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pytorch-transformer-ts/tft/tft.ipynb
T
Kashif Rasul 5cc02e42b7 train with cat features
2022-03-30 23:38:06 +02:00

392 KiB
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In [1]:
%matplotlib inline
from matplotlib import pyplot as plt
import matplotlib.dates as mdates

from itertools import islice
In [2]:
from gluonts.evaluation import make_evaluation_predictions, Evaluator
from gluonts.dataset.repository.datasets import get_dataset

from estimator import TFTEstimator
/home/kashif/.env/pytorch/lib/python3.8/site-packages/xgboost/compat.py:36: FutureWarning: pandas.Int64Index is deprecated and will be removed from pandas in a future version. Use pandas.Index with the appropriate dtype instead.
  from pandas import MultiIndex, Int64Index
In [3]:
dataset = get_dataset("electricity")
In [14]:
estimator = TFTEstimator(
    freq=dataset.metadata.freq,
    prediction_length=dataset.metadata.prediction_length,
    num_feat_static_cat=1,
    cardinality=[321],

    batch_size=128,
    num_batches_per_epoch=100,
    trainer_kwargs=dict(max_epochs=20, accelerator='gpu', gpus=1),
)
In [ ]:
predictor = estimator.train(
    training_data=dataset.train,
    num_workers=16,
    shuffle_buffer_length=1024
)
GPU available: True, used: True
TPU available: False, using: 0 TPU cores
IPU available: False, using: 0 IPUs
/home/kashif/.env/pytorch/lib/python3.8/site-packages/pytorch_lightning/trainer/configuration_validator.py:122: UserWarning: You defined a `validation_step` but have no `val_dataloader`. Skipping val loop.
  rank_zero_warn("You defined a `validation_step` but have no `val_dataloader`. Skipping val loop.")
LOCAL_RANK: 0 - CUDA_VISIBLE_DEVICES: [0]
/home/kashif/gluon-ts-PR/src/gluonts/transform/feature.py:343: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  self._freq_base = start.freq.base
/home/kashif/gluon-ts-PR/src/gluonts/transform/feature.py:343: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  self._freq_base = start.freq.base
/home/kashif/gluon-ts-PR/src/gluonts/transform/feature.py:343: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  self._freq_base = start.freq.base
/home/kashif/gluon-ts-PR/src/gluonts/transform/feature.py:343: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  self._freq_base = start.freq.base
/home/kashif/gluon-ts-PR/src/gluonts/transform/feature.py:343: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  self._freq_base = start.freq.base
/home/kashif/gluon-ts-PR/src/gluonts/transform/feature.py:343: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  self._freq_base = start.freq.base
/home/kashif/gluon-ts-PR/src/gluonts/transform/feature.py:343: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  self._freq_base = start.freq.base
/home/kashif/gluon-ts-PR/src/gluonts/transform/feature.py:343: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  self._freq_base = start.freq.base
/home/kashif/gluon-ts-PR/src/gluonts/transform/feature.py:343: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  self._freq_base = start.freq.base
/home/kashif/gluon-ts-PR/src/gluonts/transform/feature.py:343: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  self._freq_base = start.freq.base
/home/kashif/gluon-ts-PR/src/gluonts/transform/split.py:36: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  return _shift_timestamp_helper(ts, ts.freq, offset)
/home/kashif/gluon-ts-PR/src/gluonts/transform/split.py:36: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  return _shift_timestamp_helper(ts, ts.freq, offset)
/home/kashif/gluon-ts-PR/src/gluonts/transform/split.py:36: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  return _shift_timestamp_helper(ts, ts.freq, offset)
/home/kashif/gluon-ts-PR/src/gluonts/transform/split.py:36: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  return _shift_timestamp_helper(ts, ts.freq, offset)
/home/kashif/gluon-ts-PR/src/gluonts/transform/split.py:36: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  return _shift_timestamp_helper(ts, ts.freq, offset)
