XploRe Help : hegy

Keywords - Function groups - @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Library:	times
See also:	adf

Quantlet:		hegy
Description:		Test procedure proposed by Hylleberg, Engle, Granger, Yoo (HEGY) for seasonal unit roots in quarterly time series. Deterministic components (constant, seasonal dummies and trend) can be included. The procedure renders a table with estimated coefficients and non-standard critical values given by HEGY. Additionally, the output consists of the estimated coefficients and the regression residuals.

Reference(s):

Hylleberg, S., Engle, R.F., Granger, C.W.J., and Yoo, B.S. (1990). Seasonal Integration and Cointegration. Journal of Econometrics, 44, 215-238. Franses, P.H. (1998). Time Series Models for Business and Economic Forecasting. Chapter 5. Cambridge University Press, Cambridge.

Usage:	`{coeff,residuals} = hegy(y,p,constant,dummies,trend)`
Input:
	`y`	(T x 1) vector, quarterly time series
	`p`	column vector with positive integers in increasing order, indicates which lags should be included. Set p = 0 if no lags should be included.
	`constant`	scalar with value 0 or 1, indicates whether a constant should be included in the regression. A constant is included for constant = 1. A constant must be included if dummies and/or a trend are included.
	`dummies`	scalar with value 0 or 1, indicates whether seasonal dummy variables should be included. Three dummies are included for dummies = 1.
	`trend`	scalar with value 0 or 1, indicates whether a time trend should be included. A trend is included for trend = 1.
Output:
	`coeff`	(4+n) x 2 matrix, first column contains the estimated coefficients and the second one the respective t-values. n is the total number of additionally included terms like trend, dummies and lags.
	`residuals`	(T-4-max(p)) x 1 vector with the residuals from the regression, where max(p) is the maximum of the vector p.

Note:

(1-B^4)y_t = c_t + pi1*y1_t-1 + pi2*y2_t-1 + pi3*y3_t-2 + pi4*y3_t-1 + u_t,

where B is the backshift (lag) operator and y1_t = (1+B+B^2+B^3)y_t, y2_t = -(1-B+B^2-B^3)y_t, y3_t = -(1-B^2)y_t. c_t may consist of a constant, seasonal dummies and a trend. u_t is the residual. The regression equation can be augmented by including lags of the dependent variable. Estimated residuals can be used for selecting the number of lagged dependent variables.

Example:

library("times") ; loads the quantlets from times library consume = read("ukconsume.dat") ; quarterly UK consumption non-durables {coeff,residuals} = hegy(log(consume),(1|4|5),1,1,1) ; lags are at 1,4, and 5, constant, dummies and trend are included ; and n = 8 additional coefficients are estimated acfplot(residuals,12) ; plots the acf for 12 lags

Result:

Display of the acf of regression residuals, which indicates white noise.
Moreover, the following table is rendered:

 Contents of out

 ==================================================
  HEGY regression results
  Included observations:      127
 +------------------------------------------------
                Coeff.      t-stat      p-value
 +-------------------------------------------------
  constant       1.127       2.647       0.008
  dummy[1,]      0.035       2.078       0.038
  dummy[2,]      0.023       2.108       0.035
  dummy[3,]      0.043       2.524       0.012
  trend          0.001       2.749       0.006
  lag[ 1,]       0.671       6.879       0.000
  lag[ 4,]      -0.252      -2.491       0.013
  lag[ 5,]       0.314       3.397       0.001
 +-------------------------------------------------
                Coeff.      t-stat
 +-------------------------------------------------
  pi[1,]        -0.028      -2.703
  pi[2,]        -0.174      -1.997
  pi[3,]        -0.120      -1.928
  pi[4,]        -0.076      -1.228
 +-------------------------------------------------
  Hypothesis: pi3 and pi4 are zero (pi34)
 +-------------------------------------------------
  F-stat         2.499
 +-------------------------------------------------
  Critical values     0.01      0.05     0.1
 +-------------------------------------------------
  pi1                -4.15     -3.52    -3.21
  pi2                -3.57     -2.93    -2.61
  pi34                8.77      6.62     5.55
 ==================================================

  We cannot reject the hypotheses that pi1, pi2, pi3 and pi4
  are zero at the conventional significance levels. The filter
  (1-B^4) is the most appropriate for the UK consumption
  series. For a thorough discussion, see Franses (1998).

Example:

library("times") ; loads the quantlets from times library production = read("usaproduction.dat") ; quarterly USA industrial production {coeff,residuals} = hegy(log(production),(1|2|3),1,1,1) ; lags are at 1,2, and 3, constant, dummies and trend are included ; and n = 8 additional coefficients are estimated acfplot(residuals,12) ; plots the acf for 12 lags

Result:

Display of the acf of regression residuals, which indicates white noise.
Moreover, the following table is rendered:

 Contents of out

 ==================================================
  HEGY regression results
  Included observations:      121
 +-------------------------------------------------
                Coeff.      t-stat      p-value
 +-------------------------------------------------
  constant       0.331       3.050       0.002
  dummy[1,]     -0.007      -1.327       0.185
  dummy[2,]     -0.003      -0.500       0.617
  dummy[3,]      0.006       1.152       0.249
  trend          0.001       2.612       0.009
  lag[ 1,]       0.833       6.215       0.000
  lag[ 2,]      -0.590      -3.911       0.000
  lag[ 3,]       0.163       1.774       0.076
 +-------------------------------------------------
                Coeff.      t-stat
 +-------------------------------------------------
  pi[1,]        -0.021      -2.952
  pi[2,]        -0.153      -1.751
  pi[3,]        -0.325      -3.175
  pi[4,]        -0.381      -3.866
 +-------------------------------------------------
  Hypothesis: pi3 and pi4 are zero (pi34)
 +-------------------------------------------------
  F-stat        12.319
 +-------------------------------------------------
  Critical values     0.01      0.05     0.1
 +-------------------------------------------------
  pi1                -4.15     -3.52    -3.21
  pi2                -3.57     -2.93    -2.61
  pi34                8.77      6.62     5.55
 ==================================================

We cannot reject the hypotheses that pi1 and pi2  are zero
at the conventional significance levels. However, we reject
that pi3 and pi4 are jointly zero. The filter (1-B^2) is
the most appropriate for the USA industrial production series.
For a thoroughly discussion, see Franses (1998).

Author: R. Schulz, 20030214 license MD*Tech