C4 — Exogenous inputs to the current VEC, dispatched by their order of integration, as in drtran. The VEC without inputs is the base, and the LR against it is the test.

An input of the SAME order (I(1), a series of the system): series names it; it stays in the system with its alpha row at zero and none of the others' short run (drvec -xsys: STRONG exogeneity, the LR against the free VEC). It cannot be in the Y1 block, and drvec needs q = 0.

An input of ANOTHER order (an I(0) input on I(1) outputs): inputs are its fue files (a JSON list or comma-separated; their .pre stays frozen) and links the network, "OUT <- IN b r s; OUT2 <- IN b r s" (r <= 2): it is subtracted in levels (drvec -xpre/-xlink). drvec fits the VEC without the inputs first; with omega = 0 the bridge must reproduce it. Refused by drvec (inherited): a rank test with inputs (the rank is C1's, without them), -xlink with forecasts or bootstraps, -xsys with q > 0 or with a restriction on alpha. adopt makes the fit with inputs current.

N0u — ROUTE U from raw data (docs/STUDY-raw-entry.md): build each series' univariate model with art's engine, then climb the ladder as always (Jenkins and Alavi: the univariate models first).

On each series' characterization (characterize): the orders art ranks first, the mean (d = D = 0) or a drift kept only if |t| >= 2, a fue fit, a residual check; <SERIES>_u.inp/.pre/.out written to out_dir (default: <data>_sima/ next to the table). Every .pre carries the line "Built by sima's raw entry (route U), not reviewed in art". This is art's autonomous lane in miniature — no over-parameterisation, calendar effects, formal tests or interventions: the report offers art for any series with a tie or a residual problem.

It then opens the ladder session of the same name with those files (the guion goes on): next, run_gate. Existing files are kept unless overwrite.

N1b — Box and Tiao's (1977) canonical analysis of the transformed LEVELS (each series' Box-Cox and seasonal differences; NOT its regular ones): the combinations of the series ordered from least to most predictable. Nearly white ones are relations among the series that stay stable over time; nearly non-stationary ones (sqrt(lam) >= near, the scale of a root: for an AR(1) component lam = phi^2) their common growth. When two or more series are differenced and fewer components look non-stationary, the joint model may not need every difference — the question of cointegration, which N1c asks (prepare_vec) and C1 answers (rank_test, by parametric bootstrap on drvec); this reading is not a test, and sima never changes a d on its own. p is the VAR order (0: the last significant M(l) of Tiao and Box's stepwise table on the levels). Run it after the gate, before the identification, when two or more series are differenced; with raw data (load_data, characterize), right after characterize, on the characterization's levels.

N0c — Each raw series' transformation, with art's engine and in art's order: lambda (Box-Cox, 0 or 1), d (ADF + KPSS, art's policy: one step at a time), seasonality (HAC F-test; harmonics proposed when detected) and a preliminary outlier scan (reported, not treated). Each series keeps its OWN lambda and d — no joint consensus: forcing them alike was the old sima's first fault.

set records the analyst's changes on top of the proposal: "MINK: lam=0, d=0; MUSKRAT: d=1, harmonics=no" (keys lam, d, D, harmonics). It is the starting point of both routes (U: the univariate models first; V: the vector first).

N4 — Check the last estimated model as Jenkins and Alavi (1981, §5.2) do, and show it as art's diagnosis: the report, then the figures.

The report: 1 · TABLE — (1) the large residuals, judged on the UNCORRELATED transformed residuals (the a_it correlate at lag 0, so one by one they cannot be judged), with their dates — a known cause goes to intervention analysis, in art, before anything else is read; (2) the residual correlation matrices R_k(a), with what is beyond the band; (3) the portmanteau matrix Q_ij, as a summary. 2 · WHAT IT SHOWS, 3 · CONCLUSIONS, 4 · DECISION. If the matrices show structure, a model for the residuals is entertained and combined with the fitted one, as at identification.

The figures, as drvus drew the diagnosis and their figure 7: fue's panel for each residual series (the residuals with +-2 bands, the acf with its Q, the pacf), and the residual ccf of each pair (GraphMaker's, with Hosking's P). nlags (the matrices) defaults to max(6, frequency). The portmanteaus keep at least 2 lags beyond the parameters: the legacy lags move up when a long model in annual data would leave none.

