Hylleberg-Engle-Granger-Yoo (HEGY) Seasonal unit root test for quarterly data -----------------------------------------------------------------------------
^hegy4^ varname [^if^ exp] [^in^ range] [, ^L^ags(numlist) ^D^et(none|const|seas|trend|strend|mult) ^GEN^erate(newvar) ^NOT^est ^LEV^el(int > eger)]
^hegy4^ is for use with quarterly time-series data. You must ^tsset^ your data > before using ^hegy4^; see help @tsset@.
^varname^ may contain time-series operators; see help @varlist@.
Description -----------
^hegy4^ performs the Hylleberg et al. (HEGY, 1990) test for seasonal unit roots in a quarterly timeseries. It estimates the four roots of the timeseries representation (1-B^^4) x(t) = e(t), where B is the backshift operator, and presents estimates of these roots as Pi(1)..Pi(4). A joint test for Pi(3)=Pi(4) > =0 is also presented. Critical values are those appropriate for T=100, taken from HEGY Table 1. Joint tests for Pi(2)=Pi(3)=Pi(4)=0 and Pi(1)=Pi(2)=Pi(3)=Pi(4)=0 > , with critical values, are those presented by Ghysels et al. (1994). Critical values for the case of muliplicative seasonality (see below) are from tables 1a > -c in Smith and Taylor (1998). Critical values are linearly interpolated for sampl > e sizes in the ranges (48,100) and (100,200).
Options -------
^Det^, which may take on values ^none^, ^const^, ^seas^, ^trend^, ^strend^ or ^ > mult^, specifies the process to be tested. The default, as suggested by HEGY and Ghysels et al. > (1994), is ^seas^, indicating that a set of 3 seasonal dummies plus constant are to be included in the regression. ^none^ specifies that no deterministic variables ar > e to be included; ^const^ specifies only a constant. ^trend^ specifies that a tre > nd is to be included along with a constant term. ^strend^ specifies that a trend i > s to be included along with seasonal dummies and a constant term. ^mult^ specifie > s that seasonal intercepts (the case of multiplicative seasonality, recommended by Smith and Taylor (1998)) are to be included along with seasonal dummies and > a constant term.
^Lags(^numlist^)^ specifies the lag orders to be used in augmenting the model w > ith lags of the fourth difference of the timeseries. Its default is zero. If sequen > tial lags are specified starting with 1, HEGY4 automatically conducts a sequential t > -test to determine the optimal lag length and optimal lags to be included in the auxi > liary regression. The ^LEVel(^#^)^ option may be used to control the size of the lag > length test. Note that the test size equals 1 minus the confidence interval (in percen > t). Taylor and Smith (2001, p. 204) recommend a test size of 25%, which corresponds > to ^LEV(75)^ on the command line. The ^NOTest^ option may be specified to suppress > the lag length test and utilize the lags specified in the option in generating the > test statistic.
^GEN^erate(^newvar^): as a diagnostic on the procedure, the residuals from the > HEGY regression may themselves be regressed on four lags and the original regressors > . The residuals from that auxiliary regression may optionally be saved via the ^GEN^erate() option, which saves them as a new variable. Other diagnostic procedures (such as a portmanteau test, e.g. ^wntestq^, or tests for normality, skewness and kurtosis) may be then applied to this variable.
Examples --------
. ^use http://fmwww.bc.edu/ec-p/data/Mills2d/exchq^
. ^hegy4 exchq^ . ^hegy4 exchq, det(strend) lag(1/4)^ . ^hegy4 exchq, lag(1/4) level(75)^ . ^hegy4 exchq, det(seas) lag(1 3 5)^ . ^hegy4 exchq, det(mult) lag(1/8) notest^
. ^hegy4 exchq, gen(hegyres)^ . ^wntestq hegyres^
References ----------
Franses, P. H., and B. Hobijn. 1997. Critical Values for Unit Root Tests In Seasonal Time Series. Journal of Applied Statistics 24: 25-47.
Ghysels, E., Lee, H.S., and J. Noh. 1994. Testing for Unit Roots in Seasonal Time Series: Some Theoretical Extensions and a Monte Carlo Investigation. Journal of Econometrics, 62, 415-442.
Hylleberg, S., Engle, R.F., Granger, C.W.J. and B.S. Yoo. 1990. Seasonal Integration and Cointegration. Journal of Econometrics, 44, 215-238.
Smith, R. J., and A. M. R. Taylor. 1998. Additional Critical Values and Asymptotic Representations for Seasonal Unit Root Tests, Journal of Econometrics, 85, 269-88.
Taylor, A. M. R., and R. J. Smith. 2001. Tests of the Seasonal Unit-Root Hypothesis Against Heteroscedastic Seasonal Integration, Journal of Business & Economic Statistics, 19, 192-207.
Acknowledgements ----------------
This routine is based on the HEGY.SRC RATS code written by Jean-Philip Bellotteau and available from the SSC-IDEAS archive. We thank M. Bellotteau and P.H. Franses for clarifying remarks. Remaining errors are ours.
Authors -------
Christopher F Baum, Boston College, USA baum@@bc.edu
Richard Sperling, The Ohio State University, USA rsperling@@boo.net
Also see --------
Manual: ^[R] dfuller^ On-line: help for @dfuller@, @time@, @tsset@, @dfgls@ (if installed)