1996issue C041-4
Constructing a log-change stationarity screen with regression or binomial tests
A level series is rewritten as period-to-period log changes. A stationarity-split chi-square-test and a serial-dependence-screen are locked next. A spreadsheet linear-regression or a binomial-probability-model for a hit count is then attached as the specified in-sample construction.
- Apply a log-change-transform so later tests use period-to-period log changes rather than raw levels.
- A stationarity-split chi-square-test on five to ten bins is read against a tabled critical value at the 0.05 probability level.
- After stationarity is accepted, a serial-dependence-screen compares mass inside and beyond 1.96 standard deviations of the mean with a normal shape.
- Editorial: attach a linear-regression or a binomial-probability-model only after those screens so a later out-of-sample check has a fully specified in-sample baseline.
A level series is prepared for later tests with a log-change-transform. Take the logarithm of each observation and subtract the prior-period logarithm to obtain period-to-period log changes. The historical workflow then builds a stationarity construction and a serial-dependence-screen before a linear-regression or a binomial-probability-model is specified.
Convert levels with a log-change-transform
Replace each level with the difference between its logarithm and the prior-period logarithm before any later test. The resulting period-to-period log changes are the series that the stationarity and serial-dependence constructions receive.
Build the stationarity-split and chi-square-test
The stationarity construction divides the series range into five to ten equal-width bins and leaves the two extreme bins unbounded away from the mean. A stationarity-split then counts the same bins in the first half of the sample and in the second half so the chi-square-test can treat one half as expected and the other as observed.
The chi-square-test is built from cumulative bin frequencies as the sum of squared observed-minus-expected differences divided by the expected values, with degrees of freedom equal to the number of bins minus one. The finished total is compared with a tabled critical value at the 0.05 probability level. A larger total is treated as nonstationary and a smaller total as stationary.
Lock the serial-dependence-screen
After the stationarity screen, and once stationarity is accepted, the serial-dependence-screen records the share of observations inside 1.96 standard deviations of the mean and the shares beyond that distance in each tail. The same chi-square-test layout is then applied to those three observed shares against the proportions expected if the series followed a normal shape with no serial dependence.
Specify the linear-regression or binomial-probability-model
A linear-regression construction in a spreadsheet is specified by identifying the input series and the output range so the software can write the fitted baseline.
A binomial-probability-model for a hit count is the closed-form probability of that count given the sample length, the success chance, and the complementary miss count. It is constructed as the number of observation-orderings that produce the count, multiplied by the success probability raised to the hit count and the complementary probability raised to the miss count.
All readings on this track · 7 readings
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