Time Series

Time series data has a temporal ordering that fundamentally changes how you approach modeling. You cannot randomly shuffle it, you must respect chronological order, and specialized algorithms exist to handle its unique characteristics like trend, seasonality, and autocorrelation.

Components of Time Series

Every time series can be decomposed into these components:

Component	What It Is	Example
Trend	Long-term increase or decrease	Population growth, rising stock market over decades
Seasonality	Regular, repeating patterns at fixed intervals	Higher ice cream sales in summer, holiday shopping spikes
Cyclical	Long-term fluctuations without fixed period	Business cycles, economic booms and recessions
Residual (Noise)	Random, unexplained variation	Unexpected events, measurement error

# Decompose a time series into its components
from statsmodels.tsa.seasonal import seasonal_decompose

result = seasonal_decompose(data, model='additive', period=12)
result.plot()
# Shows: observed, trend, seasonal, and residual components

Algorithm Selection for Time Series

Algorithm	Best For	Key Capability
ARIMA / SARIMA	Single time series, statistical approach	Good for stationary data with clear trend/seasonality. Cannot use related time series
Exponential Smoothing (ETS)	Simple time series with trend and/or seasonality	Lightweight and fast. Cannot use related time series or metadata
DeepAR	Multiple related time series, cold-start scenarios	Learns patterns across related series. Handles missing values (NaN). Probabilistic forecasts
CNN-QR	Forecasting with related data, promotions, holidays	Supports related time series, item metadata, and future known values

Decision Guide

Single series, simple                    → ARIMA
Multiple related series OR new products  → DeepAR (cold-start capability)
Need related features + promotions       → CNN-QR
Simple trend/seasonality                 → Exponential Smoothing

Key Insight

"Predict demand for a NEW product with no history" = DeepAR. It can generate forecasts for new items by learning patterns from similar items in the training set (cold-start capability). No other approach handles this as naturally.

Critical Rules for Time Series

Rule	Why It Matters
NEVER randomly split time series data	Random splitting leaks future information into training. Always split chronologically: train on past, test on future
Check stationarity before ARIMA	ARIMA assumes stationarity (constant mean and variance). Use the Dickey-Fuller test or STL decomposition to verify
DeepAR handles missing values as NaN	A unique capability — no need to impute missing target values
DeepAR handles cold-start	Can predict for new items based on patterns learned from similar items

caution

The single most important rule for time series validation: always split chronologically. Train on the past, validate on the future. Random splitting creates data leakage that produces unrealistically optimistic results.

Stationarity

A stationary time series has a constant mean and variance over time. Many statistical models (ARIMA) require stationarity.

How to check:

• Visual inspection of the time series plot
• Dickey-Fuller test (statistical test for unit root)
• STL decomposition to separate trend and seasonality

How to make data stationary:

• Differencing (subtract previous value)
• Log transformation (stabilize variance)
• Detrending (remove trend component)

from statsmodels.tsa.stattools import adfuller

# Augmented Dickey-Fuller test
result = adfuller(time_series)
p_value = result[1]
if p_value < 0.05:
    print("Stationary (reject null hypothesis)")
else:
    print("Non-stationary — apply differencing")

Time Series Validation

from sklearn.model_selection import TimeSeriesSplit

# Expanding window cross-validation
tscv = TimeSeriesSplit(n_splits=5)
for train_idx, test_idx in tscv.split(X):
    # train_idx always precedes test_idx chronologically
    X_train, X_test = X[train_idx], X[test_idx]
    y_train, y_test = y[train_idx], y[test_idx]

Flashcards

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Question

What are the four components of a time series?

Click to reveal

Answer

1) Trend — long-term direction. 2) Seasonality — regular repeating patterns at fixed intervals. 3) Cyclical — long-term fluctuations without fixed period. 4) Residual — random unexplained variation (noise).