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Week 1: Mastering Trend Analysis

NCEA Level 3 Statistics (Time Series 3.8)

Introduction to Time Series

Scenario: You are an analyst for Tourism New Zealand. You need to report on visitor numbers to help hotel chains plan future capacity.

Before we look at the seasonal bumps, we need to understand the Long Term Trend. Imagine wearing "Trend Glasses" that blur out the monthly spikes and only show the smooth movement.

Tip: The Green line is the Trend. The Black line is the Raw Data. For this week, ignore the black spikes and focus on the green path.

How to Write About Trend

Look at the graph below (Visitor Arrivals). Try to describe what is happening to the trend before seeing the criteria.

Draft your description here:

🔵 Achieved: The "What"

Requirement: Describe the overall direction.

Example: "Overall, there is an increasing trend in the number of visitor arrivals to New Zealand from 2000 to 2024."

🟠 Merit: The "Quantification"

Requirement: Add Start/End values and the Average Rate (Gradient).

Example: "The trend starts at approx 130,000 visitors in Jan 2000 and rises to approx 320,000 visitors in Jan 2020. This is an average increase of about 9,500 visitors per year."

🔴 Excellence: The "Context & Nuance"

Requirement 1: Piecewise Detail. Don't just give one average. Calculate the gradient for different sections to show *how* the rate changed.

Requirement 2: References. Link changes to real-world events and cite a source.

Example: "The trend is not consistent.
• 2000-2008: Steady growth (approx +5,000/year).
• 2008-2010: The trend flattens (rate ≈ 0). This corresponds to the Global Financial Crisis [Source: Reserve Bank NZ].
• 2010-2019: The growth accelerated to +15,000/year, driven by the tourism boom.
• 2020: A catastrophic drop due to COVID-19."

Guided Practice: Arctic Sea Ice

Challenge: This graph looks "boring" because it just goes down. How do we get Excellence if there are no big spikes to talk about?

Strategy: Look for Acceleration. Is the line getting steeper? Calculate the gradient for the first half vs. the second half.

Your Turn

1. Achieved (Direction): 2. Merit (Overall Rate): 3. Excellence (Enriched Analysis): Compare the rate of drop in the 1990s vs the 2010s. Cite a likely cause.

Excellence Model Answer (Handling Monotonic Trends):
"Overall, there is a decreasing trend. However, the rate of decline is accelerating.

Between 1990 and 2005, the ice decreased from 6.8 to 6.2 million sq km, a rate of roughly -0.04m per year.
However, from 2005 to 2024, it dropped from 6.2 to 4.2 million sq km, a much steeper rate of -0.10m per year.

Context: This acceleration aligns with reports on Global Warming feedback loops, where less ice reflects less sunlight, speeding up further melting [Source: NASA Climate Data]."

Solo Exercise: Penguin Colony

Context: A conservation group monitors a Yellow-eyed Penguin colony. Write a paragraph describing the trend.

Write your Report Paragraph

Excellence Self-Assessment Checklist

Did I state the overall direction? Did I calculate the Average Rate for the whole period? Piecewise: Did I calculate separate rates for the stable periods vs the drop? Context: Did I identify the specific year (2015) the change happened? Reference: Did I suggest a reason (e.g. disease) and mention that I would verify this with a source (e.g. DOC website)?

Teacher Feedback:
A secured Excellence answer would quantify the magnitude of the shock.
"The population was stable at ~1200 until 2015. In 2015, the trend line plummeted to 800, and continued to drop to 400 by 2016. This represents a 66% loss of population in just two years. Such a rapid decline suggests an acute event like a disease outbreak or mass starvation event [Source needed: e.g., Dept of Conservation reports]."