/home/kashif/gluon-ts-PR/src/gluonts/transform/feature.py:343: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  self._freq_base = start.freq.base
/home/kashif/gluon-ts-PR/src/gluonts/transform/split.py:36: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  return _shift_timestamp_helper(ts, ts.freq, offset)
/home/kashif/gluon-ts-PR/src/gluonts/transform/split.py:36: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  return _shift_timestamp_helper(ts, ts.freq, offset)
/home/kashif/gluon-ts-PR/src/gluonts/transform/feature.py:343: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  self._freq_base = start.freq.base
/home/kashif/gluon-ts-PR/src/gluonts/transform/split.py:36: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  return _shift_timestamp_helper(ts, ts.freq, offset)
/home/kashif/gluon-ts-PR/src/gluonts/transform/split.py:36: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  return _shift_timestamp_helper(ts, ts.freq, offset)
/home/kashif/gluon-ts-PR/src/gluonts/transform/split.py:36: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  return _shift_timestamp_helper(ts, ts.freq, offset)
/home/kashif/gluon-ts-PR/src/gluonts/transform/feature.py:343: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  self._freq_base = start.freq.base
/home/kashif/gluon-ts-PR/src/gluonts/transform/split.py:36: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  return _shift_timestamp_helper(ts, ts.freq, offset)
/home/kashif/gluon-ts-PR/src/gluonts/transform/split.py:36: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  return _shift_timestamp_helper(ts, ts.freq, offset)
/home/kashif/gluon-ts-PR/src/gluonts/transform/feature.py:384: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  ..., i0 : i0 + length * start.freq.n : start.freq.n
/home/kashif/gluon-ts-PR/src/gluonts/transform/feature.py:384: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  ..., i0 : i0 + length * start.freq.n : start.freq.n
/home/kashif/gluon-ts-PR/src/gluonts/transform/feature.py:343: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  self._freq_base = start.freq.base
/home/kashif/gluon-ts-PR/src/gluonts/transform/feature.py:384: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  ..., i0 : i0 + length * start.freq.n : start.freq.n
/home/kashif/gluon-ts-PR/src/gluonts/transform/split.py:36: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  return _shift_timestamp_helper(ts, ts.freq, offset)
/home/kashif/gluon-ts-PR/src/gluonts/transform/split.py:36: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  return _shift_timestamp_helper(ts, ts.freq, offset)
/home/kashif/gluon-ts-PR/src/gluonts/transform/feature.py:384: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  ..., i0 : i0 + length * start.freq.n : start.freq.n
/home/kashif/gluon-ts-PR/src/gluonts/transform/feature.py:384: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  ..., i0 : i0 + length * start.freq.n : start.freq.n
/home/kashif/gluon-ts-PR/src/gluonts/transform/feature.py:340: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  self._freq_base is None or self._freq_base == start.freq.base
/home/kashif/gluon-ts-PR/src/gluonts/transform/feature.py:384: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  ..., i0 : i0 + length * start.freq.n : start.freq.n
/home/kashif/gluon-ts-PR/src/gluonts/transform/feature.py:384: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  ..., i0 : i0 + length * start.freq.n : start.freq.n
/home/kashif/gluon-ts-PR/src/gluonts/transform/feature.py:384: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  ..., i0 : i0 + length * start.freq.n : start.freq.n
/home/kashif/gluon-ts-PR/src/gluonts/transform/feature.py:340: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  self._freq_base is None or self._freq_base == start.freq.base
/home/kashif/gluon-ts-PR/src/gluonts/transform/feature.py:340: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  self._freq_base is None or self._freq_base == start.freq.base
/home/kashif/gluon-ts-PR/src/gluonts/transform/feature.py:340: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  self._freq_base is None or self._freq_base == start.freq.base