N3/N4 — Estimate a candidate: cross orders p, q; full or diagonal covariance.

Each series keeps its univariate model on the diagonal (its ARMA factors are re-estimated jointly, its deterministic terms stay as in its file). Reports the parameters, the LR test against the univariates (in sample: necessary, not sufficient), the innovation correlations, the residual portmanteau and how the optimiser stopped. reason is recorded in the guion: say why this candidate.

links restricts the cross dynamics to the pairs the evidence points at: "A<-B, C<-A" (B enters the equation of A, AR and MA, every lag up to p and q; names as in identify_cross). Empty (default): every pair. identify_cross proposes it as option (d) when only some pairs showed anything.

start: where the cross terms start — "zero" (the default for the VARMA) or "preliminary", Jenkins and Alavi's preliminary estimates (the cross MA from the univariate residuals' cross covariances, the cross AR from Yule-Walker). Usually the same optimum in fewer iterations; on an ill-defined estimation (the MA wall) a second path worth comparing. The echelon form starts at Lutkepohl and Poskitt's least-squares estimates ("echelon", its default).

cross: how the cross MA enters — "additive" (default: a cross polynomial beside the univariate operators) or "residual", Jenkins and Alavi's form (3.22): a model for the univariate residuals, multiplied by each series' univariate MA. The same when the univariate models have no MA factors; when they have (an airline), the two are different candidates — on m6 the residual form converged inside where the additive one stopped on the MA wall. identify_matrices' method 2 proposes it.

zeros: coefficients held at zero, by their printed names — Tiao and Box's simplification (simplify proposes them): cross ones "AR3[A<-B], MA1[B<-A]" on either route; a series' own "phi_A[B^4], theta_A[B^1]" on route V, and on route U in the echelon form (with indices), whose own AR(n_i)/MA(n_i) is sima's; otherwise route U's diagonal is the univariate model, art's. A fit already made with the same arguments is reused, not refitted.

indices: the ECHELON FORM with these Kronecker indices, one per series in the files' order, e.g. "1, 2, 1" (identify_echelon proposes them). Series i gets a free AR(n_i)/MA(n_i) of its own, the cross terms follow Lutkepohl and Poskitt's (1996) table, and the contemporaneous AR0[i<-j] terms make A_0 lower triangular: the order of the series is part of the model. p and q are then max(n_i); leave them at 0. links and zeros restrict it further. On route U the free AR(n_i)/MA(n_i) replaces the univariate model's regular ARMA, and its seasonal and fixed-frequency factors multiply the whole row (the row FACTOR), checked by an LR test against the same rows with the factor's restriction dropped.

C2 — The adopted VEC at rank r (drvec.fit with -fdhess: the standard errors from the Hessian at the optimum). REFUSES without a FINISHED rank_test for the same specification (p, q, case, drifts, files), unless the analyst adopts r on THEORY: theory says why, and it is written in the guion as such, with the bootstrap's numbers beside it when they exist. A rank other than the bootstrap's proposal needs theory too. r = 0 is the VARMA in differences (drvarma, N2); r = M is not a VEC.

THE ROLES are asked for: normalise_on names the r series beta is normalised on (the Y1 block); drvec's order is the others in the session's order, then these. That order is also the Cholesky order of the level responses, so another normalisation is ANOTHER FIT (this tool again), never a reorder. Default: the last r of prepare_vec's order (the I(0) series in the mixed case).

Reports drvec's .out blocks verbatim (parameters, the VEC's matrices, the normalisation share, the residual diagnostics), alpha read from the matrix (Johansen's sign), the canonical weights beside beta-hat, and the optimiser's stopping criterion: a fit that stopped on a ridge (E1's 2 1 1 -case 2) is declared NOT A DEMONSTRATED MAXIMUM, with multistart and a lower q offered. The .out's Wald tests are not citable (they depend on the normalisation): restrictions go by LR (test_restriction).

N5 — The yardstick: does the candidate forecast better than the univariates?

