# Introduction
Time series feature engineering doesn’t follow the same rules as tabular data. Observations aren’t independent, row order isn’t incidental, and the most useful features are rarely individual readings. You’ll have to identify patterns across time like rates of change, lag comparisons, deviations from a rolling baseline, and more.
Building lags, sliding windows, and grouping across resolutions are all, at their core, iteration problems over ordered sequences. Python’s itertools module is a natural fit for this kind of work. It doesn’t replace high-level pandas abstractions like .rolling(), but it gives you lower-level building blocks to construct exactly the features you need, with full control over the logic.
In this article, you’ll build seven categories of time series features using itertools. You’ll also apply each to a sample dataset.
You can get the code on GitHub.
# Creating a Sample Dataset
Before we start building the features, let’s spin up a sample sensor dataset to work with throughout the article.
import numpy as np
import pandas as pd
import itertools
np.random.seed(42)
periods = 168 # one week of hourly readings
index = pd.date_range(start="2024-03-01", periods=periods, freq="h")
hours = np.arange(periods)
# Temperature (°C): daily cycle + gradual drift + noise
temp_base = 3.5
temp_daily = 1.2 * np.sin(2 * np.pi * hours / 24)
temp_drift = 0.003 * hours
temp_noise = np.random.normal(0, 0.3, periods)
temperature = temp_base + temp_daily + temp_drift + temp_noise
# Humidity (%): inverse relationship with temperature + noise
humidity = 78 - 2.1 * (temperature - temp_base) + np.random.normal(0, 1.2, periods)
# Power draw (kW): peaks during business hours, higher on weekdays
day_of_week = index.dayofweek
business_hours = ((index.hour >= 8) & (index.hour <= 18)).astype(int)
weekend_factor = np.where(day_of_week >= 5, 0.6, 1.0)
power = (
42.0
+ 18.0 * business_hours * weekend_factor
+ np.random.normal(0, 2.1, periods)
)
df = pd.DataFrame({
"temperature_c": np.round(temperature, 3),
"humidity_pct": np.round(humidity, 2),
"power_kw": np.round(power, 2),
}, index=index)
df.index.name = "timestamp"
print(df.head(8))
print(f"\nShape: {df.shape}")
Output:
temperature_c humidity_pct power_kw
timestamp
2024-03-01 00:00:00 3.649 77.39 40.27
2024-03-01 01:00:00 3.772 76.52 41.33
2024-03-01 02:00:00 4.300 75.25 42.87
2024-03-01 03:00:00 4.814 74.26 40.82
2024-03-01 04:00:00 4.481 75.85 40.27
2024-03-01 05:00:00 4.604 76.09 42.51
2024-03-01 06:00:00 5.192 74.78 42.51
2024-03-01 07:00:00 4.910 76.03 40.94
Shape: (168, 3)
We now have 168 hourly readings across three sensor channels. Now let’s build features.
# 1. Generating Lag Features with islice
Lag features are the most fundamental time series feature: the value of a variable at a fixed number of steps in the past. For example, values from 1 step ago, 6 steps ago, or 24 steps ago can each capture distinct patterns such as short-term fluctuations, recurring intra-period behavior, and longer-term trends or seasonality.