/home/kashif/gluon-ts-PR/src/gluonts/transform/feature.py:384: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  ..., i0 : i0 + length * start.freq.n : start.freq.n
/home/kashif/gluon-ts-PR/src/gluonts/transform/feature.py:340: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  self._freq_base is None or self._freq_base == start.freq.base
/home/kashif/gluon-ts-PR/src/gluonts/transform/feature.py:384: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  ..., i0 : i0 + length * start.freq.n : start.freq.n
/home/kashif/gluon-ts-PR/src/gluonts/transform/feature.py:384: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  ..., i0 : i0 + length * start.freq.n : start.freq.n
/home/kashif/gluon-ts-PR/src/gluonts/transform/feature.py:384: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  ..., i0 : i0 + length * start.freq.n : start.freq.n
/home/kashif/gluon-ts-PR/src/gluonts/transform/feature.py:340: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  self._freq_base is None or self._freq_base == start.freq.base
/home/kashif/gluon-ts-PR/src/gluonts/transform/feature.py:384: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  ..., i0 : i0 + length * start.freq.n : start.freq.n
/home/kashif/gluon-ts-PR/src/gluonts/transform/feature.py:340: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  self._freq_base is None or self._freq_base == start.freq.base
/home/kashif/gluon-ts-PR/src/gluonts/transform/feature.py:384: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  ..., i0 : i0 + length * start.freq.n : start.freq.n
/home/kashif/gluon-ts-PR/src/gluonts/transform/feature.py:340: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  self._freq_base is None or self._freq_base == start.freq.base
/home/kashif/gluon-ts-PR/src/gluonts/transform/feature.py:340: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  self._freq_base is None or self._freq_base == start.freq.base
/home/kashif/gluon-ts-PR/src/gluonts/transform/feature.py:343: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  self._freq_base = start.freq.base
/home/kashif/gluon-ts-PR/src/gluonts/transform/feature.py:340: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  self._freq_base is None or self._freq_base == start.freq.base
/home/kashif/gluon-ts-PR/src/gluonts/transform/feature.py:340: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  self._freq_base is None or self._freq_base == start.freq.base
/home/kashif/gluon-ts-PR/src/gluonts/transform/feature.py:340: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  self._freq_base is None or self._freq_base == start.freq.base
/home/kashif/gluon-ts-PR/src/gluonts/transform/feature.py:340: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  self._freq_base is None or self._freq_base == start.freq.base
/home/kashif/gluon-ts-PR/src/gluonts/transform/split.py:36: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  return _shift_timestamp_helper(ts, ts.freq, offset)
/home/kashif/gluon-ts-PR/src/gluonts/transform/feature.py:340: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  self._freq_base is None or self._freq_base == start.freq.base
/home/kashif/gluon-ts-PR/src/gluonts/transform/feature.py:343: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  self._freq_base = start.freq.base
/home/kashif/gluon-ts-PR/src/gluonts/transform/split.py:36: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  return _shift_timestamp_helper(ts, ts.freq, offset)
/home/kashif/gluon-ts-PR/src/gluonts/transform/feature.py:384: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  ..., i0 : i0 + length * start.freq.n : start.freq.n
/home/kashif/gluon-ts-PR/src/gluonts/transform/feature.py:384: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  ..., i0 : i0 + length * start.freq.n : start.freq.n
/home/kashif/gluon-ts-PR/src/gluonts/transform/feature.py:340: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  self._freq_base is None or self._freq_base == start.freq.base
/home/kashif/gluon-ts-PR/src/gluonts/transform/feature.py:340: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  self._freq_base is None or self._freq_base == start.freq.base

  | Name  | Type                  | Params
------------------------------------------------
0 | model | TFTModel              | 104 K 
1 | loss  | NegativeLogLikelihood | 0     
------------------------------------------------
104 K     Trainable params
0         Non-trainable params
104 K     Total params
0.417     Total estimated model params size (MB)

