1988issue C041-5
Serial correlation is not an independence test
A serial correlogram tallies how prices pair at a stated lag and summarizes that pairing with a coefficient. The same reading is a reliable test of correlation and a weak gauge of statistical independence.
- A serial correlogram is a pairing grid: each price is matched to another at a stated lag and the matching cell is incremented.
- The coefficient marks matching, none, or inverse association; a t statistic from that coefficient and n minus 2 degrees of freedom must exceed 2.0 before sequential prices are treated as correlated.
- Trend, mixed-direction pair cells, and jitter pull the coefficient toward zero and can hide a sequential pattern the grid still shows.
- Serial correlation is a reliable test of correlation and a weak, inadequate test of independence-style market hypotheses.
A pairing grid, not a trading signal
The autocorrelation test is a same-series pairing test. It tallies how values at a stated lag travel together and summarizes that pairing with a coefficient, not a trading signal.
A lag-1 serial correlogram is built by pairing each price with the immediately prior price and incrementing the matching cell for every sequential pair. A lagged serial correlogram pairs prices separated by a chosen interval.
The same interval may be labeled differently depending on whether intervening observations are counted. The lag convention must be confirmed before the grid is interpreted.
What the coefficient marks
Linear regression is the straight-line association measure behind the serial coefficient. It scores how one member of each ordered pair tracks the other from inverse through none to matching.
The serial correlation coefficient is bounded by +1, 0, and -1, marking matching high-or-low pairing, no pairing association, and inverse pairing respectively. Those meanings do not depend on the lag.
When a coefficient is treated as nonzero
A follow-up t statistic asks whether an observed coefficient is distinguishable from zero given the number of pairs. A coefficient is treated as different from zero when that t statistic, formed from the coefficient and n minus 2 degrees of freedom, exceeds 2.0.
A smaller t means sequential prices are not treated as correlated even if the coefficient is nonzero.
A worked pairing count
In the worked series the coefficient uses 50 pairs, a price sum of 202, a sum of squared prices of 1,070, and a paired-product sum of 837. With few prices, the last and first observations are also treated as a pair.
Trend warps the reading
A trend in the raw series tends to warp and shrink the measured coefficient.
To remeasure pairing after removing trend, price changes can be shifted onto a strictly positive scale. For a change range of -10 to 9, adding 11 maps the series onto 1 to 20. The correlogram, the coefficient, and the t statistic are then recomputed on those detrended changes.
Mixed pair cells and jitter
When a lag mixes matching-direction pairs with opposite-direction pairs, the coefficient is pulled toward zero. The same pull appears when a related second price jitters across a wide band. In both cases a genuine sequential pattern can be missed.
A weak gauge of independence
Serial correlation at any lag is a weak gauge of statistical independence. That makes it an inadequate test of independence-style market hypotheses, even though the same procedure remains a reliable test of correlation itself.
All readings on this track · 15 readings
- 1987Evaluating weekly price cycles with autocorrelation cutoffs
- 1988Serial correlation is not an independence test
- 1988Event-triggered chi-square tests for jittered serial links
- 1988Reverse the rule before you trust the system
- 1990Chi-square evaluation of lagged breadth correlations
- 1990Two-gate out-of-sample tests for trading rules
- 1990Sign-cell correlation, chi-square checks, and lag shifts
- 1998Test serial dependence before you optimize a mechanical system
- 2003How a one-rank rotation is constructed for an offset autocorrelation check
- 2004Constructing first-order residual autocorrelation tests
- 2004A two-stage Durbin-Watson residual screen
- 2011Constructing trend labels from increment correlation atoms
- 2012Overnight versus daytime return evaluation
- 2012Constructing a multi-horizon folded-correlation reversal filter
- 2016Tuning indicators to measured market cycles