Tests for Seasonal Moving Average Unit Root in ARIMA Models
研究了季节性ARIMA模型中移动平均算子是否存在单位根的检验方法，用于区分确定性季节模式和随机性季节模式，并给出了季度和月度数据的临界值表及检验功效分析。
Abstract Procedures to test for a unit root in the seasonal moving average (MA) operator for seasonal autoregressive integrated moving average (ARIMA) models are examined. Such procedures are useful to distinguish deterministic from stochastic seasonal patterns. The simple (integrated) seasonal MA(1) model Z t ≡ Y t - Yt-s = (1 - θB s)ϵt, where {Y t} is the observed seasonal series and {ϵt} is a white noise sequence, is considered, and tests for H 0: θ = 1 versus H 1: θ < 1 are studied. The locally best invariant unbiased and point-optimal invariant tests are investigated. The finite-sample and asymptotic distributions of the test statistics under both the null hypothesis and local alternatives are derived. Quantiles of the null distributions are tabulated for quarterly and monthly data cases, and a limited study of the powers of the tests is reported. The test procedures are extended to more general seasonal ARMA models of the form Z t = (1 - θB s)Nt, where N t follows a general stationary and invertible ARMA model φ(B)Nt = θ*(B)ϵt. The generalizations suggested involve modifying the test procedures for the seasonal MA(1) case parametrically, based on the estimated ARMA structure for the noise process {N t}. Simulation results are presented to study the performance of the modified procedure, and numerical examples involving monthly and quarterly seasonal time series data are given.