📊 Part 1: Time Series Components

1. Which of the following best describes a trend in time series data?

Regular patterns that repeat over fixed periods

The long-term direction of movement in the data

Random fluctuations with no pattern

Short-term variations around the trend

2. Identify all components that are typically found in time series data:

Trend

Seasonal variation

Cyclical variation

Irregular variation

Standard deviation

3. A shop's ice cream sales show higher values in December-February each year. This is an example of:

Trend

Seasonal variation

Cyclical variation

Irregular variation

📈 Part 2: Moving Averages and Smoothing

4. Calculate the 3-period moving average for the following Auckland temperature data (°C):
Week 1: 18°C, Week 2: 21°C, Week 3: 24°C, Week 4: 19°C, Week 5: 22°C

5. Why do we use moving averages in time series analysis?

6. The quarterly sales data (in thousands of dollars) for a Wellington company shows:
Q1: $45k, Q2: $52k, Q3: $48k, Q4: $61k, Q1: $49k, Q2: $56k
Calculate the 4-quarter moving average where possible:

🔍 Part 3: Analysis and Interpretation

7. A time series graph shows New Zealand's monthly rainfall data. The trend line slopes downward from left to right. What does this indicate about rainfall patterns over time?

8. Describe the difference between seasonal variation and cyclical variation in time series data:

9. A company's monthly sales data shows an overall increasing trend but with regular dips every December. Explain what time series components are present and suggest why this pattern might occur: