View Jupyter notebook on the GitHub.

Mechanics of forecasting#

Binder

This notebook uncovers the details of forecasting by pipelines in ETNA library. We are going to explain how pipelines are dealing with dataset, transforms and models to make a prediction.

Table of contents

  • Loading dataset

  • Forecasting

    • Context-free models

    • Context-required models

    • ML models

  • Summary

[1]:

!pip install "etna[prophet]" -q

[2]:

import warnings

warnings.filterwarnings("ignore")

[3]:

import pandas as pd

from etna.datasets import TSDataset

1. Loading dataset#

Let’s load and look at the dataset

[4]:

df = pd.read_csv("data/example_dataset.csv")
df.head()

[4]:
timestamp segment target
0 2019-01-01 segment_a 170
1 2019-01-02 segment_a 243
2 2019-01-03 segment_a 267
3 2019-01-04 segment_a 287
4 2019-01-05 segment_a 279 
[5]:

ts = TSDataset(df, freq="D")
ts.plot()
../_images/tutorials_209-mechanics_of_forecasting_8_0.png

2. Forecasting#

Now let’s dive deeper into forecasting without pipelines. We are going to use only TSDataset, transforms and models.

[6]:

HORIZON = 14

[7]:

train_ts, test_ts = ts.train_test_split(test_size=HORIZON)

[8]:

test_ts.info()

<class 'etna.datasets.TSDataset'>
num_segments: 4
num_exogs: 0
num_regressors: 0
num_known_future: 0
freq: D
end_timestamp: 2019-11-30 00:00:00
          start_timestamp  length  num_missing
segments
segment_a      2019-11-17      14            0
segment_b      2019-11-17      14            0
segment_c      2019-11-17      14            0
segment_d      2019-11-17      14            0

3.1 Context-free models#

Let’s start by using the ProphetModel, because it doesn’t require any transformations and doesn’t need any context.

Fitting the model is very easy

[9]:

from etna.models import ProphetModel

model = ProphetModel()
model.fit(train_ts)

14:49:37 - cmdstanpy - INFO - Chain [1] start processing
14:49:37 - cmdstanpy - INFO - Chain [1] done processing
14:49:38 - cmdstanpy - INFO - Chain [1] start processing
14:49:38 - cmdstanpy - INFO - Chain [1] done processing
14:49:38 - cmdstanpy - INFO - Chain [1] start processing
14:49:38 - cmdstanpy - INFO - Chain [1] done processing
14:49:38 - cmdstanpy - INFO - Chain [1] start processing
14:49:38 - cmdstanpy - INFO - Chain [1] done processing

[9]:

ProphetModel(growth = 'linear', changepoints = None, n_changepoints = 25, changepoint_range = 0.8, yearly_seasonality = 'auto', weekly_seasonality = 'auto', daily_seasonality = 'auto', holidays = None, seasonality_mode = 'additive', seasonality_prior_scale = 10.0, holidays_prior_scale = 10.0, changepoint_prior_scale = 0.05, mcmc_samples = 0, interval_width = 0.8, uncertainty_samples = 1000, stan_backend = None, additional_seasonality_params = (), timestamp_column = None, )

To make a forecast we should create a dataset with future data by using make_future method. We are currently interested in only future_steps parameter, it determines how many timestamps should be created after the end of the history.

As a result we would have a dataset with future_steps timestamps.

[10]:

future_ts = train_ts.make_future(future_steps=HORIZON)
future_ts

[10]:
segment segment_a segment_b segment_c segment_d
feature target target target target
timestamp
2019-11-17 NaN NaN NaN NaN
2019-11-18 NaN NaN NaN NaN
2019-11-19 NaN NaN NaN NaN
2019-11-20 NaN NaN NaN NaN
2019-11-21 NaN NaN NaN NaN
2019-11-22 NaN NaN NaN NaN
2019-11-23 NaN NaN NaN NaN
2019-11-24 NaN NaN NaN NaN
2019-11-25 NaN NaN NaN NaN
2019-11-26 NaN NaN NaN NaN
2019-11-27 NaN NaN NaN NaN
2019-11-28 NaN NaN NaN NaN
2019-11-29 NaN NaN NaN NaN
2019-11-30 NaN NaN NaN NaN

