Normal Distribution
nothing is called 95% until it has been counted
Concept

Augmented dickey fuller — where it appears

A regression of a series' change on its own previous level, used to test whether that level wanders without returning. Its statistic is computed as a t and is not one, so the value it is read against has to be simulated for the specification actually run.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

Also named here as deterministic trend, near-unit root, trend-stationary — the same set of essays touches all of them, so they are one junction rather than several.

The damage and the warning, against the same dial. Two readings at each persistence. In the darker colour, how often a regression between two independent series of 200 steps is called significant at 5%: 4.9% at φ = 0, 34.2% at 0.8, 52.4% at 0.9, 83.4% at a unit root. In the lighter, how often the standard unit-root test refuses a unit root on one of those series — the chance the analyst is told the series is stationary and may be regressed: 87.2% at φ = 0.9 and 31.9% at 0.95. At φ = 0.9 both are high at once, which is a correct diagnostic licensing a regression that is wrong half the time.

The cliff that is a slope

A regression between two independent series is called significant 4.9% of the time at no persistence, 52.4% at a lag-one correlation of 0.9, and 83.4% at a unit root. The rule the field offers asks whether the last of those holds, and at 0.9 the unit-root test correctly refuses one 87.2% of the time.

timeseries · Spurious Six cells, and 5% is the right answer in all of them. How often a regression between two independently generated series is called significant at the 5% level, for two worlds and three treatments, at 200 observations. Every pair is independent by construction, so 5% is correct everywhere and every other reading is a failure. Untreated: 82.9% and 100.0%. With a fitted line removed: 74.2% and 33.5%. Differenced: 5.0% and 5.2%. The treatment that controls the rate in both worlds is the one that discards the level and the trend, which is the quantity a study of trending series was about.

The repair that keeps the question

A regression between two independent trending series is significant 82.9% of the time on random walks and 100.0% on trend-stationary ones. Subtracting a fitted line leaves 74.2% and 33.5%; differencing leaves 5.0% and 5.2% and throws away the trend the study was about.

timeseries · Spurious

Named alongside it

The objects these essays reach for when they reach for this one.

AutocorrelationClosed formDeterministic trendFalse positiveNear-unit rootR²Random walkSpurious regressionStationarityStatistical powerTrend-stationaryUnit root

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