BAYESTST Procedure

Tests a series for a unit root using the Bayesian procedure outlined in Sims(1988). This generalizes Sims' formula to allow for intercept and trend. These however, are, in effect, given flat priors, which is not necessarily realistic: the priors on constant, trend and rho should be correlated since the three coefficients combined determine the level and trend of the series.

@BAYESTST( options ) series start end

Parameters

series	series to analyze
start end	range of series to use (not range over which test is run, which will be adjusted for lags). By default, the defined range of series.

Options

LAGS=number of total AR lags to be estimated [1]

ALPHA=prior probability on stationary rhos [.8]

LIMIT=stationary prior concentrated on (LIMIT,1) [.5]

TREND/[NOTREND]

TREND allows for a trending series

Example

cal(q) 1947

open data gnptbill.txt

data(format=prn,org=obs) 1947:1 1989:1

@bayestst tbill

Sample Output

Bayesian Unit Root Test

Squared t Schwarz Limit Small Sample Limit Marginal Alpha

2.991 7.913 1.916 0.7003

Squared t	the square of the t-statistic for the unit root
Schwarz limit	the asymptotic Bayesian rejection limit
Sample sample limit	the small-sample rejection limit (depends upon ALPHA and LIMIT)
Marginal Alpha	With ALPHA set at this value (given LIMIT) the posterior odds ratio is even. A small value indicates that only a very strong prior on the unit root will overcome the data evidence against it.

The result in this case is that the data slightly favors a unit root. The "Marginal Alpha" is the statistic that probably is easiest to interpret. Here, it means that if you put 70% probability on the stationary roots, the posterior is 50-50.