Now we are ready to make a forecast

[11]:

forecast_ts = model.forecast(future_ts)
forecast_ts

[11]:
segment segment_a segment_b segment_c segment_d
feature target target target target
timestamp
2019-11-17 417.673477 196.558737 143.788667 723.130705
2019-11-18 530.657704 248.126734 181.274089 900.628287
2019-11-19 547.467047 252.990611 173.441251 938.119256
2019-11-20 538.082365 248.468823 169.359185 921.984471
2019-11-21 531.357617 244.777693 169.557257 916.241514
2019-11-22 519.183714 240.262203 167.973756 906.370764
2019-11-23 431.966427 203.855615 147.703800 759.319762
2019-11-24 420.674705 197.069259 146.028192 735.773681
2019-11-25 533.658932 248.637256 183.513615 913.271263
2019-11-26 550.468274 253.501133 175.680777 950.762232
2019-11-27 541.083592 248.979345 171.598710 934.627447
2019-11-28 534.358844 245.288215 171.796782 928.884490
2019-11-29 522.184942 240.772725 170.213282 919.013740
2019-11-30 434.967654 204.366137 149.943325 771.962738

We should note that forecast_ts isn’t a new dataset, it is the same object as future_ts, but filled with predicted values

[12]:

forecast_ts is future_ts

[12]:

True

Now let’s look at a metric and plot the prediction.

[13]:

from etna.metrics import SMAPE

smape = SMAPE()
smape(y_true=test_ts, y_pred=forecast_ts)

[13]:

{'segment_a': 5.782173639024761,
 'segment_b': 4.176505858890025,
 'segment_c': 9.115732497272823,
 'segment_d': 6.191490704821549}

[14]:

from etna.analysis import plot_forecast

plot_forecast(forecast_ts, test_ts, train_ts, n_train_samples=10)
../_images/tutorials_209-mechanics_of_forecasting_23_0.png

3.2 Context-required models#

First of all, let’s clarify that context is. The context is a history data the precedes the forecasting horizon.

And now let’s expand our scheme to models that require some history context for forecasting. The example is NaiveModel, because it needs to know the value lag steps ago.

The fitting doesn’t change

[15]:

from etna.models import NaiveModel

model = NaiveModel(lag=14)
model.fit(train_ts)

[15]:

NaiveModel(lag = 14, )

The models has context_size attribute that in this particular case is equal to lag

[16]:

model.context_size

[16]:

14

Future generation now needs a new parameter: tail_steps, it determines how many timestamps should be created before the end of the history.

The result will contain future_steps + tail_step timestamps.

[17]:

future_ts = train_ts.make_future(future_steps=HORIZON, tail_steps=model.context_size)
future_ts

[17]:
segment segment_a segment_b segment_c segment_d
feature target target target target
timestamp
2019-11-03 346.0 184.0 149.0 604.0
2019-11-04 378.0 196.0 153.0 652.0
2019-11-05 510.0 256.0 185.0 931.0
2019-11-06 501.0 248.0 178.0 885.0
2019-11-07 525.0 249.0 175.0 860.0
2019-11-08 534.0 251.0 181.0 838.0
2019-11-09 430.0 204.0 157.0 668.0
2019-11-10 422.0 194.0 154.0 630.0
2019-11-11 556.0 260.0 187.0 894.0
2019-11-12 558.0 273.0 182.0 970.0
2019-11-13 558.0 265.0 181.0 971.0
2019-11-14 576.0 272.0 181.0 938.0
2019-11-15 575.0 270.0 174.0 904.0
2019-11-16 460.0 224.0 148.0 697.0
2019-11-17 NaN NaN NaN NaN
2019-11-18 NaN NaN NaN NaN
2019-11-19 NaN NaN NaN NaN
2019-11-20 NaN NaN NaN NaN
2019-11-21 NaN NaN NaN NaN
2019-11-22 NaN NaN NaN NaN
2019-11-23 NaN NaN NaN NaN
2019-11-24 NaN NaN NaN NaN
2019-11-25 NaN NaN NaN NaN
2019-11-26 NaN NaN NaN NaN
2019-11-27 NaN NaN NaN NaN
2019-11-28 NaN NaN NaN NaN
2019-11-29 NaN NaN NaN NaN
2019-11-30 NaN NaN NaN NaN

Forecasting is slightly changed too. We need to pass prediction_size parameter that determines how many timestamps we want to see in our result.