Estimates the candidate AND the diagonal system (the univariate models) on the first estwin observations, holds the parameters fixed, and forecasts from every origin to the end of the data, horizon steps ahead. Compares RMSE and MAPE series by series and horizon by horizon. A VARMA that does not gain here has no reason to exist, whatever its in-sample significance.

estwin counts observations of the FIRST series; leave enough data after it (at least a few dozen origins) or the comparison says little. links, zeros and indices: as in estimate, the same candidate.

ON A VEC (the current model is one, estimate_vec): the VEC's rolling-origin forecasts (drvec's -estwin/-f: the fit on the first rows, parameters held, errors in each series' own units) against the univariates on the same origins, and against the VARMA in differences when one was estimated. THE RULE depends on the purpose recorded at N1c: a VETO when it is "forecast", a CAVEAT (always reported) for a "long run" claim. p, q and the VARMA arguments are then ignored.

yardstick (route V): the analyst's univariate models, one fue file per series (a JSON list or comma-separated paths), e.g. their .pre from art. Without it the yardstick is route U's light builder, which takes the first of a tie in art's ranking; the report names the models either way. Once given it stays for the session (forecast_uncertainty and structure use it). On route U the yardstick is already the loaded files.

The worked examples that come with sima, to see how it works in real time: each is a real analysis, from the univariate models built in art, run node by node with the same tools and pauses as any other. load_example() starts one.

The path of the analysis, node by node, with its evidence and decisions.

This is what makes the analysis reviewable and repeatable: every tool call and every recorded decision, in order. Saved next to the first file as .sima.json when save, so that the record travels with the data; with html (default) also .sima.html, a self-contained page in art's style: the steps in a table, a section per node with the evidence, the decisions highlighted (who decided, what was set aside) and the figures drawn at each step (they are saved in figs/ next to the files).

N6 — Forecast every series in its level with the last estimated model.

Each series goes back to its level with its own univariate model: deterministic terms (known in the future), its differencing, its Box-Cox. The 95% band is built on the transformed scale and mapped back. On a VEC (the current model is one): the VEC written in levels (drvec.to_levels_varma) and forecast by drvarma's forecaster — one forecaster for every system — with each file's deterministic path and Box-Cox; drvec's band multiplier.

N5/N6 — Jenkins and Alavi's comparison of forecast uncertainty (their Table VIII): the standard deviation of the forecast errors by lead time, V(l) = SUM psi_j Sigma psi_j', of the last estimated model against the univariate models, per cent for series in logs. In sample, parameters taken as known: a quick reading of where the multivariate model could help; evaluate is the test. horizon defaults to the frequency (4 for annual data).

estwin (optional): re-estimate the model AND the univariate models on the first estwin observations of the first series, as Jenkins and Alavi did for their Table VIII (§6.3: the muskrat-mink models refitted on 48 observations, the rest withheld). 0 = the last fit, on all the data.

N2 — What the univariate models do NOT carry: residual cross-correlations.

Reads the CCFs of the residuals of the diagonal system, pair by pair. Those residuals are each series' own innovations — prewhitened by construction — so a cross-correlation beyond the band is evidence of a dynamic between the series. Contemporaneous correlation points to a full innovation covariance; lead-lag correlation points to cross orders p (and q). Returns the evidence and the menu of candidates, each with its argument. It does not choose.

nlags defaults to twice the frequency (24 for monthly data).

N2 — the third form, the ECHELON VARMA of Lutkepohl and Poskitt (1996), and its Kronecker indices from the data.

The indices n_i are the row degrees of the system's unique echelon form: series i gets its own AR(n_i)/MA(n_i), and their table says which cross terms are free, the contemporaneous ones included. Unlike the VARMA(p, q), the form is identified: no common factors, no MA driven to the wall by spare parameters. The univariate orders do NOT give the indices (every component's marginal is ARMA(N, N), N = the sum of the indices), so they are searched on the stationary vector: a long VAR (its residuals stand for the innovations), then least squares on each candidate's echelon form with one round of Hannan and Kavalieris' correction, and a criterion. SC (default) or HQ, which overfits. Every candidate with each index in 0..max_index while there are at most 256, Hannan and Kavalieris' two steps beyond.

