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The Chronological Data Models Compendium
This compendium gathers the ideas that a careful student meets when following a single thread: how a random quantity settles into a shape, how two such quantities share that shape, and how a run of them changes as time passes. It is arranged as five ascending steps, each holding three short papers, so that the reading builds from a single bell to the spectral view of a long series.
Why a compendium rather than a course
A course demands attendance, deadlines and a teacher's voice. A compendium asks something quieter from its reader: patience, and a willingness to return to a paragraph until the symbols stop resisting. Every page here is written to stand alone, yet also to carry forward a habit of notation built on the pages before it. You may begin at the first step and climb, or you may enter at any tile that catches your attention and work outward from there.
The five steps at a glance
Step 01 — Distributions
The normal curve read from its centre outward, moments and expectation as summaries, and the empirical quantile tables that turn a sample into a readable ladder.
Step 02 — Densities and Matrices
Joint density surfaces in two variables, the anatomy of a covariance matrix, and the clean conditional forms that the Gaussian law permits.
Step 03 — Stochastic Series
Random sequences laid out over time, the meaning of stationarity, and the slow decay of autocorrelation that tells a series apart from a shuffle.
Step 04 — Spectral and Models
The spectral density as a portrait of how variance is spread across frequencies, the autoregressive and moving-average forms, and the ergodic promises that make one long record informative.
Step 05 — Reference
Terms and notation in one place, the editorial aims behind the compendium, and a way to reach the desk that keeps it.
How to cite
Each paper carries its own heading so that a reader may quote a single section without carrying the whole compendium along. Use the title of the paper together with the step name.
A single thread, followed honestly
The temptation with statistics is to memorise a formula and move on. This compendium resists that temptation in a small way. When a variance appears, it is first described in words, then drawn, then written as a symbol; only then does it earn its place in an equation. The reader who wants only the symbol will find it, but the reader who wants the reason will find that too, sitting beside it.
Time is the second thread. A quantity observed once is a snapshot; a quantity observed again and again becomes a record, and a record has texture. Some of that texture is noise and some of it is memory. Telling the two apart is the central labour of the later steps, and it is why the compendium waits until the density and the matrix are secure before it turns to the series.
What the compendium does not claim
Nothing here is a substitute for a full course of study, and nothing here is offered as professional guidance of any kind. The papers describe settled mathematical ideas for readers who wish to understand them. Where a choice of notation could be made in several ways, the compendium states its choice plainly and holds to it, because consistency is a kindness to a reader moving from page to page.
Where to begin
If you are new to the material, open the first step and read its three papers in sequence. If you already know the normal curve well, begin with the covariance matrix and let the later steps pull you toward the series. Whichever door you choose, the rail above will always show you the step you are standing in, and the panels will show you the two companions that share it.