How is the differenced series $z_t$ defined from the original series $q_t$?

Conditions

• The original series is indexed by time $t$.
• The values represent observations at discrete time points (e.g., months).

Reasoning, step by step

1. Identify the original series values $q_t$ and $q_{t+1}$.
2. Subtract the current value $q_t$ from the next value $q_{t+1}$.
3. Assign the result to the new series variable $z_t$.
4. Use the example of monthly anchor sales: February sales minus January sales equals one point of the differenced series.

Example

The board explicitly writes the formula $z_t = q_{t+1} - q_t$. The speaker explains it using an anchor sales example: "taking your number of anchors sold in thousands at some month, let's say February, minus the number of anchors sold in thousands from the previous month, say January."

Common misconceptions

• Calculating $q_t - q_{t+1}$ instead of $q_{t+1} - q_t$.
• Thinking $z_t$ represents the average of the two values.
• Confusing the differenced series with the original level series.

Watch the explanation

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