Let’s build lag features for our sample dataset using islice:
sensor_readings = df["temperature_c"].tolist()
lag_offsets = [1, 6, 12, 24]
lag_features = {}
for lag in lag_offsets:
lagged = list(itertools.islice(sensor_readings, 0, len(sensor_readings) - lag))
# Pad the beginning with None to preserve index alignment
lag_features[f"temp_lag_{lag}h"] = [None] * lag + lagged
lag_df = pd.DataFrame(lag_features, index=df.index)
lag_df["temperature_c"] = df["temperature_c"]
print(lag_df.iloc[24:30])
Output:
temp_lag_1h temp_lag_6h temp_lag_12h temp_lag_24h \
timestamp
2024-03-02 00:00:00 2.831 2.082 3.609 3.649
2024-03-02 01:00:00 3.409 1.974 2.654 3.772
2024-03-02 02:00:00 3.919 2.960 2.425 4.300
2024-03-02 03:00:00 3.833 2.647 2.528 4.814
2024-03-02 04:00:00 4.542 2.986 2.205 4.481
2024-03-02 05:00:00 4.443 2.831 2.486 4.604
temperature_c
timestamp
2024-03-02 00:00:00 3.409
2024-03-02 01:00:00 3.919
2024-03-02 02:00:00 3.833
2024-03-02 03:00:00 4.542
2024-03-02 04:00:00 4.443
2024-03-02 05:00:00 4.659
islice(sensor_readings, 0, len - lag) extracts the sequence shifted back by lag steps without creating a copy of the full list. The None padding at the front keeps every lag feature aligned with the original index. This matters when you later drop NaNs for model training.
# 2. Building Rolling Window Features with islice and accumulate
A single lag value tells you what the sensor read at a point in the past. A rolling statistic tells you what the sensor has been doing over a window of time, which is often far more useful.
readings = df["temperature_c"].tolist()
window_size = 6 # 6-hour rolling window
rolling_features = []
for i in range(len(readings)):
if i < window_size:
rolling_features.append({
"rolling_mean_6h": None,
"rolling_std_6h": None,
"rolling_min_6h": None,
"rolling_max_6h": None,
})
continue
window = list(itertools.islice(readings, i - window_size, i))
# Use accumulate to compute running sum for mean
running_sum = list(itertools.accumulate(window))
window_mean = running_sum[-1] / window_size
window_mean_sq = sum(x**2 for x in window) / window_size
rolling_features.append({
"rolling_mean_6h": round(window_mean, 4),
"rolling_std_6h": round((window_mean_sq - window_mean**2) ** 0.5, 4),
"rolling_min_6h": round(min(window), 4),
"rolling_max_6h": round(max(window), 4),
})
roll_df = pd.DataFrame(rolling_features, index=df.index)
roll_df["temperature_c"] = df["temperature_c"]
print(roll_df.iloc[6:12])
Output:
rolling_mean_6h rolling_std_6h rolling_min_6h \
timestamp
2024-03-01 06:00:00 4.2700 0.4256 3.649
2024-03-01 07:00:00 4.5272 0.4386 3.772
2024-03-01 08:00:00 4.7168 0.2929 4.300
2024-03-01 09:00:00 4.7372 0.2662 4.422
2024-03-01 10:00:00 4.6912 0.2728 4.422
2024-03-01 11:00:00 4.6095 0.3769 3.991
rolling_max_6h temperature_c
timestamp
2024-03-01 06:00:00 4.814 5.192
2024-03-01 07:00:00 5.192 4.910
2024-03-01 08:00:00 5.192 4.422
2024-03-01 09:00:00 5.192 4.538
2024-03-01 10:00:00 5.192 3.991
2024-03-01 11:00:00 5.192 3.704
The accumulate call here computes the running sum of the window so we get the total in one pass — running_sum[-1] — without calling sum() separately. For large datasets processed in a streaming fashion, avoiding redundant passes over the same data is efficient.
# 3. Creating Seasonal Interaction Features with product
Many time series exhibit layered seasonality, where multiple temporal cycles interact — such as time of day, day of week, and broader operational or cyclical periods. Interaction features that combine these dimensions can capture patterns that individual time components alone may overlook.
