VAR & Granger Causality

Analyze → Time Series → Vector Autoregression. The single-series tools model one series at a time; a vector autoregression (VAR) models two or more series together, regressing each one on p lags of all of them. That answers the standard multi-series questions in one fit: how the series move together over time, which lag order the data support, and — the headline — whether one series's history improves the prediction of another (Granger causality).

The data layout

One column per series, cases in time order. The analyzed sample is the rows where all selected series are non-missing (a row missing any one is dropped, and the output names the aligned count). Like every time-series tool the estimate is unweighted by design — a frequency weight has no defined meaning for an ordered series; an active weight only selects cases, and the output says so.

The dialog

Tick two or more Series, then choose how the lag order is set:

Lag order (p) — a fixed order (default 1). Each equation regresses its series on lags 1..p of every series.
Choose the lag order automatically — compares orders 1..maximum with the four standard information criteria and fits the one your chosen criterion picks. Every candidate is scored on the same trimmed sample, so the criteria are comparable across orders.
Deterministic terms — a constant (default), a linear trend, both, or none.

Reading the output

VAR Model Summary — the aligned and effective observation counts, the fitted order and how it was chosen, parameters per equation, the log-likelihood, and AIC / HQ / BIC / FPE for the fitted model. (BIC is Lütkepohl's SC; under automatic selection these values use the model's own sample and so can differ from the selection table's row.)
Lag Order Selection (automatic mode) — one row per candidate order with all four criteria; the note names each criterion's minimum and the order actually fitted. Criteria often disagree (BIC is the most parsimonious) — that disagreement is information, not a malfunction.
VAR Coefficients — one table per series: each lag term (x.l1 is series x at lag 1), the deterministic terms, with standard errors, t and Sig.; the note carries the equation's residual SE and R². Individual lag coefficients are hard to read in isolation — the Granger table below tests them in meaningful blocks.
Residual Covariance / Correlation Matrix — how the equations' surprises co-move at the same time point. A large residual correlation means shocks hit the series together (contemporaneously) — something the lag structure deliberately does not model.
Granger Causality Tests — for every ordered pair, an F test that all p lag coefficients of the Cause are zero in the Effect's equation. A small Sig. means the cause's history improves the prediction of the effect beyond the effect's own history (and the other series' lags). "Causality" here is predictive, not mechanistic — the note on the table says the same.

Practical notes

Stationarity matters. A VAR assumes the series are stationary; run Stationarity Tests first and difference trending series (Data → Compute, or model the trend with the trend deterministic term when it is deterministic rather than stochastic).
Lags are expensive. Each extra lag adds one coefficient per series to every equation; with K series and order p each equation carries p·K slopes. Automatic selection with BIC is a sensible default when the series are short.
Two series only? The pairwise Granger test in a bivariate VAR is exactly the classical Granger test (R's lmtest::grangertest).

Scope (v1). Estimation, lag-order selection and pairwise Granger tests: no impulse-response functions or forecast-error variance decompositions, no forecasting from the fitted VAR, no seasonal dummies or exogenous regressors, no joint ("cause → all others") or instantaneous causality, no stability (companion-root) table, and no SVAR / VECM — cointegration analysis is a different tool. A declared survey design is not covered and the output says so.