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
          start_timestamp end_timestamp  length  num_missing
segments
segment_a      2019-11-17    2019-11-30      14            0
segment_b      2019-11-17    2019-11-30      14            0
segment_c      2019-11-17    2019-11-30      14            0
segment_d      2019-11-17    2019-11-30      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)

11:01:25 - cmdstanpy - INFO - Chain [1] start processing
11:01:25 - cmdstanpy - INFO - Chain [1] done processing
11:01:25 - cmdstanpy - INFO - Chain [1] start processing
11:01:25 - cmdstanpy - INFO - Chain [1] done processing
11:01:25 - cmdstanpy - INFO - Chain [1] start processing
11:01:25 - cmdstanpy - INFO - Chain [1] done processing
11:01:25 - cmdstanpy - INFO - Chain [1] start processing
11:01:25 - 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 = (), )

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
2019-11-17 415.300214 196.610084 143.769761 723.287233
2019-11-18 528.270723 248.186730 181.336869 900.630429
2019-11-19 544.854787 253.049163 173.502291 938.072558
2019-11-20 535.458739 248.527842 169.407795 921.954696
2019-11-21 528.720640 244.837321 169.601296 916.216922
2019-11-22 516.531192 240.322263 168.009967 906.355884
2019-11-23 429.297574 203.910951 147.698344 759.476794
2019-11-24 417.935844 197.126646 146.009019 735.950357
2019-11-25 530.906353 248.703292 183.576126 913.293554
2019-11-26 547.490417 253.565726 175.741548 950.735683
2019-11-27 538.094369 249.044404 171.647052 934.617821
2019-11-28 531.356269 245.353883 171.840553 928.880047
2019-11-29 519.166821 240.838825 170.249224 919.019009
2019-11-30 431.933204 204.427513 149.937602 772.139919

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': 6.179808820305944,
 'segment_c': 9.107343268713644,
 'segment_d': 6.197016763401841,
 'segment_b': 4.162295213860478}

[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_c': 6.930906591160424,
 'segment_d': 4.304033333591803,
 'segment_b': 7.520927594702097}

[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 2.554696 6 2.267172 2.285557 2.372912 ... 2.184691 2.222716 2 2.174978 6 2.781755 2.833147 2.948902 3 2.799752
2019-11-18 0 2.578639 2.540329 2.585461 0 2.644735 0 2.294466 2.267172 2.285557 ... 2.176091 2.184691 2 2.232267 0 2.814913 2.781755 2.833147 3 2.822211
2019-11-19 1 2.708421 2.578639 2.540329 0 2.688596 1 2.409933 2.294466 2.267172 ... 2.187521 2.176091 2 2.213589 1 2.969416 2.814913 2.781755 3 2.931579
2019-11-20 2 2.700704 2.708421 2.578639 0 2.685920 2 2.396199 2.409933 2.294466 ... 2.269513 2.187521 2 2.233358 2 2.947434 2.969416 2.814913 3 2.938511
2019-11-21 3 2.720986 2.700704 2.708421 0 2.691248 3 2.397940 2.396199 2.409933 ... 2.252853 2.269513 2 2.239043 3 2.935003 2.947434 2.969416 3 2.941839
2019-11-22 4 2.728354 2.720986 2.700704 0 2.688338 4 2.401401 2.397940 2.396199 ... 2.245513 2.252853 2 2.245082 4 2.923762 2.935003 2.947434 3 2.949272
2019-11-23 5 2.634477 2.728354 2.720986 0 2.628840 5 2.311754 2.401401 2.397940 ... 2.260071 2.245513 2 2.185261 5 2.825426 2.923762 2.935003 3 2.844858
2019-11-24 6 2.626340 2.634477 2.728354 0 2.615757 6 2.290035 2.311754 2.401401 ... 2.198657 2.260071 2 2.175019 6 2.800029 2.825426 2.923762 3 2.803249
2019-11-25 0 2.745855 2.626340 2.634477 0 2.703159 0 2.416641 2.290035 2.311754 ... 2.190332 2.198657 2 2.227224 0 2.951823 2.800029 2.825426 3 2.929104
2019-11-26 1 2.747412 2.745855 2.626340 0 2.712927 1 2.437751 2.416641 2.290035 ... 2.274158 2.190332 2 2.245364 1 2.987219 2.951823 2.800029 3 2.929635
2019-11-27 2 2.747412 2.747412 2.745855 0 2.719205 2 2.424882 2.437751 2.416641 ... 2.262451 2.274158 2 2.258761 2 2.987666 2.987219 2.951823 3 2.945222
2019-11-28 3 2.761176 2.747412 2.747412 0 2.738940 3 2.436163 2.424882 2.437751 ... 2.260071 2.262451 2 2.250948 3 2.972666 2.987666 2.987219 3 2.939975
2019-11-29 4 2.760422 2.761176 2.747412 0 2.732807 4 2.432969 2.436163 2.424882 ... 2.260071 2.260071 2 2.239400 4 2.956649 2.972666 2.987666 3 2.941243
2019-11-30 5 2.663701 2.760422 2.761176 0 2.661203 5 2.352183 2.432969 2.436163 ... 2.243038 2.260071 2 2.168509 5 2.843855 2.956649 2.972666 3 2.856539

