Week 7: Time Series & Trends

STAT 80B - Data Visualization

Overview

Topics for this week:

• Time series visualization fundamentals
• Multiple time series and comparisons
• Connected scatter plots
• Smoothing techniques (LOESS, moving averages)
• Trend lines and regression visualization

Reading: Wilke Ch 13-14

What is a Time Series?

A time series is a sequence of data points measured at successive time intervals.

• One variable changes over time
• Time imposes a natural order on data
• We care about trends, patterns, and changes

Examples:

• Daily temperature readings
• Stock prices over months
• Monthly preprint submissions
• Annual CO₂ emissions

Why Visualize Time Series?

1. Identify trends - Is there an overall increase/decrease?
2. Spot patterns - Are there seasonal effects or cycles?
3. Detect anomalies - Are there unusual events or outliers?
4. Make comparisons - How do multiple series relate?
5. Communicate change - Show temporal evolution clearly

Basic Time Series: Scatter Plot

Approach: Plot time on x-axis, variable on y-axis

When to use

When you want to emphasize individual data points and their exact values

Example: Monthly submissions to bioRxiv preprint server

• Each dot = one month’s submissions
• Shows steady growth over time
• Individual points are visible

See example here

Line Graphs

Connect the dots to emphasize continuity

Key principle

Lines suggest continuous change between time points

When to use line graphs:

• Data collected at regular intervals
• Want to show overall trend/pattern
• Have many time points
• Continuity between points makes sense

See example here

Line Graph Best Practices

1. Always start y-axis at zero (unless there’s a good reason not to)
2. Label axes clearly with units
3. Use appropriate time intervals on x-axis
4. Don’t overplot - too many lines = confusion
5. Consider aspect ratio - affect perception of trends

Common mistake

Manipulating the y-axis range to exaggerate or minimize trends

Area Charts

Fill the area under the line

When to use

• Emphasize magnitude/cumulative effect
• Compare proportions over time
• Show “weight” of the trend

Important: Y-axis must start at zero!

Why? The area represents the quantity - if you don’t start at zero, the visual is misleading

Multiple Time Series

Challenge: How to compare multiple series effectively?

Options:

1. Multiple line graphs (same plot)
2. Small multiples (facets)
3. Stacked areas (for parts of a whole)

See example

Multiple Lines: Design Choices

Direct labeling vs. Legend

• Direct labels (preferred): Place labels near the lines
  • Reduces cognitive load
  • Easier to match line to label
  • More professional appearance
• Legend: Use when space is limited
  • Can be far from the data
  • Requires back-and-forth eye movement

Multiple Lines: Color Strategy

Use color purposefully:

1. Highlight what matters - Make one line stand out
2. Use colorblind-friendly palettes
3. Consider line types - solid, dashed, dotted
4. Limit the number - 3-5 lines maximum for clarity

Pro tip

When comparing many series, consider small multiples (facets) instead

Small Multiples for Time Series

Same scale, different panels

Advantages:

• Easy to compare across categories
• Reduces overplotting
• Each series gets its own space
• Patterns more visible

When to use: 5+ time series to compare

See example

Work in pairs: The Overcrowded Plot

The Problem:

A colleague shows you a draft visualization: 8 countries’ COVID-19 trends on one plot as different colored lines (red, blue, green, orange, purple, yellow, pink, brown) with a legend.

Work in pairs: The Overcrowded Plot

Your task (Part 1)

1. Name TWO problems with this design
2. What would you do instead? Choose ONE:
   • Multiple lines with direct labeling
   • Small multiples (facets)
   • Highlight one, gray out others
   • Other approach?

Post your answers on Ed Discussion

Connected Scatter Plots

Plot two variables against each other, connect points in temporal order

Also called

Phase portrait, trajectory plot

Purpose:

• Show relationship between two variables
• Reveal cyclical patterns
• Display multi-dimensional change over time

See Example

Connected Scatter Plots: Example

House price changes vs. unemployment rate

• Each point = one time period
• Connected in chronological order
• Can use color/size to show time
• Reveals counter-clockwise spiral pattern

Important

Readers more likely to confuse order/direction compared to line graphs, but higher engagement!

When to Use Connected Scatter Plots?

Good for:

• Two variables changing together over time
• Showing cyclical relationships
• Engaging storytelling
• Phase space representations

Not ideal for:

• Reading exact values
• Simple time trends (use line graph)
• More than 2 variables at once

Smoothing Techniques

Goal: Reveal the underlying trend by reducing noise

Why smooth?

