A level regression can mistake two independent asset-price paths for an economically valuable hedge. That is dangerous because the familiar OLS output—high , large -ratios, narrow confidence intervals—assumes the stationary setting introduced in time-series foundations. A unit root breaks that setting.
This note establishes the I(0)/I(1) distinction, shows why independent random walks generate spurious regressions, and separates a stochastic trend from a deterministic one. The next lesson makes the diagnosis formal; later lessons retain I(1) level combinations when cointegration supports them. I(0) levels can be modelled directly.
Learning objectives. By the end of this note you should be able to:
- define I(0), I(1), and a unit root using the lag operator;
- distinguish a random walk with drift from a trend-stationary process;
- identify the empirical symptoms of a spurious regression;
- explain why differencing is a repair but not a universal default.
In this lesson
- Integrated processes are shocks with memory
- The unit-root representation
- Why a convincing regression can be worthless
- Difference, detrend, or keep levels?
Before you start
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