GAUSS vs R vs BEAR: Side-by-Side#

Same model, same data, three platforms. All code is copy-paste runnable. The Task ——–

Estimate a Bayesian VAR(4) on 200 quarters of US macroeconomic data (GDP growth, CPI inflation, federal funds rate), compute impulse responses, and forecast 8 quarters ahead. GAUSS —–

library timeseries;

data = loadd(getGAUSSHome("pkgs/timeseries/examples/data/us_macro_quarterly.csv"));

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

struct bvarResult result;
result = bvarFit(data, ctl);

// IRF
struct varResult rv;
rv = varFit(data, 4, quiet=1);
irf = irfCompute(rv, 20);

// Forecast
fc = bvarForecast(result, 8);

12 lines of code. Estimation, IRF, and forecast in one script, one language. R (vars + BVAR packages) ————————-

library(vars)
library(BVAR)

y <- as.matrix(read.csv("us_macro_quarterly.csv"))

# BVAR(4)
set.seed(42)
bv <- bvar(y, lags = 4, n_draw = 6000, n_burn = 1000,
           n_thin = 1, verbose = FALSE)

# IRF (from OLS VAR — BVAR package doesn't do Cholesky IRF directly)
v <- VAR(y, p = 4, type = "const")
ir <- irf(v, n.ahead = 20, boot = FALSE)

# Forecast
fc <- predict(bv, horizon = 8, conf_bands = 0.68)

11 lines of code. Requires two packages (vars for OLS/IRF, BVAR for Bayesian estimation). The BVAR package uses Gibbs sampling with hierarchical hyperparameter tuning — a different algorithm than both GAUSS and BEAR. MATLAB (ECB BEAR Toolbox) ————————–

addpath(genpath('tbx'));

opts = BEARsettings(2);
opts.frequency  = 2;
opts.startdate  = '1970q2';
opts.enddate    = '2019q4';
opts.varendo    = 'YER HICSA STN';
opts.lags       = 4;
opts.prior      = 21;
opts.It         = 10000;
opts.Bu         = 5000;
opts.IRF        = 1;
opts.IRFperiods = 20;
opts.F          = 1;
opts.Fendsmpl   = 1;
opts.Fstartdate = '2020q1';
opts.Fenddate   = '2021q4';

BEARmain(opts);

17 lines of code. Data path, date range, and variable names are configured as strings. Output is saved to Excel and .mat files — not returned to the workspace. Applications (IRF, forecast) must be enabled via flags. Each BEARmain() call re-estimates the model from scratch. Timing Comparison —————–

All timings on the same 200-quarter, 3-variable dataset. GAUSS and R timed on Apple M-series. BEAR on MATLAB R2025b.

Task

GAUSS

R

BEAR

OLS VAR(4)

0.003s

0.004s

0.058s

BVAR(4), 5K draws

0.08s

0.66s

3.69s

8-step forecast

0.02s

0.12s

4.34s 1

Cholesky IRF (20h)

0.001s

0.003s

4.23s 1

1 BEAR re-estimates the full model for each application. Marginal IRF/forecast time is ~0.5s after subtracting re-estimation.

Why GAUSS is faster than R: GAUSS uses the conjugate Normal-Inverse-Wishart posterior, which produces exact draws without MCMC. R’s BVAR package uses a Gibbs sampler. Both are correct Bayesian inference — the conjugate form is an algorithmic advantage, not an approximation.

Why GAUSS is faster than BEAR: BEAR uses an independent Normal-Wishart prior with Gibbs sampling (MATLAB interpreted loops). GAUSS uses conjugate posterior draws (compiled Rust backend). The speed difference compounds with draws: at 50K draws, BEAR takes 4 minutes vs GAUSS’s 0.8 seconds. Numerical Agreement ——————-

GAUSS matches BEAR to \(10^{-8}\) on OLS coefficients (same data, same model). BVAR posterior means agree within 0.06 with matched hyperparameters (conjugate vs independent NW prior form). R’s BVAR package uses a different prior (hierarchical hyperparameter tuning), so posterior means differ by design.

Full verification details: Verification and Cross-Validation. What You Get With Each Platform ——————————-

GAUSS

R

BEAR

OLS VAR

varFit()

vars::VAR

VARtype=1

Bayesian VAR

bvarFit()

BVAR::bvar

VARtype=2

Stochastic volatility

bvarSvFit()

bsvars

VARtype=5

Cholesky IRF

irfCompute()

vars::irf

opts.IRF=1

Sign restrictions

svarIdentify()

bayesianVARs

opts.IRFt=4

Conditional forecast

condForecast()

(manual)

opts.CF=1

Density forecast

bvarSvForecast()

bayesianVARs

(manual)

Hyperparameter opt

bvarHyperopt()

Built-in

opts.hogs=1

MCMC diagnostics

varDiagnose()

coda

(manual)

Forecast evaluation

dmTest() pitTest()

forecast

(not included)

FRED data access

fred_load

fredr

(not included)

Verified against

R + BEAR (428 tests)

—

—

Multi-Run Timing (5 runs, median)#

GAUSS timing variability is minimal — the compiled Rust backend produces deterministic execution times:

Task

Median

Min

Max

IQR

OLS VAR(4)

0.0001s

0.0001s

0.0023s

0.0000s

BVAR(4), 5K draws

0.077s

0.076s

0.082s

0.000s

SV-BVAR(4), 10K draws

1.161s

1.154s

1.166s

0.006s

Cholesky IRF

0.0005s

0.0005s

0.0011s

0.0000s

BVAR Forecast

0.024s

0.024s

0.024s

0.000s

All measurements on 3-variable, 200-quarter data. 5 runs each, Apple M-series. GAUSS runs under Rosetta 2 (x86_64 on ARM) — native arm64 GAUSS will be faster. Scaling: Large Systems ———————-

GAUSS handles large BVAR systems efficiently. Memory scales with \(n_{draws} \times K \times m\):

m

p

K

BVAR (5K draws)

SV (2K draws)

Memory (B draws)

3

4

13

0.08s

0.34s

1.5 MB

5

4

21

0.19s

0.66s

4.0 MB

10

4

41

0.71s

2.0s

15.6 MB

20

4

81

2.9s

7.8s

61.8 MB

50

4

201

18.0s

—

383 MB

For systems above m=10, use bvarSvFit() with sv_keep = "online" to reduce memory from O(n_draws * T * m) to O(reservoir_size * m). .. seealso:: Guides Getting Started, Choosing a VAR Model, Verification and Cross-Validation

On this page