• Raw data can be noisy/jumpy
• Want to see the “big picture”
• Identify long-term trends vs. short-term fluctuations

Moving Averages

Technique: Average over a sliding window

Example: 7-day moving average

• Each point = average of that day + surrounding days
• Smooths out day-to-day variability
• Window size affects smoothness

Choosing window size

• Larger window = smoother, loses detail
• Smaller window = retains detail, less smooth

Moving Average Types

1. Simple moving average
   • Equal weights for all points in window
2. Weighted moving average
   • Center points weighted more heavily
3. Exponential moving average
   • Recent data weighted more heavily
   • Common in financial analysis

LOESS Smoothing

LOESS = LOcally Estimated Scatterplot Smoothing

How it works:

1. For each point, fit a local regression using nearby points
2. Use weighted distances (closer points = more weight)
3. Produces smooth curve through the data

Parameters:

• span or bandwidth: controls smoothness
  • Smaller span = more wiggly, follows data closely
  • Larger span = smoother, more general trend

LOESS: Strengths and Weaknesses

Strengths:

• No assumption about functional form
• Flexible, adapts to local patterns
• Good for exploratory analysis

Weaknesses:

• Can overfit with too small span
• Computationally intensive for large datasets
• Cannot extrapolate beyond data range

Trend Lines with Defined Functional Form

Alternative to smoothing: Fit a mathematical model

Common forms:

1. Linear: \(y = A + mx\)
   • Straight line trend
   • Constant rate of change
2. Exponential: \(y = A \cdot e^{bx}\)
   • Exponential growth/decay
3. Polynomial: \(y = A + Bx + Cx^2 + ...\)
   • Curved trends

Linear Trend Lines

When to use:

• Relationship appears approximately linear
• Want to quantify rate of change
• Need to make predictions

How to fit:

• Ordinary least squares (OLS) regression
• Minimize sum of squared residuals
• Get slope and intercept

Linear Regression for Trends

In R:

ggplot(data, aes(x = time, y = value)) +
  geom_point() +
  geom_smooth(method = "lm", se = TRUE)

Key options:

• se = TRUE: Show confidence band
• method = "lm": Linear model
• Can add formula = y ~ x for control

In Tableau

Non-linear Trend Lines

Polynomial regression:

geom_smooth(method = "lm", 
            formula = y ~ poly(x, 2))

Other options:

• Exponential models (transform or use nls)
• Logistic growth models
• Periodic functions (sine waves for seasonality)

Warning

Be careful of overfitting with high-order polynomials!

Confidence Bands

Show uncertainty in the trend estimate

• Wider bands = more uncertainty
• Typically 95% confidence interval
• Curve at the edges (more uncertainty far from center)

Graded confidence bands:

• Show multiple confidence levels (50%, 80%, 95%)
• Emphasizes increasing uncertainty
• Forces reader to confront uncertainty

See example

Detrending

Remove the trend to see what’s left

Why?

• Isolate seasonal effects
• Identify anomalies/outliers
• Understand cyclical components

Residuals = Actual values - Trend

Before and After

Example: The Keeling Curve

CO₂ measurements at Mauna Loa

Decomposed into:

• Long-term trend: Steady increase (~50 ppm over 30 years)
• Seasonal fluctuation: Annual cycle (~8 ppm range)
• Remainder: Small random variation (~1.6 ppm)

Shows: Seasonal effects are real but small compared to overall trend

See results here

Choosing the Right Visualization

Use line graphs when:

• Single or few time series
• Regular time intervals
• Want to show trends
• Need to compare series

Use connected scatter plots when:

• Two variables over time
• Cyclical relationships
• Engaging narrative
• Phase space analysis

Choosing the Right Visualization (cont.)

Use smoothing when:

• Data is noisy
• Want overall trend
• Exploratory analysis
• Don’t know functional form

Use trend lines when:

• Have theoretical model
• Want to quantify change
• Need to predict
• Relationship is clear

Work in pairs: Choose Your Viz

Scenario 2: Noisy Daily Temperatures

Climate scientist has daily temperature data for one year (very noisy, day-to-day fluctuations). Goal: show if there’s an overall warming trend.

Best choice?

• 1. Simple line graph
     
• 2. LOESS smoothing
     
• 3. Linear trend line

Post on Ed Discussion

Common Pitfalls to Avoid

1. Truncated y-axis (when area is used)
2. Too many lines on one plot
3. Poor color choices (not colorblind-safe)
4. Ignoring uncertainty
5. Overfitting with too complex models
6. Wrong smoothing bandwidth
7. Forgetting units on axes

Best Practices Summary

✓ Choose appropriate visualization for your story

✓ Use direct labeling when possible

✓ Show uncertainty (confidence bands)

✓ Consider aspect ratio and scale

✓ Keep it simple - avoid chart junk

✓ Test for colorblind accessibility

✓ Label everything clearly

Preparing for Lab 4

This week’s lab will cover:

• Creating scatter plots (bivariate and multivariate)
• Time series with trend lines
• Bubble charts

Important Reminder

This course is NOT about learning tools

The software (Tableau, R, Python) is a tool - a means to an end.

What matters:

• Understanding visualization principles
• Choosing appropriate charts
• Communicating effectively with data
• Critical thinking about design choices

Learning the tool requires practice: trial and error, experimentation, exploration!

Tips for Lab Success

1. Don’t just follow instructions - understand WHY
2. Experiment - try different chart types
3. Ask yourself: “Does this visualization tell the story clearly?”
4. Review the material before class come prepared, download the data and examine it on your own
5. Learn by doing - make mistakes and fix them
6. Compare outputs - how does Tableau differ from R/Python?
7. Think before you code/click

Next Class

Thursday: Lab 4

• Hands-on practice with:
  • Time series visualizations
  • Trend lines in Tableau/R/Python

Come prepared to experiment!

Questions?

Time for discussion and clarification

Office hours: today after class. Bring your questions about the project, class material, or any other concern.

Resources:

• Textbook
• Lab 4 materials
• TidyTuesday datasets
• Tableau How-to videos