The Currency Times

Notation

Every symbol used across the site, and the conventions it follows. Nothing here should require a reader to guess.

Conventions

Variables are set in italic, operators upright. The differential is an upright following the international convention, not an italic one. A hat denotes an estimate rather than the true value, so is what was calculated and is what is unknown. A tilde means is distributed as. An asterisk marks an optimum.

Anatomy of an expression

One equation from the mean reversion field, annotated. Every convention on this page is visible in it.

dXt = θ (μ Xt ) dt + σ dWt UPRIGHTan operator, here a differential ITALICa variable, the thing that changes SUBSCRIPTindexed by time GREEKa parameter, estimated rather than observed Wthe random part, a Wiener process

Read it as a sentence: the change in the thing equals how fast it is pulled, times how far it currently sits from where it settles, plus a random shove. All five conventions are doing work, and none of them is decoration.

Time and indexing

Discrete time index
Window length in periods
Total sample length
Lag
Backshift operator
First difference or change

Random variables and processes

The process and the price level
Return over one period
Standard Wiener process
Innovation, or shock
Latent regime state
Integrated of order zero, stationary

Moments and statistics

Mean, or long-run level
Standard deviation and variance
Correlation
Standardised score
Hurst exponent, or entropy in context
Price impact coefficient
Speed of mean reversion
Model weights, and significance level in testing

Probability and inference

Probability
Probability of A given B
Expected value
Null hypothesis
Proportional to
Is distributed as
Inverse standard normal
Euler-Mascheroni constant

Validation

Score of a candidate model
Number of trials in a search
Number of hypothesis tests
Family-wise error rate
Effective sample size
Growth-optimal fraction

Market conventions

Moving average at t
Average true range
Realised volatility
Implied volatility
Signed order size
Interest rate differential
NextErratawhat we have had to correct