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04 · Random walk or not

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Time Series, lesson 4

Random walk or not

Testing whether a series has any memory at all.

You know autocorrelation, and that volatility grows with the square root of time when days are independent.

Part 1. Original or shuffled?

Each pair below is one simulated price and the same daily moves in a shuffled order. Shuffling keeps every move and throws away their order. Spot the original.

Original or shuffled?Live

A shuffle has the same daily moves, so the same volatility. What it loses is any link between them. If moves lean on each other, the original travels further than its shuffle over many days. If they undo each other, it travels less. If they're independent, the two look alike, and nothing can tell them apart.

Random walk

A series where each step can't be predicted from the steps before: price today = price yesterday + a move nobody could forecast. Its returns have no memory. Asking "is this price a random walk?" asks whether past returns help predict future ones.

Your turn

A price follows a random walk with no drift. What's the best forecast of its price a week from now?

Every future move is unpredictable and averages zero, so the best guess for any future date is today's price. That's why "tomorrow equals today" is the baseline every price forecast has to beat, which "Forecasting honestly" builds on.

Part 2. The variance ratio

Keep going with Pro

You've done the first part. Pro opens the rest of this lesson, and every other one.

Still to come
  1. The variance ratio
  2. A worked problem
  3. The same thing, for real
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Next lessonStationarityWhich series you can model directly, and how to transform the rest. Start lesson 5

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