Training: 0it [00:00, ?it/s]
In [6]:
forecast_it, ts_it = make_evaluation_predictions(
    dataset=dataset.test, 
    predictor=predictor
)
In [7]:
forecasts = list(forecast_it)
/home/kashif/gluon-ts-PR/src/gluonts/dataset/common.py:324: FutureWarning: The 'freq' argument in Timestamp is deprecated and will be removed in a future version.
  timestamp = pd.Timestamp(timestamp_input, freq=freq)
/home/kashif/gluon-ts-PR/src/gluonts/dataset/common.py:327: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  if isinstance(timestamp.freq, Tick):
/home/kashif/gluon-ts-PR/src/gluonts/dataset/common.py:329: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  timestamp.floor(timestamp.freq), timestamp.freq
/home/kashif/gluon-ts-PR/src/gluonts/dataset/common.py:328: FutureWarning: The 'freq' argument in Timestamp is deprecated and will be removed in a future version.
  return pd.Timestamp(
/home/kashif/gluon-ts-PR/src/gluonts/transform/feature.py:343: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  self._freq_base = start.freq.base
/home/kashif/gluon-ts-PR/src/gluonts/transform/split.py:36: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  return _shift_timestamp_helper(ts, ts.freq, offset)
/home/kashif/gluon-ts-PR/src/gluonts/transform/feature.py:384: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  ..., i0 : i0 + length * start.freq.n : start.freq.n
/home/kashif/gluon-ts-PR/src/gluonts/transform/feature.py:340: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  self._freq_base is None or self._freq_base == start.freq.base
In [8]:
tss = list(ts_it)
In [9]:
evaluator = Evaluator()
In [10]:
agg_metrics, ts_metrics = evaluator(iter(tss), iter(forecasts))
Running evaluation: 2247it [00:00, 3696.80it/s]/home/kashif/gluon-ts-PR/src/gluonts/evaluation/_base.py:306: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  date_before_forecast = forecast.index[0] - forecast.index[0].freq
/home/kashif/gluon-ts-PR/src/gluonts/evaluation/_base.py:306: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  date_before_forecast = forecast.index[0] - forecast.index[0].freq
/home/kashif/gluon-ts-PR/src/gluonts/evaluation/_base.py:306: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  date_before_forecast = forecast.index[0] - forecast.index[0].freq
/home/kashif/gluon-ts-PR/src/gluonts/evaluation/_base.py:306: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  date_before_forecast = forecast.index[0] - forecast.index[0].freq
/home/kashif/gluon-ts-PR/src/gluonts/evaluation/_base.py:306: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  date_before_forecast = forecast.index[0] - forecast.index[0].freq
/home/kashif/gluon-ts-PR/src/gluonts/evaluation/_base.py:306: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  date_before_forecast = forecast.index[0] - forecast.index[0].freq
/home/kashif/gluon-ts-PR/src/gluonts/evaluation/_base.py:306: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  date_before_forecast = forecast.index[0] - forecast.index[0].freq
/home/kashif/gluon-ts-PR/src/gluonts/evaluation/_base.py:306: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  date_before_forecast = forecast.index[0] - forecast.index[0].freq
/home/kashif/gluon-ts-PR/src/gluonts/evaluation/_base.py:306: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  date_before_forecast = forecast.index[0] - forecast.index[0].freq
/home/kashif/gluon-ts-PR/src/gluonts/evaluation/_base.py:306: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  date_before_forecast = forecast.index[0] - forecast.index[0].freq