The ORDER of the series is part of the echelon form (A_0 is lower triangular): the indices are those of the files' order. Measured on simulated systems (drvarma docs/STUDY-echelon-search.md): the true indices in 80-97 % of the replications, more with more data; weak cross dynamics are missed (the search underfits), which check_residuals then shows.

On ROUTE U each univariate model's seasonal and fixed-frequency factors are its row's FACTOR (they multiply the whole row; drvarma's echelon stage 4) and the search runs on each row filtered by them; the univariate regular ARMA is replaced by the row's own AR(n_i)/MA(n_i).

N2 — Jenkins and Alavi's (1981) two identifications, as matrices.

Method 2, prewhitened: the correlation matrices R_k of the residuals of the diagonal system (the univariate models' residuals), which suggest an MA residual model and its links. Method 1, not prewhitened: R_k, the partial correlation matrices S_k (multivariate Yule-Walker) and Alavi's q-conditioned S_k(q) of the stationary series of the same files, which suggest the AR (and ARMA) orders; determinants with three or more series. Then the comparison as a menu, with their warning when a cross AR shows: prewhitening can mis-specify it. nlags defaults to max(6, frequency); qmax the largest q-conditioning. Complements identify_cross (the pairwise CCFs).

N6 — Orthogonalised impulse responses of the last estimated model.

Cholesky in the ORDER OF THE FILES: an identifying assumption, stated in the output. With a strong contemporaneous correlation, reload the files in another order and compare before reading a response as a finding. With bands (default): 95% Monte-Carlo bands from the covariance of the estimates, redrawing the whole model through the ladder's cast; a response whose band covers zero is not a finding. On a VEC: the responses of the LEVELS (drvec), in drvec's order — the VEC's normalisation order — and their permanent effect; the bands come only from the parametric bootstrap (irf_bands, a job), never from the covariance.

C6 — Bands for the level responses and the FEVD of the current VEC, by PARAMETRIC BOOTSTRAP (drvec -irfboot N): N simulations of the fitted model, each REFITTED as the data were — same r, same restrictions, same ladder — and Efron's percentiles (90 % and 95 %). No delta method and no covariance Monte Carlo: the level responses are a long non-linear chain to the permanent effect, and a linearisation is what not to trust here.

A JOB, like rank_test: detached, cached by content, on drvec C when its binary is there (the engine in the provenance); a short wait (wait seconds), then the job id. Once finished, impulse_response, variance_decomposition and their plots draw the bands. The bands are conditional on r, the restrictions and the orthogonalisation order (drvec's file order): reordering is a refit and a new job. The horizon is drvec's (10 lags when n < 40, else 20). seed: 0 is the C's; another is a Monte Carlo check (Python engine).

Cancel a job: a queued one leaves the queue; a running one has its whole process tree killed (the runner, drvec C or the Python pool) and its folder marked cancelled, with no result written. A finished job is not touched. The same call later starts it again from the beginning (a cancelled run leaves nothing to resume).

The FINAL result of a finished job, with its report: a rank test's table and proposed rank (recorded at C1), the IRF bands (then used by impulse_response and the plots), a sweep cell. A job that is not finished has no result: this tool says so and returns nothing partial — a decision waits for it (the autonomous lane does not decide a node before).

Every job sima knows on this machine (the registry, ~/.sima/jobs or SIMA_JOBS_HOME): id, tool, status, label and progress, the running and queued first. name keeps only one session's. Jobs outlive the server and the conversation; their folders (sima_jobs//, next to the first file) hold the engine's files and the result.

A job's state — queued, running, done, failed or cancelled — its progress ("replication k of B, comparison r -> r + 1, ok/simfail/fitfail so far" for a rank test; the replications for the IRF bands; the cells for a sweep), the elapsed time and the rate. Never a provisional number: a finished comparison is said finished, an unfinished one shows its counts only. The result itself comes from job_result once the job is done. Jobs survive the server: an id from an earlier conversation still answers here.

