Lag Features, Autocorrelation & Stationarity Checks0%
Exponential Smoothing & Moving Average Baseline Models

Lag Features, Autocorrelation & Stationarity Checks

Beginner12 min read•Updated: Jul 11, 2026
Study Materials

Lag Features, Autocorrelation & Stationarity Checks

Machine learning algorithms (such as XGBoost, Random Forest, or Ridge Regression) do not naturally understand chronological sequence order. To enable supervised learning models to forecast future timestamps, data analysts engineer lag features and rolling statistics, while validating stationarity using statistical tests like the Augmented Dickey-Fuller (ADF) test.

1. Creating Lag Features with .shift()

A lag feature takes the value of a metric at time $t-k$ and maps it to the current row at time $t$:

Python
import pandas as pd
import numpy as np
 
# Ensure time order
df = df.sort_values('date').reset_index(drop=True)
 
# Engineer lag features
df['sales_lag_1'] = df['sales'].shift(1) # Yesterday's sales
df['sales_lag_7'] = df['sales'].shift(7) # Same day last week
df['sales_lag_14'] = df['sales'].shift(14) # Same day two weeks ago
 
# Engineer rolling features based on lagged data to prevent data leakage!
df['rolling_mean_7'] = df['sales'].shift(1).rolling(window=7).mean()
df['rolling_std_7'] = df['sales'].shift(1).rolling(window=7).std()
Important Warning
When engineering rolling features for predicting time $t$, always call .shift(1) before .rolling(). Otherwise, the target observation at time $t$ will leak into the rolling feature!

2. Autocorrelation & The ACF Plot

Autocorrelation measures the correlation of a time series with its own past lagged values:

Python
from statsmodels.graphics.tsaplots import plot_acf, plot_pacf
import matplotlib.pyplot as plt
 
# Plot Autocorrelation Function (ACF) up to 30 lags
fig, ax = plt.subplots(figsize=(10, 4))
plot_acf(df['sales'].dropna(), lags=30, ax=ax)
plt.title("Autocorrelation Function (ACF)")
plt.show()
  • If lag 7 exhibits a tall vertical bar breaching the blue confidence band, the data has strong weekly autocorrelation.

3. What is Stationarity and Why Does it Matter?

A time series is stationary if its statistical properties (mean, variance, and covariance) do not change over time:

  • Non-Stationary: Series with an upward trend or changing volatility. Models trained on non-stationary data fail to generalize because past distributions differ from future distributions.
  • Stationary: Series oscillating around a constant mean with constant variance.

4. Testing Stationarity: Augmented Dickey-Fuller (ADF) Test

The ADF hypothesis test evaluates whether a unit root is present:

  • $H_0$ (Null Hypothesis): Series is Non-Stationary (has unit root).
  • $H_1$ (Alternative Hypothesis): Series is Stationary ($p$-value $< 0.05$).
Python
from statsmodels.tsa.stattools import adfuller
 
def check_stationarity(series):
result = adfuller(series.dropna())
adf_statistic = result[0]
p_value = result[1]
print(f"ADF Statistic: {adf_statistic:.4f}")
print(f"p-value: {p_value:.4f}")
if p_value < 0.05:
print(">> Reject H0: Series IS STATIONARY (Ready for modeling)")
else:
print(">> Fail to reject H0: Series is NON-STATIONARY (Differencing needed)")
 
check_stationarity(df['sales'])

5. Achieving Stationarity: Differencing (.diff())

If a series is non-stationary, apply first-order differencing ($Delta Y_t = Y_t - Y_{t-1}$):

Python
# 1st order differencing to remove trend
df['sales_diff'] = df['sales'].diff(1)
check_stationarity(df['sales_diff'])
Interactive Quiz

Multiple Choice Questions

Question 1
In time series feature engineering, what error occurs if you compute df['sales'].rolling(7).mean() without shifting by 1 period before forecasting $t$?
Question 2
In the Augmented Dickey-Fuller (ADF) test, what does a $p$-value of 0.012 indicate?
Question 3
Which Pandas method creates a lag feature representing the value from 7 periods ago?
Question 4
What does a significant positive spike at lag 12 in a monthly sales ACF plot signify?
Question 5
How does first-order differencing ($Delta Y_t = Y_t - Y_{t-1}$) help stabilize a non-stationary series?
Next Lesson

Exponential Smoothing & Moving Average Baseline Models

Continue learning with hands-on practice, examples, and exercises in the upcoming topic.

Related Lessons

Previous LessonNext Lesson
Trend, Seasonality & Residual DecompositionExponential Smoothing & Moving Average Baseline Models

Practice Quiz

Test your understanding of this lesson with 5 questions. Each question has one correct answer.

PreviousNext
PrevNext