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 0 357.670821 6 2.267172 2.285557 2.372912 ... 2.184691 2.222716 2 148.615840 6 2.781755 2.833147 2.948902 3 629.597755
2019-11-18 0 2.578639 2.540329 2.585461 0 440.301186 0 2.294466 2.267172 2.285557 ... 2.176091 2.184691 2 169.713075 0 2.814913 2.781755 2.833147 3 663.065558
2019-11-19 1 2.708421 2.578639 2.540329 0 487.197559 1 2.409933 2.294466 2.267172 ... 2.187521 2.176091 2 162.526997 1 2.969416 2.814913 2.781755 3 853.237810
2019-11-20 2 2.700704 2.708421 2.578639 0 484.198921 2 2.396199 2.409933 2.294466 ... 2.269513 2.187521 2 170.142625 2 2.947434 2.969416 2.814913 3 866.982377
2019-11-21 3 2.720986 2.700704 2.708421 0 490.187832 3 2.397940 2.396199 2.409933 ... 2.252853 2.269513 2 172.397425 3 2.935003 2.947434 2.969416 3 873.660154
2019-11-22 4 2.728354 2.720986 2.700704 0 486.908139 4 2.401401 2.397940 2.396199 ... 2.245513 2.252853 2 174.825622 4 2.923762 2.935003 2.947434 3 888.758312
2019-11-23 5 2.634477 2.728354 2.720986 0 424.441403 5 2.311754 2.401401 2.397940 ... 2.260071 2.245513 2 152.200917 5 2.825426 2.923762 2.935003 3 698.613976
2019-11-24 6 2.626340 2.634477 2.728354 0 411.816246 6 2.290035 2.311754 2.401401 ... 2.198657 2.260071 2 148.629965 6 2.800029 2.825426 2.923762 3 634.695616
2019-11-25 0 2.745855 2.626340 2.634477 0 503.846045 0 2.416641 2.290035 2.311754 ... 2.190332 2.198657 2 167.742420 0 2.951823 2.800029 2.825426 3 848.382904
2019-11-26 1 2.747412 2.745855 2.626340 0 515.329473 1 2.437751 2.416641 2.290035 ... 2.274158 2.190332 2 174.939942 1 2.987219 2.951823 2.800029 3 849.422478
2019-11-27 2 2.747412 2.747412 2.745855 0 522.847495 2 2.424882 2.437751 2.416641 ... 2.262451 2.274158 2 180.451565 2 2.987666 2.987219 2.951823 3 880.498819
2019-11-28 3 2.761176 2.747412 2.747412 0 547.201141 3 2.436163 2.424882 2.437751 ... 2.260071 2.262451 2 177.216379 3 2.972666 2.987666 2.987219 3 869.914298
2019-11-29 4 2.760422 2.761176 2.747412 0 539.514121 4 2.432969 2.436163 2.424882 ... 2.260071 2.260071 2 172.540258 4 2.956649 2.972666 2.987666 3 872.459235
2019-11-30 5 2.663701 2.760422 2.761176 0 457.356159 5 2.352183 2.432969 2.436163 ... 2.243038 2.260071 2 146.404010 5 2.843855 2.956649 2.972666 3 717.685857

14 rows × 24 columns

The result of forecasting

[29]:

smape(y_true=test_ts, y_pred=forecast_ts)

[29]:

{'segment_a': 11.24334950038253,
 'segment_c': 8.825418480914147,
 'segment_d': 6.412716995027116,
 'segment_b': 8.12104834404452}

[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