N0r — RAW DATA: an analyst with series and no univariate models (docs/STUDY-raw-entry.md). An Excel (.xlsx/.xls) or CSV table, one column per series in ORIGINAL levels (never transformed or differenced), a header row with the names, and optionally a first column of dates (a year, or year-period: 1972-08, 1972Q3).

freq: 1, 4 or 12 (0: inferred from the date column). start: the first date, "1972-08" or "1850" (empty: from the date column). The table must be complete on one common calendar: missing values are refused, with where. Next: characterize — each series' transformation with art's engine.

N0 for a worked example: copy its files to a working folder (dest, default ~/sima-examples/; files already there are kept) and load them. An example from univariate models loads them as load_pre does, and goes on with run_gate. An example from RAW DATA (the vector first, as Tiao and Box or Lutkepohl and Poskitt) loads the table as load_data does, and goes on with characterize. From there the analysis is the usual one, node by node, the analyst deciding at every pause.

Before going on, READ its tutorial, sima://example/<name>: at each step it says what to look at and what the original analysis found, which you add after each report ("In the paper: ..."). The tools do not change in a tutorial; the explanation of the method is the manual it names.

N0 — Start a session from the univariate models: one fue file per series.

paths_json is a JSON list of paths to fue files — .pre (optima, from art or fue) or .inp (specifications) — in the order you want the system (it is also the Cholesky order of the impulse responses). This is how you arrive from mtram when it found a cycle: load the SAME .pre files it had.

The files are read by fue's own parser and recognised by their content. The series must share their frequency and their LAST date (BUG-2): different start dates are aligned at the end; different ends are refused.

C5 — The long run of the current VEC, read: theta (beta normalised, with its sign: Y1 = theta' Y2 + a stationary error), and two half-lives, both computed by sima because drvec computes neither — the TEXTBOOK one, ln 0.5 / ln(1 - |alpha|) on the variable the relation is solved for (orientation: exact only for one relation with no short-run dynamics), and the MODEL's, the half-life of the equilibrium error beta'Y in the fitted model's own response (the same weights as the level IRF; its norm over the shocks, which does not depend on the Cholesky order). Then Gonzalo and Ng's permanent/transitory decomposition: alpha_perp (the common trends), the share of each level's forecast-error variance due to the permanent shocks, and the self-check that a transitory shock has no long-run effect. Point values: bands only through the bootstrap (irf_bands). horizon: how far the responses go (0: 60 periods, or 8 years of seasonal data).

FIGURE — The forecasts of the last estimated model in the format of FUF and art: on top the annual rate of change (%) of the last horizon observations and the horizon forecasts, +-1 sigma dashed (the LEVEL with +-2 sigma when the series is not in logs); below, ERR, the residuals of those observations with +-2 sigma. The numbers are forecast's.

One figure PER SERIES, as FUF draws one page per series, so that the forecast report can go series by series: series empty (default) returns one figure for each; a series' name, only that one; "all", every series in a single grid. path (optional) is a directory, or with one series a file. On a VEC: the levels and the 95 % band of forecast (drvarma's forecaster on the VEC in levels), with ERR the level innovations.

FIGURE — Jenkins and Alavi's (1981) identification, pair by pair: the figure of identify_matrices. For each pair of series, in GraphMaker's CCF panel (Treadway's, the one drtran reads), the correlation function R_k above the partial S_k, both two-sided, same lag axis and scale — as art's ACF over PACF.

method=2 (default): the residuals of the univariate models (prewhitened, each series by ITS OWN model — Haugh's CCF, not a transfer function's). Band 2/sqrt(n); between the panels Haugh's S* (1976), the test that the two are independent, in total and by side (k > 0, k < 0: who leads). The CCF's cut-off after q suggests an MA(q) residual model. method=1: the stationary series w_t, not prewhitened. The CCF band is Bartlett's (3.13) for unrelated series, lag by lag: the series are not white, and a 2/sqrt(n) band would show their common cycles as cross terms. Here the partial is the decisive one: a cut-off after p suggests an AR(p). Each panel is titled "A - B", GraphMaker's order: A leads at k > 0. With three or more series the partial of a pair comes from the VAR of all of them — given the others — and pairs ("A-B, A-C") draws only those; read identify_matrices' determinants and + - . table first to choose them. nlags defaults to max(10, 2 x frequency); the partial stops at the order the sample supports (n / (3m)), marked on the panel.

