_loss=5.32]
100%|██████████| 100/100 [00:00<00:00, 147.17it/s, epoch=2/5, avg_epoch_loss=5.01]
100%|██████████| 100/100 [00:00<00:00, 142.43it/s, epoch=3/5, avg_epoch_loss=4.73]
100%|██████████| 100/100 [00:00<00:00, 150.42it/s, epoch=4/5, avg_epoch_loss=4.74]
100%|██████████| 100/100 [00:00<00:00, 134.21it/s, epoch=5/5, avg_epoch_loss=4.67]

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:
 [684.8325  635.53595 494.76782 561.3388  479.0061  442.5     454.8131
 482.5905  549.34937 586.6445  549.4081  635.369   775.8512  838.21765
 890.62    871.81555 897.04474 898.7128  840.22345 830.84814 784.7109
 795.3854  720.64703 706.86804 637.3232  610.79443 537.41724 456.40167
 486.57446 542.0178  485.59473 479.56458 471.29733 539.1186  581.99976
 686.7993  753.6526  814.9157  860.84985 810.2138  898.1918  885.90405
 840.5069  866.22546 862.02814 771.99744 722.235   731.01263]
0.5-quantile (median) of the future window:
 [698.55566 634.1172  514.9095  567.0837  472.5158  450.6757  465.07016
 483.41937 560.4748  569.3977  549.1683  629.4425  792.2873  848.0067
 891.28174 891.1728  880.39716 886.77704 833.47064 830.9956  787.23083
 792.1454  721.2762  696.585   630.2839  612.7456  542.78705 457.29886
 488.00967 530.6522  467.966   472.357   467.8788  543.5559  574.86
 679.9731  738.013   829.455   861.77466 826.6015  874.8204  904.0215
 857.32635 840.46326 826.688   771.4469  735.8817  739.9135 ]

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 [00:02<00:00, 166.25it/s]

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

In [28]:
print(json.dumps(agg_metrics, indent=4))
{
    "MSE": 5703569.059183516,
    "abs_error": 8330231.667835236,
    "abs_target_sum": 145558863.59960938,
    "abs_target_mean": 7324.822041043146,
    "seasonal_error": 336.9046924038305,
    "MASE": 3.1608160011760544,
    "MAPE": 0.24568924836225695,
    "sMAPE": 0.1880313526752749,
    "OWA": NaN,
    "MSIS": 34.444366446504866,
    "QuantileLoss[0.1]": 4630027.635045434,
    "Coverage[0.1]": 0.10381441223832527,
    "QuantileLoss[0.5]": 8330231.62656641,
    "Coverage[0.5]": 0.4696557971014493,
    "QuantileLoss[0.9]": 6350158.670071601,
    "Coverage[0.9]": 0.8694142512077294,
    "RMSE": 2388.2146174880336,
    "NRMSE": 0.3260440464090677,
    "ND": 0.05722929859324342,
    "wQuantileLoss[0.1]": 0.03180862724911971,
    "wQuantileLoss[0.5]": 0.05722929830972358,
    "wQuantileLoss[0.9]": 0.04362605280801768,
    "mean_wQuantileLoss": 0.04422132612228699,
    "MAE_Coverage": 0.021581454643048864
}

