Inverse transform of quantiles after differentiation #1342
Description
🚀 Feature Request
Currently, we treat quantiles in the inverse transforms the same way as the target series. When using differentiation (DifferencingTransform) this might result in very wide and not meaningful intervals.
Mainly, this affects cases when the expected value of
Code to reproduce
from etna.datasets.datasets_generation import generate_ar_df
from etna.datasets import TSDataset
from etna.pipeline import Pipeline
from etna.models import SeasonalMovingAverageModel
from etna.transforms import DifferencingTransform
from etna.analysis import plot_forecast
df = generate_ar_df(100, "2020-01-01")
ts = TSDataset(df=TSDataset.to_dataset(df=df), freq="D")
train_ts, test_ts = ts.train_test_split(test_size=20)
pipeline = Pipeline(
transforms=[DifferencingTransform(in_column="target")],
model=SeasonalMovingAverageModel(seasonality=1),
horizon=20
)
pipeline.fit(train_ts)
forecast = pipeline.forecast(prediction_interval=True)
plot_forecast(forecast_ts=forecast, test_ts=test_ts, prediction_intervals=True)Proposal
Implement interface for separate treatment of quantiles in transforms.
Use DifferencingTransform, where
Test cases
No response
Additional context
Here is a comparison between current and proposed approaches.
import numpy as np
import matplotlib.pyplot as plt
# setting timeline and generating noise
t = np.arange(100)
eps = np.random.normal(0, 1, 100)
eps[0] += 10
level = eps[0]
# generating random walk series
y = np.cumsum(eps)
# differentiating series
r = np.diff(y)
# estimate quantiles for the first difference
r_q_upper = r + np.quantile(r, q=0.975)
r_q_lower = r + np.quantile(r, q=0.025)
# current approach
y_q_upper = np.cumsum(r_q_upper) + level
y_q_lower = np.cumsum(r_q_lower) + level
# proposed approach
int_r = np.roll(np.cumsum(r) + level, 1) # integration
int_r[0] = level
y_q_upper_adj = int_r + r_q_upper
y_q_lower_adj = int_r + r_q_lower
plt.figure(figsize=(6, 12))
plt.subplot(3, 1, 1)
plt.plot(t[1:], r, color="orange", label="first difference")
plt.fill_between(t[1:], r_q_upper, r_q_lower, alpha=0.3, color="orange", label="interval")
plt.legend()
plt.subplot(3, 1, 2)
plt.title("Current approach")
plt.plot(t[1:], y[1:], label="series")
plt.fill_between(t[1:], y_q_upper, y_q_lower, alpha=0.3, label="interval", color="g")
plt.legend()
plt.subplot(3, 1, 3)
plt.title("Proposed approach")
plt.plot(t[1:], y[1:], label="series")
plt.fill_between(t[1:], y_q_upper_adj, y_q_lower_adj, alpha=0.3, label="interval", color="g")
plt.legend()