Now let’s build interaction features with product:
hours_of_day = list(range(24))
day_types = ["weekday", "weekend"]
operational_shifts = ["off_peak", "on_peak"] # on_peak: 08:00–18:00
# Build a full lookup grid for all combinations
season_grid = list(itertools.product(hours_of_day, day_types, operational_shifts))
season_df = pd.DataFrame(season_grid, columns=["hour", "day_type", "shift"])
# Simulate expected baseline temperature per combination
np.random.seed(14)
season_df["baseline_temp_c"] = np.round(
3.5
+ 0.8 * np.sin(2 * np.pi * season_df["hour"] / 24)
+ np.where(season_df["day_type"] == "weekend", 0.3, 0.0)
+ np.where(season_df["shift"] == "on_peak", 0.5, 0.0)
+ np.random.normal(0, 0.1, len(season_df)),
3
)
print(season_df[season_df["hour"].isin([0, 8, 14, 20])].head(16).to_string(index=False))
print(f"\nTotal grid combinations: {len(season_df)}")
Output:
hour day_type shift baseline_temp_c
0 weekday off_peak 3.655
0 weekday on_peak 4.008
0 weekend off_peak 3.817
0 weekend on_peak 4.293
8 weekday off_peak 4.325
8 weekday on_peak 4.601
8 weekend off_peak 4.446
8 weekend on_peak 4.978
14 weekday off_peak 3.370
14 weekday on_peak 3.628
14 weekend off_peak 3.279
14 weekend on_peak 3.959
20 weekday off_peak 2.726
20 weekday on_peak 3.256
20 weekend off_peak 3.056
20 weekend on_peak 3.530
Total grid combinations: 96
This grid merges back onto your main dataset as a baseline_temp_c feature per row — giving every reading a context-aware expected value. The deviation from that baseline, temperature_c - baseline_temp_c, is then a useful anomaly detection feature.
# 4. Extracting Sliding Window Statistics with tee
Sometimes you need to process the same sequence through multiple statistical lenses simultaneously — mean, variance, rate of change — without iterating over it multiple times. itertools.tee creates independent iterators from a single source, which is exactly what you need.
def sliding_window_stats(series, window_size):
"""Compute mean, range and rate-of-change over sliding windows using tee."""
results = []
it = iter(series)
window = list(itertools.islice(it, window_size))
if len(window) < window_size:
return results
results.append({
"window_mean": round(sum(window) / window_size, 4),
"window_range": round(max(window) - min(window), 4),
"rate_of_change": round(window[-1] - window[0], 4),
})
for next_val in it:
window = window[1:] + [next_val]
# tee creates two independent iterators over the same window
iter_a, iter_b = itertools.tee(iter(window))
values_a = list(iter_a)
values_b = list(iter_b)
mean_val = sum(values_a) / window_size
results.append({
"window_mean": round(mean_val, 4),
"window_range": round(max(values_b) - min(values_b), 4),
"rate_of_change": round(window[-1] - window[0], 4),
})
return results
power_readings = df["power_kw"].tolist()
stats = sliding_window_stats(power_readings, window_size=8)
stats_df = pd.DataFrame(stats, index=df.index[7:])
stats_df["power_kw"] = df["power_kw"].iloc[7:].values
print(stats_df.iloc[0:8])
Output:
window_mean window_range rate_of_change power_kw
timestamp
2024-03-01 07:00:00 41.4400 2.60 0.67 40.94
2024-03-01 08:00:00 43.7825 18.74 17.68 59.01
2024-03-01 09:00:00 46.1775 20.22 17.62 60.49
2024-03-01 10:00:00 47.9387 20.22 16.14 56.96
2024-03-01 11:00:00 49.9663 20.22 16.77 57.04
2024-03-01 12:00:00 52.2437 19.55 15.98 58.49
2024-03-01 13:00:00 54.3738 19.55 17.04 59.55
2024-03-01 14:00:00 56.6412 19.71 19.71 60.65
As seen, tee lets you pass the same window iterator into two separate downstream computations without rewinding or copying the list yourself.