FIGURE — The orthogonalised impulse responses of the last estimated model.

Drawn as what an impulse response is, a function of the lag like an ACF: one panel per (response, shock), thick impulses at h = 0..H, the seasonal grid, and the 95 % Monte-Carlo band dashed (it follows h). Cholesky in the order of the files, as impulse_response. The numbers are impulse_response's. On a VEC: the level responses (drvec), with the bootstrap's 90 % band from irf_bands when it has run.

FIGURE — The rank test's bootstrap: for each comparison r -> r + 1, the histogram of the B bootstrap statistics LR*, the OBSERVED LR (solid), the bootstrap's 90/95/99 % critical values (dashed) and, for cases 1 and 2, the asymptotic 5 % value (dotted: orientation only). From the finished rank test of the current specification (the one with the largest B), or job_id's. Read from the job's .boot file with drvec's own reader.

FIGURE — The residual cross-correlations of the last estimated model, pair by pair: GraphMaker's two-sided CCF (Treadway's, the suite's reference), titled "A - B" with A leading at k > 0, and Hosking's portmanteau below as GraphMaker labels it, P (not Ljung-Box's Q). What is left beyond the band is what the model does not carry. nlags defaults to twice the frequency. On a VEC: the residuals of its stationary form (nabla Y2 and the equilibrium errors, drvec's).

FIGURE — The forecast-error variance decomposition, in the IRF's layout.

Panel (i, j): the % of the h-step forecast-error variance of i due to the shock of j, h = 1..H, as impulses on a 0-100 axis with the 95 % band dashed. A row reads the same as in plot_impulse_response. On a VEC: the levels' decomposition (drvec), the bootstrap's band from irf_bands.

N1c/C0 — The cointegration question, and the VEC's specification with its checks (docs/STUDY-vec.md §2.3-2.4, §3.1-3.2). Offered after canonical_analysis when TWO OR MORE series have d = 1, whatever its count: the question is the analyst's (in the autonomous lane, yours, with the reason written down). Feedback is not a precondition: it is tested inside the VEC (weak exogeneity).

purpose is REQUIRED and recorded at N1c: "forecast" or "long run". It decides the yardstick's role later (C8): a VETO when the purpose is to forecast, a CAVEAT beside a long-run claim (an equilibrium, who corrects).

The checks, each a refusal with its reason or a warning: d >= 2 (drvec models I(1) systems; back to art), D > 0 (drvec refuses a seasonal difference: deterministic seasonality in art, objective "multivariante"), a deterministic variable drvec refuses (its message), d = 0 series (the MIXED case: an option, mixed=True, never the default; they go in the Y1 block and r >= their number), a file that moved at the gate, and the sample (drvec's window against the gate's).

p: drvec's AR order on (nabla Y2, W) (0: proposed — the univariate AR order in nabla plus 1, or Tiao and Box's M(l) on the levels when canonical_analysis ran, up to its first run of non-significant lags). q: the MA order (0 by default). case: 1, 2, 3 or "pre" (default: each drift as its file's mean says). nodrift: series whose drift is held at 0 (case 3/pre). Never offered: drvec's refused options (-warma, -mawarma, -specs, -matest, -artest, -m 2, -rankadm, the instruments and the writers). Next: rank_test, the only way to a rank.

C1 — The cointegration rank, by PARAMETRIC BOOTSTRAP (drvec's sequential exact-LR test r -> r + 1, r = 0..M-2): THE ONLY WAY TO A RANK in sima. The bootstrap decides; the asymptotic table (cases 1 and 2 only) is shown as orientation and is never the verdict. Reads the critical values, not the p-value; proposes r-hat and never adopts it.

A JOB (sima.jobs): it runs detached, at most cores - 1 at once, on drvec C when its binary is there (drvec's engine="auto"; the engine is in the result's provenance), cached by content: the same files, spec, B, engine and versions return the stored result at once. It waits up to wait seconds (about 20) and then returns the job id with its progress ("replication k of B, comparison r -> r + 1"); job_status/job_result follow it. Never a partial result as final.

