Using the HEGY Procedure When Not All Roots Are Present
研究了当季度时间序列中并非所有单位根都存在时，HEGY检验程序的统计性质，通过向量表示和协整关系推导了检验统计量的分布，并用蒙特卡洛模拟验证。
Abstract. Empirical studies have shown little evidence to support the presence of all unit roots present in the Δ 4 filter in quarterly seasonal time series. This paper analyses the performance of the Hylleberg, Engle, Granger and Yoo [ Journal of Econometrics (1990) Vol. 44, pp. 215–238] (HEGY) procedure when the roots under the null are not all present. We exploit the vector of quarters representation and cointegration relationship between the quarters when factors (1 − L ), (1 + L ), (1 + L 2 ), (1 − L 2 ) and (1 + L + L 2 + L 3 ) are a source of nonstationarity in a process in order to obtain the distribution of tests of the HEGY procedure when the underlying processes have a root at the zero, Nyquist frequency, two complex conjugates of frequency π /2 and two combinations of the previous cases. We show both theoretically and through a Monte Carlo analysis that the t ‐ratios t and t and the F‐ type tests used in the HEGY procedure have the same distribution as under the null of a seasonal random walk when the root(s) is (are) present, although this is not the case for the t ‐ratio tests associated with unit roots at frequency π /2.