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. |
- 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).