varLagSelect#

Purpose#

Select VAR lag order by information criteria.

Format#

ls = varLagSelect(y, max_p)#

ls = varLagSelect(y, max_p, ic="bic")

Parameters:

y (TxM matrix or dataframe) – endogenous variables.
max_p (scalar) – maximum lag order to test.
ic (string) – Optional keyword, selection criterion. "aic" (default), "bic", or "hq".
xreg (TxK matrix) – Optional keyword, exogenous regressors.
include_const (scalar) – Optional keyword, 1 to include constant (default), 0 to exclude.
quiet (scalar) – Optional keyword, set to 1 to suppress the IC table. Default = 0.

Returns:

ls (struct) –

An instance of a lagSelectResult structure containing:

ls.best_p	Scalar, selected lag order (argmin of chosen criterion).
ls.criterion	String, criterion used for selection (`"aic"`, `"bic"`, or `"hq"`).
ls.ic_table	max_p x 3 matrix, information criterion values for each lag order. Columns: AIC, BIC, HQ.
ls.max_p	Scalar, maximum lag tested.
ls.ic_names	3x1 string array, `{"AIC", "BIC", "HQ"}`.

Examples#

Basic Lag Selection#

new;
library timeseries;

data = loadd(getGAUSSHome("pkgs/timeseries/examples/macro.dat"));

// Test lags 1 through 8, select by AIC
ls = varLagSelect(data, 8);

================================================================================
VAR Lag Selection (M=3, T=200)
================================================================================
Lag      AIC         BIC         HQ
----------------------------------------
  1   -12.384     -11.927*    -12.198*
  2   -12.401*    -11.689     -12.115
  3   -12.378     -11.410     -11.993
  4   -12.356     -11.133     -11.871
  5   -12.331     -10.853     -11.746
  6   -12.312     -10.578     -11.627
  7   -12.289     -10.300     -11.504
  8   -12.270     -10.026     -11.385
================================================================================
Selected: p=2 (AIC)
================================================================================

Pipe into Estimation#

new;
library timeseries;

data = loadd(getGAUSSHome("pkgs/timeseries/examples/macro.dat"));

// Select lag order, then estimate
ls = varLagSelect(data, 8, ic="bic", quiet=1);
result = varFit(data, ls.best_p);

Remarks#

The full IC table (ls.ic_table) reports all three criteria (AIC, BIC, HQ) regardless of which criterion was used for selection. This allows comparison when the criteria disagree — AIC tends to select more lags than BIC.

Model#

For each candidate lag order \(p = 1, \ldots, p_{\max}\), the VAR(p) is estimated by OLS and the information criteria are computed:

\[\begin{split}\text{AIC}(p) &= \log|\hat\Sigma_p| + \frac{2 K_p m}{T_p} \\ \text{BIC}(p) &= \log|\hat\Sigma_p| + \frac{K_p m \log T_p}{T_p} \\ \text{HQ}(p) &= \log|\hat\Sigma_p| + \frac{2 K_p m \log \log T_p}{T_p}\end{split}\]

where \(K_p = mp + 1\) and \(T_p = T - p\) (sample shrinks with more lags).

The selected \(p^*\) minimizes the chosen criterion. AIC tends to select larger models; BIC tends to select smaller models (Lutkepohl 2005, Section 4.3).

Troubleshooting#

AIC and BIC disagree: This is common. AIC optimizes forecast accuracy; BIC optimizes model consistency (converges to the true order as T → ∞). For forecasting, prefer AIC. For structural analysis, prefer BIC. When in doubt, report both.

References#

Lutkepohl, H. (2005). New Introduction to Multiple Time Series Analysis. Springer. Section 4.3.

Library#

timeseries

Source#

var.src