/home/kashif/gluon-ts-PR/src/gluonts/evaluation/_base.py:306: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  date_before_forecast = forecast.index[0] - forecast.index[0].freq
/home/kashif/gluon-ts-PR/src/gluonts/evaluation/_base.py:306: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  date_before_forecast = forecast.index[0] - forecast.index[0].freq
/home/kashif/gluon-ts-PR/src/gluonts/evaluation/_base.py:306: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  date_before_forecast = forecast.index[0] - forecast.index[0].freq
/home/kashif/gluon-ts-PR/src/gluonts/evaluation/_base.py:306: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  date_before_forecast = forecast.index[0] - forecast.index[0].freq
/home/kashif/gluon-ts-PR/src/gluonts/evaluation/_base.py:306: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  date_before_forecast = forecast.index[0] - forecast.index[0].freq
/home/kashif/gluon-ts-PR/src/gluonts/evaluation/_base.py:306: FutureWarning: Timestamp.freq is deprecated and will be removed in a future version.
  date_before_forecast = forecast.index[0] - forecast.index[0].freq
/home/kashif/.env/pytorch/lib/python3.8/site-packages/pandas/core/construction.py:781: UserWarning: Warning: converting a masked element to nan.
  subarr = np.array(arr, dtype=dtype, copy=copy)
In [12]:
agg_metrics
Out [12]:
{'MSE': 2268670.185238203,
 'abs_error': 12053610.225944996,
 'abs_target_sum': 128632956.0,
 'abs_target_mean': 2385.272140631954,
 'seasonal_error': 189.49338196116761,
 'MASE': 1.115612490152452,
 'MAPE': 0.15282696886510425,
 'sMAPE': 0.15643239726127742,
 'MSIS': 8.31069379824802,
 'QuantileLoss[0.1]': 6807481.895313849,
 'Coverage[0.1]': 0.318331849873906,
 'QuantileLoss[0.2]': 9639934.200819714,
 'Coverage[0.2]': 0.46717846016911435,
 'QuantileLoss[0.3]': 11212656.535200916,
 'Coverage[0.3]': 0.5766021361815754,
 'QuantileLoss[0.4]': 11978553.100825835,
 'Coverage[0.4]': 0.6592679127725857,
 'QuantileLoss[0.5]': 12053610.195398472,
 'Coverage[0.5]': 0.7272288977896454,
 'QuantileLoss[0.6]': 11435207.664433796,
 'Coverage[0.6]': 0.7807261533897047,
 'QuantileLoss[0.7]': 10287538.289494911,
 'Coverage[0.7]': 0.8345386441180834,
 'QuantileLoss[0.8]': 8401266.733424887,
 'Coverage[0.8]': 0.8838265835929388,
 'QuantileLoss[0.9]': 5519886.29474154,
 'Coverage[0.9]': 0.931538347426198,
 'RMSE': 1506.210538151358,
 'NRMSE': 0.6314627637215025,
 'ND': 0.09370545932214289,
 'wQuantileLoss[0.1]': 0.052921755878126975,
 'wQuantileLoss[0.2]': 0.07494140304775172,
 'wQuantileLoss[0.3]': 0.08716783695152676,
 'wQuantileLoss[0.4]': 0.09312196091354563,
 'wQuantileLoss[0.5]': 0.09370545908467245,
 'wQuantileLoss[0.6]': 0.08889796223320715,
 'wQuantileLoss[0.7]': 0.0799759144887793,
 'wQuantileLoss[0.8]': 0.06531193089759119,
 'wQuantileLoss[0.9]': 0.042911913605884484,
 'mean_absolute_QuantileLoss': 9704014.989961546,
 'mean_wQuantileLoss': 0.07543957078900951,
 'MAE_Coverage': 0.18658210947930576,
 'OWA': nan}
In [13]:
plt.figure(figsize=(20, 15))
date_formater = mdates.DateFormatter('%b, %d')
plt.rcParams.update({'font.size': 15})

for idx, (forecast, ts) in islice(enumerate(zip(forecasts, tss)), 9):
    ax = plt.subplot(3, 3, idx+1)

    plt.plot(ts[-4 * dataset.metadata.prediction_length:], label="target", )
    forecast.plot( color='g')
    plt.xticks(rotation=60)
    ax.xaxis.set_major_formatter(date_formater)

plt.gcf().tight_layout()
plt.legend()
plt.show()
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