[18]:

forecast_ts = model.forecast(future_ts, prediction_size=HORIZON)
forecast_ts

[18]:
segment segment_a segment_b segment_c segment_d
feature target target target target
timestamp
2019-11-17 346.0 184.0 149.0 604.0
2019-11-18 378.0 196.0 153.0 652.0
2019-11-19 510.0 256.0 185.0 931.0
2019-11-20 501.0 248.0 178.0 885.0
2019-11-21 525.0 249.0 175.0 860.0
2019-11-22 534.0 251.0 181.0 838.0
2019-11-23 430.0 204.0 157.0 668.0
2019-11-24 422.0 194.0 154.0 630.0
2019-11-25 556.0 260.0 187.0 894.0
2019-11-26 558.0 273.0 182.0 970.0
2019-11-27 558.0 265.0 181.0 971.0
2019-11-28 576.0 272.0 181.0 938.0
2019-11-29 575.0 270.0 174.0 904.0
2019-11-30 460.0 224.0 148.0 697.0

The forecast_ts and future_ts are still the same object

[19]:

forecast_ts is future_ts

[19]:

True

The result of forecasting

[20]:

smape(y_true=test_ts, y_pred=forecast_ts)

[20]:

{'segment_a': 9.362036158596007,
 'segment_b': 7.520927594702097,
 'segment_c': 6.930906591160424,
 'segment_d': 4.304033333591803}

[21]:

plot_forecast(forecast_ts, test_ts, train_ts, n_train_samples=10)
../_images/tutorials_209-mechanics_of_forecasting_37_0.png

3.3 ML models#

Now we are going to expand our scheme even further by using transformations.

Let’s define the transformations

[22]:

from etna.transforms import DateFlagsTransform
from etna.transforms import LagTransform
from etna.transforms import LogTransform
from etna.transforms import SegmentEncoderTransform

log = LogTransform(in_column="target")
seg = SegmentEncoderTransform()
lags = LagTransform(in_column="target", lags=list(range(HORIZON, HORIZON + 3)), out_column="lag")
date_flags = DateFlagsTransform(
    day_number_in_week=True,
    day_number_in_month=False,
    week_number_in_month=False,
    is_weekend=False,
    out_column="date_flag",
)
transforms = [log, lags, date_flags, seg]

Fitting the models requires the transformations to be applied to the dataset

[23]:

train_ts

[23]:
segment segment_a segment_b segment_c segment_d
feature target target target target
timestamp
2019-01-01 170 102 92 238
2019-01-02 243 123 107 358
2019-01-03 267 130 103 366
2019-01-04 287 138 103 385
2019-01-05 279 137 104 384
... ... ... ... ...
2019-11-12 558 273 182 970
2019-11-13 558 265 181 971
2019-11-14 576 272 181 938
2019-11-15 575 270 174 904
2019-11-16 460 224 148 697

320 rows × 4 columns

[24]:

train_ts.fit_transform(transforms)
train_ts

[24]:
segment segment_a segment_b ... segment_c segment_d
feature date_flag_day_number_in_week lag_14 lag_15 lag_16 segment_code target date_flag_day_number_in_week lag_14 lag_15 lag_16 ... lag_15 lag_16 segment_code target date_flag_day_number_in_week lag_14 lag_15 lag_16 segment_code target
timestamp
2019-01-01 1 NaN NaN NaN 0 2.232996 1 NaN NaN NaN ... NaN NaN 2 1.968483 1 NaN NaN NaN 3 2.378398
2019-01-02 2 NaN NaN NaN 0 2.387390 2 NaN NaN NaN ... NaN NaN 2 2.033424 2 NaN NaN NaN 3 2.555094
2019-01-03 3 NaN NaN NaN 0 2.428135 3 NaN NaN NaN ... NaN NaN 2 2.017033 3 NaN NaN NaN 3 2.564666
2019-01-04 4 NaN NaN NaN 0 2.459392 4 NaN NaN NaN ... NaN NaN 2 2.017033 4 NaN NaN NaN 3 2.586587
2019-01-05 5 NaN NaN NaN 0 2.447158 5 NaN NaN NaN ... NaN NaN 2 2.021189 5 NaN NaN NaN 3 2.585461
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
2019-11-12 1 2.701568 2.728354 2.698970 0 2.747412 1 2.357935 2.389166 2.332438 ... 2.235528 2.164353 2 2.262451 1 2.921686 2.946943 2.880814 3 2.987219
2019-11-13 2 2.697229 2.701568 2.728354 0 2.747412 2 2.357935 2.357935 2.389166 ... 2.232996 2.235528 2 2.260071 2 2.916980 2.921686 2.946943 3 2.987666
2019-11-14 3 2.700704 2.697229 2.701568 0 2.761176 3 2.346353 2.357935 2.357935 ... 2.235528 2.232996 2 2.260071 3 2.930440 2.916980 2.921686 3 2.972666
2019-11-15 4 2.682145 2.700704 2.697229 0 2.760422 4 2.372912 2.346353 2.357935 ... 2.235528 2.235528 2 2.243038 4 2.948902 2.930440 2.916980 3 2.956649
2019-11-16 5 2.585461 2.682145 2.700704 0 2.663701 5 2.285557 2.372912 2.346353 ... 2.222716 2.235528 2 2.173186 5 2.833147 2.948902 2.930440 3 2.843855

320 rows × 24 columns

As you can see, there are several changes made by the transforms:

  • Added date_flag_day_number_in_week column;

  • Added lag_14, …, lag_19 columns;

  • Added segment_code column;

  • Logarithm applied to target column.

