Beginner

Introduction to Time Series Forecasting

Understand the fundamental concepts of time series data, including stationarity, trend, seasonality, and the standard forecasting workflow.

What is a Time Series?

A time series is a sequence of data points collected at successive, equally spaced points in time. Unlike regular tabular data, the order of observations matters — each value depends on previous values, creating temporal dependencies.

Time series data is everywhere: stock prices, weather readings, website traffic, sensor data, sales figures, energy consumption, and heart rate monitors.

Key Components

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Trend

Long-term increase or decrease in the data. A stock market index may show an upward trend over decades.

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Seasonality

Regular, repeating patterns at fixed intervals. Retail sales spike every December; ice cream sales peak in summer.

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Cyclical Patterns

Fluctuations not at a fixed frequency, often driven by economic or business cycles lasting years.

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Residual / Noise

Random variation that cannot be attributed to trend, seasonality, or cycles. The unpredictable component.

Stationarity

A time series is stationary when its statistical properties (mean, variance, autocorrelation) do not change over time. Most classical forecasting methods require stationary data.

Python — Testing for stationarity
import pandas as pd
from statsmodels.tsa.stattools import adfuller

# Augmented Dickey-Fuller test
def test_stationarity(series):
    result = adfuller(series, autolag='AIC')
    print(f"ADF Statistic: {result[0]:.4f}")
    print(f"p-value:       {result[1]:.4f}")
    if result[1] < 0.05:
        print("Series IS stationary (reject null hypothesis)")
    else:
        print("Series is NOT stationary (fail to reject)")

# Make a series stationary by differencing
df['value_diff'] = df['value'].diff()      # First difference
df['value_diff2'] = df['value'].diff().diff()  # Second difference

# Or use log transform + differencing
import numpy as np
df['value_log_diff'] = np.log(df['value']).diff()

Autocorrelation

Autocorrelation measures the correlation between a time series and its lagged version. The ACF (autocorrelation function) and PACF (partial autocorrelation function) plots are essential diagnostic tools.

Python — ACF and PACF plots
from statsmodels.graphics.tsaplots import plot_acf, plot_pacf
import matplotlib.pyplot as plt

fig, axes = plt.subplots(1, 2, figsize=(14, 5))
plot_acf(df['value'].dropna(), ax=axes[0], lags=40)
plot_pacf(df['value'].dropna(), ax=axes[1], lags=40)
axes[0].set_title("ACF")
axes[1].set_title("PACF")
plt.tight_layout()
plt.show()

The Forecasting Workflow

  1. Explore and visualize

    Plot the data, identify trend, seasonality, outliers, and missing values.

  2. Preprocess

    Handle missing values, remove outliers, apply transformations (log, Box-Cox) to stabilize variance.

  3. Check stationarity

    Use the ADF test and visual inspection. Apply differencing if needed.

  4. Select a model

    Choose between classical (ARIMA), modern (Prophet), or deep learning (LSTM) based on data characteristics.

  5. Train and validate

    Use time-series-aware splitting (no random shuffling). Apply walk-forward validation.

  6. Forecast and evaluate

    Generate predictions, compute metrics (MAPE, RMSE), and assess uncertainty with confidence intervals.

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Golden rule: Never shuffle time series data. The temporal order is information. Always train on past data and validate on future data, mimicking how the model will be used in production.

Common Applications

  • Stock market: Price prediction, volatility forecasting, algorithmic trading signals.
  • Weather: Temperature, precipitation, and wind forecasting for days to weeks ahead.
  • Demand forecasting: Retail sales, inventory management, supply chain optimization.
  • Energy: Electricity load forecasting, renewable energy output prediction.
  • Healthcare: Patient volume forecasting, epidemic curve modeling.