Uses prepare_vec's specification. B: 499 by default, 999 when a 1 % verdict matters; below 199 the result is labelled an exploration. multistart: more starts in every fit. seed: 0 is the C's (987654321); another seed is a MONTE CARLO CHECK of an edge-of-5 % verdict (always on the Python engine), never the default.

Record a decision, WHY, on WHAT evidence, and what was set aside.

Every node that opens a decision (which files, which candidate, keep the VARMA or stay with the univariates, what to do with a fit on the MA wall, which Cholesky order) should leave one. Example: node "N5", decision "stay with the univariates", reason "the VARMA gains in no cell at h >= 6", evidence "RMSE ratio 1.02-1.11 over 36 origins", alternatives "VARMA(1,0) full: better in sample (LR p 0.01), worse out of sample". In the AUTONOMOUS lane this is where your reasoning is written down, with decided_by="LLM"; a decision without its reason is not documented.

N6 — The impulse responses under ANOTHER Cholesky order, against the files'.

The reduced-form model (Phi, Theta, Sigma) does not depend on the order of the series; only the orthogonalisation does. So nothing is re-estimated: the model is permuted, the responses recomputed, and put back in the files' order to compare cell by cell. A response that changes sign or size with the order is an assumption, not a finding. With a diagonal covariance the order does not matter at all, and the tool says so. order_json: the series names in the new order, e.g. '["WTI", "IPC_ES"]'. On a VEC it REFUSES: there the order is also the normalisation, so another order is another fit (estimate_vec with normalise_on).

N1 — The diagonal gate: does the joint cast reproduce the univariate models?

Each series is fitted alone on the common window; the diagonal system is then evaluated at those optima. The identity logL_joint = SUM logL_i is exact. If it fails, the analysis STOPS: nothing estimated on top of a joint model that does not reproduce its parts can be trusted.

It also says whether each file is an OPTIMUM (it does not move when re-estimated) or a SPECIFICATION (it moves), which decides whether the yardstick is the analyst's certified model or not.

N4s — Tiao and Box's (1981, §4) simplification by coefficient, on the current fit: the cross coefficients (and, on route V or in the echelon form, each series' own AR/MA coefficients) with |t| < t are held at zero, the model is refitted, and the restriction is tested by LR against the full fit, with AIC and BIC. The restricted fit is cached: adopting it (the estimate call in the menu) is instant. Route U's univariate models are never touched — they are art's; the echelon form's own part, which replaces their regular ARMA, is sima's, and is simplified like the rest. Several rounds are normal (Tiao and Box simplified the SCC model twice).

Convert a multivariate drvarma .inp (deprecated) into one fue .inp per series.

Each file is a SPECIFICATION with the old file's transformation (and, if asked, an estimated mean, seasonal harmonics, a free regular AR/MA). Take each one through art to build its univariate model, then come back with the .pre files: the univariate models are the seed and the yardstick.

N4t — Is the system simultaneous? (Tiao and Box 1981, §3.1, §5.2.) On the current fit: for each ordered pair, the LR test that series j does not enter series i's equation (all its cross AR and MA lags at zero); with up to 4 series, every triangular ordering (each series receives only from those before it). If an ordering stands, the system is a TRANSFER NETWORK — a triangular VARMA is a transfer function model — and sima offers the hand-back to mtram with the same .pre files; it does not hand back on its own. The verdict is only as good as the order of the fit: Tiao and Box's gas furnace shows a spurious feedback at low order.

N4b — Study the current fit when the estimation may be ill-defined.

For a fit that stopped on the MA invertibility wall (estimate says so), or any fit whose optimum you doubt. Evidence, then a menu; no verdict:

1. the AR and MA inverse roots of the joint model, and the pairs that nearly cancel (a near-common factor makes the likelihood a ridge);

2. a SECOND PATH: the same model optimised with Shea's exact likelihood (AS 242) instead of elf (AS 311) -- same function, independent code, another path;

3. RESTARTS: from the stopping point, step back towards the start (x = start + retreat * (stop - start)) and re-optimise; repeat while the likelihood rises. If it keeps rising, the ridge climbs along the wall and the reported point is not a maximum.