Now we are ready to fit our model

[25]:

from etna.models import CatBoostMultiSegmentModel

model = CatBoostMultiSegmentModel()
model.fit(train_ts)

[25]:

CatBoostMultiSegmentModel(iterations = None, depth = None, learning_rate = None, logging_level = 'Silent', l2_leaf_reg = None, thread_count = None, )

In this case preparing future doesn’t require dealing with the context, all the necessary information is in the features. But we have to deal with transformations by passing them into make_future method.

[26]:

future_ts = train_ts.make_future(future_steps=HORIZON, transforms=transforms)

Making a forecast

[27]:

forecast_ts = model.forecast(future_ts)
forecast_ts

[27]:
segment segment_a segment_b ... segment_c segment_d
feature date_flag_day_number_in_week lag_14 lag_15 lag_16 segment_code target date_flag_day_number_in_week lag_14 lag_15 lag_16 ... lag_15 lag_16 segment_code target date_flag_day_number_in_week lag_14 lag_15 lag_16 segment_code target
timestamp
2019-11-17 6 2.540329 2.585461 2.682145 0 2.556740 6 2.267172 2.285557 2.372912 ... 2.184691 2.222716 2 2.174014 6 2.781755 2.833147 2.948902 3 2.819766
2019-11-18 0 2.578639 2.540329 2.585461 0 2.651815 0 2.294466 2.267172 2.285557 ... 2.176091 2.184691 2 2.230191 0 2.814913 2.781755 2.833147 3 2.826960
2019-11-19 1 2.708421 2.578639 2.540329 0 2.687395 1 2.409933 2.294466 2.267172 ... 2.187521 2.176091 2 2.231492 1 2.969416 2.814913 2.781755 3 2.928302
2019-11-20 2 2.700704 2.708421 2.578639 0 2.695143 2 2.396199 2.409933 2.294466 ... 2.269513 2.187521 2 2.233829 2 2.947434 2.969416 2.814913 3 2.942484
2019-11-21 3 2.720986 2.700704 2.708421 0 2.681276 3 2.397940 2.396199 2.409933 ... 2.252853 2.269513 2 2.243859 3 2.935003 2.947434 2.969416 3 2.949650
2019-11-22 4 2.728354 2.720986 2.700704 0 2.687179 4 2.401401 2.397940 2.396199 ... 2.245513 2.252853 2 2.259357 4 2.923762 2.935003 2.947434 3 2.952880
2019-11-23 5 2.634477 2.728354 2.720986 0 2.612151 5 2.311754 2.401401 2.397940 ... 2.260071 2.245513 2 2.191276 5 2.825426 2.923762 2.935003 3 2.840746
2019-11-24 6 2.626340 2.634477 2.728354 0 2.602040 6 2.290035 2.311754 2.401401 ... 2.198657 2.260071 2 2.174478 6 2.800029 2.825426 2.923762 3 2.808645
2019-11-25 0 2.745855 2.626340 2.634477 0 2.704428 0 2.416641 2.290035 2.311754 ... 2.190332 2.198657 2 2.236019 0 2.951823 2.800029 2.825426 3 2.926138
2019-11-26 1 2.747412 2.745855 2.626340 0 2.717247 1 2.437751 2.416641 2.290035 ... 2.274158 2.190332 2 2.250306 1 2.987219 2.951823 2.800029 3 2.941435
2019-11-27 2 2.747412 2.747412 2.745855 0 2.728090 2 2.424882 2.437751 2.416641 ... 2.262451 2.274158 2 2.269917 2 2.987666 2.987219 2.951823 3 2.954827
2019-11-28 3 2.761176 2.747412 2.747412 0 2.741196 3 2.436163 2.424882 2.437751 ... 2.260071 2.262451 2 2.263858 3 2.972666 2.987666 2.987219 3 2.949533
2019-11-29 4 2.760422 2.761176 2.747412 0 2.738022 4 2.432969 2.436163 2.424882 ... 2.260071 2.260071 2 2.239212 4 2.956649 2.972666 2.987666 3 2.949205
2019-11-30 5 2.663701 2.760422 2.761176 0 2.667598 5 2.352183 2.432969 2.436163 ... 2.243038 2.260071 2 2.162335 5 2.843855 2.956649 2.972666 3 2.869409

14 rows × 24 columns

The forecasted values are too small because we forecasted the target after the logarithm transformation. To get the predictions in original domain we should apply inverse transformation to the predicted values.

