Choosing a VAR Model#

This guide helps you select the right VAR estimator and prior for your data. Start with your research question and follow the branches.

Decision Tree#

Step 1: Do you need time-varying volatility?

If your data spans a period with obvious volatility changes — e.g., quarterly macro data covering both the Great Moderation and the 2008 crisis — use bvarSvFit() (stochastic volatility). Otherwise, continue to Step 2.

Step 2: How many variables?

Variables	Recommendation	Why
m = 1	`arimaFit()`	Univariate models are more appropriate.
m = 2-5	`bvarFit()` or `varFit()`	Standard VAR territory. BVAR is preferred for forecasting.
m = 6-20	`bvarFit()` with tight prior	Shrinkage is essential. Set lambda1 = 0.01-0.1 or use `bvarHyperopt()`.
m = 20-100	`bvarSvFit()` with SSVS	Large system needs variable selection to identify relevant predictors.

Step 3: Levels or growth rates?

Data	Setting	Explanation
Levels (GDP, price index)	`ar = 1`	Random walk prior. Variables are assumed to be persistent.
Growth rates, log-differences	`ar = 0`	White noise prior. Variables are assumed to be mean-reverting.
Mixed or uncertain	Use `bvarHyperopt()`	Let the data choose via marginal likelihood optimization.

Step 4: Do you need structural identification?

If you want to interpret IRF causally (e.g., “a monetary policy shock reduces output by X%”), you need structural identification:

Method	When to use
Cholesky (`irfCompute()`)	You have a clear recursive ordering (fast-moving → slow-moving variables).
Sign restrictions (`svarIdentify()`)	You want to impose economic theory (e.g., “supply shocks raise prices”).
Generalized IRF (`girfCompute()`)	You want ordering-invariant results without structural assumptions.

If you just want forecasts and don’t need causal interpretation, skip structural identification and use reduced-form IRFs. Quick Start Recipes ——————-

Recipe 1: Standard 3-variable monetary policy VAR

GDP growth, CPI inflation, federal funds rate. Quarterly data.

library timeseries;

data = loadd("macro_quarterly.csv");

ctl = bvarControlCreate();
ctl.p = 4;
ctl.ar = 0;           // Growth rates

result = bvarFit(data, ctl);
irf = irfCompute(result, 20);

Recipe 2: Large forecasting model

20 macro variables. Optimize hyperparameters automatically.

library timeseries;

data = loadd("large_macro.csv");

ctl = bvarHyperopt(data);   // Data-driven lambda
ctl.p = 4;
result = bvarFit(data, ctl, quiet=1);
fc = bvarForecast(result, 8);

Recipe 3: Financial volatility modeling

3 asset returns with time-varying volatility.

library timeseries;

data = loadd("returns.csv");

svctl = bvarSvControlCreate();
svctl.p = 2;
svctl.ar = 0;         // Returns are stationary
svctl.n_draws = 10000;
svctl.n_burn = 5000;

result = bvarSvFit(data, svctl);

Recipe 4: Oil market SVAR with sign restrictions

Identify supply, demand, and speculative shocks in the oil market (Kilian 2009).

library timeseries;

data = loadd("oil_kilian.csv");

// Estimate reduced-form BVAR
ctl = bvarControlCreate();
ctl.p = 24;           // Monthly data, 24 lags
ctl.ar = 0;
result = bvarFit(data, ctl);

// Structural identification
sctl = svarControlCreate();
sctl.sign_restrictions = { 1  1 -1,    // Output: + supply, + demand, - speculative
                           1 -1  1,    // Price:  + supply, - demand, + speculative
                          -1  1  1 };  // Inventory: - supply, + demand, + speculative

struct svarResult svar;
svar = svarIdentify(result, sctl);
svar_irf = svarIrf(svar, 48);

Function Comparison#

Function	Prior	Time-varying \(\Sigma\)	MCMC	Best for	Speed (m=3)
`varFit()`	None (OLS)	No	No	Quick estimation, diagnostics	< 0.001s
`bvarFit()`	Minnesota	No	No (conjugate)	Forecasting, model comparison	0.05-0.10s
`bvarSvFit()`	Minnesota	Yes (SV)	Yes (Gibbs)	Heteroskedastic data, density forecasting	1-2s (10K draws)