C7 — Robustness: a grid of fits over the same files, one CACHED JOB per cell, around the current VEC (its r, restrictions and normalisation). p: AR orders, e.g. "1,2,3"; case: "2, 3, pre, trend" (trend, case 4, for a single fit only); estwin: subsamples, rows 1..E of nabla Y ("60, 70, 80"; the recursive estimate). Empty: the current one. B > 0 adds a rank test per (p, case) cell, with its bootstrap (jobs too). The table — logL, parameters, the stopping criterion, theta and alpha per cell; r-hat for the rank cells — fills as the cells finish: call it again with the same grid (the cells are cached). It claims nothing beyond its cells: what it preserves is the list of what was run, and why, in the guion.

At C1, before any VEC (prepare_vec's specification, B required, no estwin): the RANK over p, each order its own bootstrap — what rank_test offers when n / (M p) is small and the verdict can flip with p.

C3 — A restriction on alpha, beta or Gamma of the current VEC, tested by LIKELIHOOD RATIO (never by the .out's Wald, which depends on the normalisation): LR, its degrees of freedom and chi2 p-value, both logLs.

weakex: a series' name — weak exogeneity, its row of alpha at zero ("who corrects": it does not adjust to the equilibrium). alpha: alpha = A psi, A as a JSON matrix (rows in drvec's order, as estimate_vec prints it) or a file in drvec's format ("M sa", then M rows) — jointly for several series. fixb2: every entry of B2 held at this VALUE (required: without one drvec holds B2 at its static OLS value, which is not a test); fixb2=0 in the mixed case is the ladder's model. fixb2row: rows of B2 held, "NAME=value, NAME2=value". weakex/alpha combine with fixb2row (the joint LR). gamma: NO FEEDBACK in the short run, "R30,R3 <- R0T" (the equations, then the regressors; "A <- B; C <- D" for several): Gamma_k[eq][reg] = 0 at every lag (drvec -gzero; p >= 2, q = 0). With weakex/alpha on the same inputs it is the CONDITIONAL model's joint test (weak exogeneity and no feedback, Johansen 1992): when it holds, the report offers mtram with the same files and the roles. gamma does not combine with fixb2/fixb2row.

drvec fits the free model of these LRs as the C does (one est() from a cold start for alpha and weakex; no ladder for fixb2row), so its free logL can be below the adopted VEC's and the LR understated: sima takes the BEST FREE FIT it knows, says which, and shows both when they differ. adopt: the restricted VEC becomes the current model. Not available (drvec): restrictions on one cointegrating vector, a bootstrap of this LR, a rank under a restriction.

N6 — Forecast-error variance decomposition of the last estimated model.

For each series and horizon, the share of its forecast-error variance that comes from each series' innovation: how much of what is not predictable in one series is really the other's surprise. Same Cholesky order as impulse_response, and the same caveat: with correlated innovations the shares of the first series in the order are inflated by construction. With bands (default): 95% Monte-Carlo bands at the last horizon. On a VEC: the decomposition of the LEVELS' forecast errors (drvec), with the bootstrap's bands when irf_bands has run.

N0v — ROUTE V from raw data (docs/STUDY-raw-entry.md): the vector first, as Tiao and Box (1981). No univariate models: each series gets a fue .inp with ONLY its characterization — lambda, d, D or harmonics, the mean when d = D = 0 — in out_dir (default <data>_sima/), and the ladder session opens on them (the guion goes on).

Then: run_gate (it certifies the cast; the diagonal here is white noise, or a random walk for d = 1, not a yardstick), canonical_analysis and identify_matrices' method 1 (R_k, S_k, Tiao and Box's M(l)) on the vector. estimate(p, q) in this route writes each series' spec with a FREE AR(p)/MA(q) of its own and fits the full VARMA(p, q): the diagonal is estimated with the cross terms. evaluate compares it with univariate models built by route U's builder, for the yardstick only. Route V writes no .pre for the system: its estimates are rows of the system, not univariate optima.