[28]:

forecast_ts.inverse_transform(transforms)
forecast_ts

[28]:
segment segment_a segment_b ... segment_c segment_d
feature date_flag_day_number_in_week lag_14 lag_15 lag_16 segment_code target date_flag_day_number_in_week lag_14 lag_15 lag_16 ... lag_15 lag_16 segment_code target date_flag_day_number_in_week lag_14 lag_15 lag_16 segment_code target
timestamp
2019-11-17 6 2.540329 2.585461 2.682145 0 359.363234 6 2.267172 2.285557 2.372912 ... 2.184691 2.222716 2 148.284301 6 2.781755 2.833147 2.948902 3 659.338222
2019-11-18 0 2.578639 2.540329 2.585461 0 447.554679 0 2.294466 2.267172 2.285557 ... 2.176091 2.184691 2 168.899245 0 2.814913 2.781755 2.833147 3 670.367743
2019-11-19 1 2.708421 2.578639 2.540329 0 485.849895 1 2.409933 2.294466 2.267172 ... 2.187521 2.176091 2 169.408727 1 2.969416 2.814913 2.781755 3 846.817556
2019-11-20 2 2.700704 2.708421 2.578639 0 494.613183 2 2.396199 2.409933 2.294466 ... 2.269513 2.187521 2 170.328273 2 2.947434 2.969416 2.814913 3 874.959979
2019-11-21 3 2.720986 2.700704 2.708421 0 479.038925 3 2.397940 2.396199 2.409933 ... 2.252853 2.269513 2 174.330918 3 2.935003 2.947434 2.969416 3 889.533321
2019-11-22 4 2.728354 2.720986 2.700704 0 485.607701 4 2.401401 2.397940 2.396199 ... 2.245513 2.252853 2 180.700706 4 2.923762 2.935003 2.947434 3 896.179874
2019-11-23 5 2.634477 2.728354 2.720986 0 408.403156 5 2.311754 2.401401 2.397940 ... 2.260071 2.245513 2 154.337508 5 2.825426 2.923762 2.935003 3 692.020491
2019-11-24 6 2.626340 2.634477 2.728354 0 398.981966 6 2.290035 2.311754 2.401401 ... 2.198657 2.260071 2 148.443830 6 2.800029 2.825426 2.923762 3 642.643396
2019-11-25 0 2.745855 2.626340 2.634477 0 505.323214 0 2.416641 2.290035 2.311754 ... 2.190332 2.198657 2 171.194270 0 2.951823 2.800029 2.825426 3 842.603449
2019-11-26 1 2.747412 2.745855 2.626340 0 520.491759 1 2.437751 2.416641 2.290035 ... 2.274158 2.190332 2 176.953209 1 2.987219 2.951823 2.800029 3 872.846999
2019-11-27 2 2.747412 2.747412 2.745855 0 533.675426 2 2.424882 2.437751 2.416641 ... 2.262451 2.274158 2 185.173306 2 2.987666 2.987219 2.951823 3 900.211426
2019-11-28 3 2.761176 2.747412 2.747412 0 550.055772 3 2.436163 2.424882 2.437751 ... 2.260071 2.262451 2 182.593736 3 2.972666 2.987666 2.987219 3 889.293412
2019-11-29 4 2.760422 2.761176 2.747412 0 546.043578 4 2.432969 2.436163 2.424882 ... 2.260071 2.260071 2 172.465049 4 2.956649 2.972666 2.987666 3 888.621079
2019-11-30 5 2.663701 2.760422 2.761176 0 464.155824 5 2.352183 2.432969 2.436163 ... 2.243038 2.260071 2 144.323108 5 2.843855 2.956649 2.972666 3 739.302815

14 rows × 24 columns

The result of forecasting

[29]:

smape(y_true=test_ts, y_pred=forecast_ts)

[29]:

{'segment_a': 11.18164789354642,
 'segment_b': 8.218437980478669,
 'segment_c': 7.648519789798347,
 'segment_d': 6.120890541970104}

[30]:

train_ts.inverse_transform(transforms)
plot_forecast(forecast_ts, test_ts, train_ts, n_train_samples=10)
../_images/tutorials_209-mechanics_of_forecasting_53_0.png

Summary#

As we can see, pipelines do a lot of work under the hood.

Training:

  • Applying transformations

  • Fitting the model

Forecasting:

  • Generating future dataset with applied transformations

  • Forecasting with the fitted model

  • Inverse transformation