Moving Averages Method 🌊

Moving Averages (MA) is a technique to smooth out short-term fluctuations to reveal the underlying trend. It essentially filters out the "noise" (seasonal/irregular) from the data.

1. Odd Period Moving Average (3-Yearly, 5-Yearly) 🟢

This is simple because the average can be centered exactly against the middle year.

Steps for 3-Yearly MA:

1. 3-Year Moving Total: Add values of Year 1, 2, 3. Place total against Year 2. Then add Year 2, 3, 4. Place against Year 3. And so on.
2. 3-Year Moving Average: Divide the totals by 3.

Example (3-Yearly)

(Note: First and Last years lose their trend values)

2. Even Period Moving Average (4-Yearly) 🔴

Since 4 is even, the middle falls between two years (e.g., between 2nd and 3rd). We need an extra step called Centering.

Steps for 4-Yearly MA (Centered):

1. 4-Year Moving Total: Add 1, 2, 3, 4. Place "between" Year 2 and 3.
2. Centering (2-Item Sum): Add the first 4-Year Total and second 4-Year Total. This sum now corresponds to Year 3.
3. 4-Year Moving Average: Divide the Centered Sum by 8 (since it sums 8 items effectively: 4+4).

^ Alternatively, just take average of the two 4-year averages.

Example (4-Yearly)

• Logic: The first total (20) is for "2011.5". The second total (26) is for "2012.5". Their average corresponds to 2012.

When to use which period? 📅

• The period of moving average should coincide with the period of the cycle in the data.
• If data shows a cycle of 3 years (up-down-up every 3 years), use 3-yearly MA.

Summary

• Odd Period (3, 5): Easy, center aligns with a year.
• Even Period (4): Needs Centering step.
• Result: A smooth trend line (Trend values).
• Data Loss: You always lose some values at the start and end.

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