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 2012.151693 1720.522949 31644.0 659.250000 42.371302 0.845955 0.054879 0.053115 NaN 5.511783 907.694110 0.000000 1720.522919 0.604167 1334.303638 1.000000
1 1.0 155022.291667 16870.503906 124149.0 2586.437500 165.107988 2.128721 0.141732 0.130178 NaN 15.767573 5077.391846 0.354167 16870.504272 1.000000 8028.832861 1.000000
2 2.0 33968.338542 6912.018555 65030.0 1354.791667 78.889053 1.825353 0.095767 0.102599 NaN 14.430417 3366.728528 0.000000 6912.018311 0.125000 2503.392004 0.770833
3 3.0 158621.031250 16604.554688 235783.0 4912.145833 258.982249 1.335722 0.069748 0.070132 NaN 6.739677 8536.901514 0.020833 16604.554199 0.375000 6854.429395 0.958333
4 4.0 68976.390625 9868.931641 131088.0 2731.000000 200.494083 1.025480 0.074224 0.071154 NaN 5.424379 3801.919519 0.000000 9868.932007 0.729167 6638.617725 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, 146.99it/s, epoch=1/5, avg_epoch_loss=2.78e+3]
100%|██████████| 100/100 [00:00<00:00, 162.19it/s, epoch=2/5, avg_epoch_loss=1.29e+3]
100%|██████████| 100/100 [00:00<00:00, 157.40it/s, epoch=3/5, avg_epoch_loss=1.39e+3]
100%|██████████| 100/100 [00:00<00:00, 162.52it/s, epoch=4/5, avg_epoch_loss=1e+3]
100%|██████████| 100/100 [00:00<00:00, 159.16it/s, epoch=5/5, avg_epoch_loss=1.08e+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 [00:02<00:00, 174.66it/s]
In [40]:
print(json.dumps(agg_metrics, indent=4))
{
    "MSE": 101219771.06286582,
    "abs_error": 30729857.90753174,
    "abs_target_sum": 145558863.59960938,
    "abs_target_mean": 7324.822041043146,
    "seasonal_error": 336.9046924038305,
    "MASE": 16.046761943063274,
    "MAPE": 0.6108468112441469,
    "sMAPE": 0.35984226589824503,
    "OWA": NaN,
    "MSIS": 641.8704771871132,
    "QuantileLoss[0.1]": 26527170.417883016,
    "Coverage[0.1]": 0.46115136876006446,
    "QuantileLoss[0.5]": 30729857.861807346,
    "Coverage[0.5]": 0.46115136876006446,
    "QuantileLoss[0.9]": 34932545.305731684,
    "Coverage[0.9]": 0.46115136876006446,
    "RMSE": 10060.803698654787,
    "NRMSE": 1.3735219288989038,
    "ND": 0.21111636315092944,
    "wQuantileLoss[0.1]": 0.18224359384153782,
    "wQuantileLoss[0.5]": 0.21111636283679955,
    "wQuantileLoss[0.9]": 0.2399891318320613,
    "mean_wQuantileLoss": 0.21111636283679955,
    "MAE_Coverage": 0.27961621041331186
}
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 2.563362e+04 6619.009766 31644.0 659.250000 42.371302 3.254468 0.219208 0.211284 NaN 130.178704 6589.444031 0.520833 6619.009705 0.520833 6648.575378 0.520833
1 1.0 5.052959e+05 28933.130859 124149.0 2586.437500 165.107988 3.650784 0.273087 0.233399 NaN 146.031352 39125.224805 0.583333 28933.129883 0.583333 18741.034961 0.583333
2 2.0 2.160044e+05 19274.253906 65030.0 1354.791667 78.889053 5.090021 0.284116 0.320057 NaN 203.600841 9292.688464 0.291667 19274.252380 0.291667 29255.816296 0.291667
3 3.0 1.849755e+06 57620.875000 235783.0 4912.145833 258.982249 4.635201 0.246426 0.257635 NaN 185.408058 47890.190186 0.520833 57620.876709 0.520833 67351.563232 0.520833
4 4.0 4.965492e+05 27546.667969 131088.0 2731.000000 200.494083 2.862373 0.210184 0.220728 NaN 114.494937 17493.333740 0.354167 27546.668701 0.354167 37600.003662 0.354167
5 5.0 2.201532e+06 59633.027344 303379.0 6320.395833 212.875740 5.836056 0.194149 0.206042 NaN 233.442231 51588.610986 0.500000 59633.027588 0.500000 67677.444189 0.500000
6 6.0 1.260900e+08 464458.406250 1985325.0 41360.937500 1947.687870 4.968053 0.235827 0.255963 NaN 198.722122 285802.652734 0.333333 464458.404297 0.333333 643114.155859 0.333333
7 7.0 6.036650e+07 309800.593750 1540706.0 32098.041667 1624.044379 3.974140 0.195329 0.205663 NaN 158.965573 203578.134766 0.395833 309800.580078 0.395833 416023.025391 0.395833
8 8.0 6.374654e+07 336266.875000 1640860.0 34184.583333 1850.988166 3.784768 0.214308 0.205253 NaN 151.390701 362652.319141 0.541667 336266.876953 0.541667 309881.434766 0.541667
9 9.0 1.240940e+04 4614.721191 21408.0 446.000000 10.526627 9.133032 0.214312 0.232372 NaN 365.321278 2977.029083 0.354167 4614.721344 0.354167 6252.413605 0.354167
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