# 5. Combining Multi-Resolution Time Features with chain
Useful time series features often come from multiple temporal resolutions simultaneously: the raw hourly reading, a 6-hour rolling mean, a 24-hour rolling mean, and a calendar feature like hour-of-day. These are usually in separate arrays and need assembling into one clean feature list. Here’s how you can use chain to combine such features:
humidity = df["humidity_pct"].tolist()
def rolling_means(series, window):
means = []
for i in range(len(series)):
if i < window:
means.append(None)
else:
w = list(itertools.islice(series, i - window, i))
means.append(round(sum(w) / window, 3))
return means
rolling_6h = rolling_means(humidity, 6)
rolling_24h = rolling_means(humidity, 24)
hour_of_day = df.index.hour.tolist()
is_business_hour = [1 if 8 <= h <= 18 else 0 for h in hour_of_day]
# chain assembles feature name list from logically grouped sublists
feature_names = list(itertools.chain(
["humidity_raw"],
["humidity_roll_6h", "humidity_roll_24h"],
["hour_of_day", "is_business_hour"],
))
multi_res_df = pd.DataFrame({
name: vals for name, vals in zip(
feature_names,
[humidity, rolling_6h, rolling_24h, hour_of_day, is_business_hour]
)
}, index=df.index)
print(multi_res_df.iloc[24:30])
Output:
humidity_raw humidity_roll_6h humidity_roll_24h \
timestamp
2024-03-02 00:00:00 78.45 79.622 78.055
2024-03-02 01:00:00 75.63 79.105 78.100
2024-03-02 02:00:00 77.51 78.190 78.062
2024-03-02 03:00:00 76.27 78.088 78.157
2024-03-02 04:00:00 74.96 77.805 78.240
2024-03-02 05:00:00 75.75 77.208 78.203
hour_of_day is_business_hour
timestamp
2024-03-02 00:00:00 0 0
2024-03-02 01:00:00 1 0
2024-03-02 02:00:00 2 0
2024-03-02 03:00:00 3 0
2024-03-02 04:00:00 4 0
2024-03-02 05:00:00 5 0
chain here assembles the feature name list from logically grouped sublists — raw sensor, rolling aggregates, calendar features. As your feature set grows across more sensor channels and more resolutions, chain keeps that assembly readable and easy to extend.
# 6. Computing Pairwise Temporal Correlations with combinations
In a multi-sensor setting, the relationships between variables over time often contain valuable signals that individual measurements alone cannot capture. For example, simultaneous increases across two sensors may reveal emerging conditions or interactions that would not be apparent when each series is analyzed in isolation.
Incorporating features that reflect these joint dynamics can improve a model’s ability to detect subtle patterns and dependencies. Let’s try building pairwise correlations using combinations:
sensor_cols = ["temperature_c", "humidity_pct", "power_kw"]
window_size = 12
pairwise_features = {}
for col_a, col_b in itertools.combinations(sensor_cols, 2):
feature_name = f"corr_{col_a[:4]}_{col_b[:4]}_12h"
correlations = []
series_a = df[col_a].tolist()
series_b = df[col_b].tolist()
for i in range(len(series_a)):
if i < window_size:
correlations.append(None)
continue
win_a = list(itertools.islice(series_a, i - window_size, i))
win_b = list(itertools.islice(series_b, i - window_size, i))
mean_a = sum(win_a) / window_size
mean_b = sum(win_b) / window_size
cov = sum((a - mean_a) * (b - mean_b) for a, b in zip(win_a, win_b)) / window_size
std_a = (sum((a - mean_a)**2 for a in win_a) / window_size) ** 0.5
std_b = (sum((b - mean_b)**2 for b in win_b) / window_size) ** 0.5
corr = round(cov / (std_a * std_b), 4) if std_a > 0 and std_b > 0 else None
correlations.append(corr)
pairwise_features[feature_name] = correlations
corr_df = pd.DataFrame(pairwise_features, index=df.index)
print(corr_df.iloc[12:18])
Output:
corr_temp_humi_12h corr_temp_powe_12h \
timestamp
2024-03-01 12:00:00 -0.6700 -0.2281
2024-03-01 13:00:00 -0.7208 -0.4960
2024-03-01 14:00:00 -0.7442 -0.6669
2024-03-01 15:00:00 -0.7678 -0.7076
2024-03-01 16:00:00 -0.8116 -0.7265
2024-03-01 17:00:00 -0.8368 -0.7482
corr_humi_powe_12h
timestamp
2024-03-01 12:00:00 0.5380
2024-03-01 13:00:00 0.6614
2024-03-01 14:00:00 0.7202
2024-03-01 15:00:00 0.7311
2024-03-01 16:00:00 0.7233
2024-03-01 17:00:00 0.7219
# 7. Accumulating Running Baselines with accumulate
A given value can carry different significance depending on when it occurs in a sequence. What matters is its deviation from the evolving baseline — the running mean up to that point in time. Using an incremental approach such as accumulate, you can compute this running mean efficiently without storing the entire history.
