ENDERSSIKLOS Procedure

@EndersSiklos does various types of the unit root regressions with threshold breaks on the residuals from an Engle-Granger cointegrating regression (assumed to be done already—input are the residuals). A related procedure for threshold unit roots is @EndersGranger. This is from Enders and Siklos(2001).

The regression run is

$\Delta {u_t} = {\rm{ }}{\rho _1}{D_{1t}}{u_{t - 1}} + {\rho _2}{D_{2t}}{u_{t - 1}} + {\text{ lags of }}\Delta u$

where ${D_{1t}}$ is the dummy for threshold series < $\tau $ and ${D_{2t}} = 1 - {D_{1t}}$. You can either input the threshold value or request a search. If you provide a value of $\tau $ (with the TAU option), the regressions are done with that fixed value for $\tau $. If you don't, the values of the threshold series (excluding the PI fraction at each end) are searched for the one that minimizes the sum of squared residuals. If ${\rho _1} = {\rho _2}$, this would be a standard cointegration test, so this allows for differentiable adjustments for positive and negative disequilibrium.

Note that all the tests have non-standard distributions with critical values provided in the paper.

@EndersSiklos(THRESHOLD=threshold series,other options) u start end

Parameters

u	series of residuals from an Engle-Granger regression.
start end	range of u to use. By default, the defined range of u.

Options

LAGS=# of lags on the differences [1]

THRESHOLD=series which determines the threshold (required!)

TAU=threshold value [not used, chosen by search]

PI=fraction of high and low empirical values for the threshold series which are omitted in the search.

If you provide a value of TAU, the regressions are done with that fixed value for tau. If you don't, the values of the threshold series (excluding the PI fraction at each end) are searched for the one that minimizes the sum of squared residuals

Variables Defined

%%BREAKVALUE	threshold value chosen or input
%%EQUALSTAT	F-test for ${\rho _1} = {\rho _2}$
%%PHISTAT	joint F-test for ${\rho _1} = 0$ and ${\rho _1} = 0$
%%TMAX	maximum t-statistic between ${\rho _1} = 0$ and ${\rho _2} = 0$

Example

* Replication file for Enders and Siklos(2001), "Cointegration and

* Threshold Adjustment," JBES, vol. 19, no. 2, 166-76.

open data rates.xls

calendar(m) 1964:1

data(format=xls,org=obs) 1964:01 1997:4

table

graph(footer="Figure 4. Interest Rate Data",$

key=upleft,klabels=||"Fed Funds","10 Year Bond"||) 2

# fed_funds

# g_10

@dfunit(lags=4) fed_funds 1980:1 *

@dfunit(lags=4) g_10 1980:1 *

set logff = log(fed_funds)

set log10 = log(g_10)

@varlagselect(crit=bic,lags=10) 1980:1 *

# logff log10

@varlagselect(crit=aic,lags=10) 1980:1 *

# logff log10

@johmle(det=rc,lags=2) 1980:1 *

# logff log10

@johmle(det=rc,lags=3) 1980:1 *

# logff log10

linreg logff 1979:10 * u

# constant log10

@egtestresids(lags=2) u

set du = u-u{1}

linreg(title="Engle-Granger Auxiliary Regression") du

# u{1} du{1 2}

*************************************************************

set tseries = u{1}

@EndersSiklos(title="Threshold Model with tau=0",threshold=tseries,tau=0.0,lags=2) u

set dseries = du{1}

@EndersSiklos(title="Momentum Model with tau=0",threshold=dseries,tau=0.0,lags=2) u

@EndersSiklos(title="Momentum Model with empirical tau",threshold=dseries,pi=.15,lags=2) u

Sample Output

This is the output from the three @EndersSiklos procedure calls in the above.

Threshold Model with tau=0

Lags 2

Threshold 0.0000

T-Max -1.5823

Phi 4.3236

Equality 0.4955

Coeff Std Error

Above -0.0846 0.0336

Below -0.0520 0.0329

DU{1} 0.1889 0.0678

DU{2} -0.1466 0.0681

Momentum Model with tau=0

Lags 2

Threshold 0.0000

T-Max -0.6283

Phi 6.3628

Equality 4.4176

Coeff Std Error

Above -0.0205 0.0327

Below -0.1173 0.0333

DU{1} 0.1834 0.0672

DU{2} -0.1606 0.0676

Momentum Model with empirical tau

Lags 2

Threshold -0.0261

T-Max -0.6795

Phi 7.5482

Equality 6.6975

Coeff Std Error

Above -0.0203 0.0298

Below -0.1412 0.0367

DU{1} 0.1864 0.0668

DU{2} -0.1550 0.0670