Time Series
A time series is a set of data points collected or recorded at regular time intervals over a period of time. It allows you to track how a variable changes and to look for patterns such as trends, seasonal effects, or cycles.
A time series is an ordered sequence of observations measured at successive, typically equally spaced points in time . Time series analysis involves decomposing the data into components—trend, seasonal variation, cyclical fluctuation, and irregular (random) variation—to describe the underlying behavior and, where appropriate, to forecast future values.
Example
Problem: A coffee shop tracks its monthly sales (in thousands of dollars) over one year: Jan 10, Feb 11, Mar 13, Apr 14, May 16, Jun 18, Jul 20, Aug 19, Sep 17, Oct 15, Nov 13, Dec 12. Describe the overall pattern.
Step 1: Plot the data with time on the horizontal axis and sales on the vertical axis. Each month gets one point, connected in order.
Step 2: Look for a trend. Sales rise from January (20k), then fall back toward December ($12k). There is no consistent long-term upward or downward trend over this single year—instead, sales rise and fall.
Step 3: Identify any seasonal pattern. The peak in summer months and the dip in winter suggest a seasonal component, likely tied to weather or customer habits.
Step 4: Note irregular variation. The drop from July (19k) is slight and may be random fluctuation rather than part of a smooth curve.
Answer: The time series shows a seasonal pattern with sales peaking in summer (July, 10k). No strong long-term trend is visible within this single year of data.
Visualization
Why It Matters
Time series data appears everywhere—stock prices, temperature records, monthly unemployment rates, and website traffic all vary over time. In AP Statistics, understanding time series helps you distinguish genuine trends from seasonal effects or random noise, which is critical for making sound predictions and informed decisions.
Common Mistakes
Mistake: Treating time series data like independent observations
Correction: Observations close together in time are often correlated (autocorrelation). Standard regression assumptions may not hold, so you need to account for the time-dependent structure rather than treating each point as independent.
Mistake: Confusing a seasonal pattern with a long-term trend
Correction: A seasonal pattern repeats at regular intervals (e.g., every 12 months), while a trend is a sustained increase or decrease over a longer period. Always examine several cycles of data before concluding a trend exists.