readings = df["temperature_c"].tolist()
running_sums = list(itertools.accumulate(readings))
running_counts = list(itertools.accumulate([1] * len(readings)))
running_means = [
round(s / c, 4)
for s, c in zip(running_sums, running_counts)
]
# Running max — highest temperature seen so far, useful for breach tracking
running_max = list(itertools.accumulate(readings, func=max))
deviation_from_baseline = [
round(r - m, 4)
for r, m in zip(readings, running_means)
]
baseline_df = pd.DataFrame({
"temperature_c": readings,
"running_mean": running_means,
"running_max": running_max,
"deviation_from_baseline": deviation_from_baseline,
}, index=df.index)
print(baseline_df.iloc[20:28])
Output:
temperature_c running_mean running_max \
timestamp
2024-03-01 20:00:00 2.960 3.5857 5.192
2024-03-01 21:00:00 2.647 3.5430 5.192
2024-03-01 22:00:00 2.986 3.5188 5.192
2024-03-01 23:00:00 2.831 3.4902 5.192
2024-03-02 00:00:00 3.409 3.4869 5.192
2024-03-02 01:00:00 3.919 3.5035 5.192
2024-03-02 02:00:00 3.833 3.5157 5.192
2024-03-02 03:00:00 4.542 3.5524 5.192
deviation_from_baseline
timestamp
2024-03-01 20:00:00 -0.6257
2024-03-01 21:00:00 -0.8960
2024-03-01 22:00:00 -0.5328
2024-03-01 23:00:00 -0.6592
2024-03-02 00:00:00 -0.0779
2024-03-02 01:00:00 0.4155
2024-03-02 02:00:00 0.3173
2024-03-02 03:00:00 0.9896
# Summary
Time series feature engineering is fundamentally about describing context — what has this signal been doing, relative to what we expect it to be doing? Every function covered here is a different way of formalizing that question into a number a model can learn from.
Here’s a summary of the patterns we’ve covered in this article:
| itertools Function | Time Series Feature | Example |
|---|---|---|
islice |
Lag features | Temperature 1h, 6h, 24h ago |
islice + accumulate |
Rolling window stats | 6h mean, std, min, max |
product |
Seasonal interaction grid | Hour × day type × shift baseline |
tee |
Parallel window statistics | Mean + range + rate of change |
chain |
Multi-resolution feature assembly | Raw + rolling + calendar features |
combinations |
Pairwise cross-sensor correlations | Temp–humidity, temp–power rolling corr |
accumulate |
Running baseline + deviation | Drift detection from historical mean |
And because itertools works at the iterator level, all of these patterns compose cleanly into streaming pipelines as well. Happy feature engineering!
Bala Priya C is a developer and technical writer from India. She likes working at the intersection of math, programming, data science, and content creation. Her areas of interest and expertise include DevOps, data science, and natural language processing. She enjoys reading, writing, coding, and coffee! Currently, she’s working on learning and sharing her knowledge with the developer community by authoring tutorials, how-to guides, opinion pieces, and more. Bala also creates engaging resource overviews and coding tutorials.
