Author
Said E. Said
Bio: Said E. Said is an academic researcher from East Carolina University. The author has contributed to research in topics: Autoregressive model & Unit root test. The author has an hindex of 3, co-authored 3 publications receiving 3202 citations.
Papers
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TL;DR: In this paper, the authors developed a test for unit roots which is based on an approximation of an autoregressive-moving average model by an auto-gression, which has a limit distribution whose percentiles have been tabulated.
Abstract: SUMMARY Recently, methods for detecting unit roots in autoregressive and autoregressivemoving average time series have been proposed. The presence of a unit root indicates that the time series is not stationary but that differencing will reduce it to stationarity. The tests proposed to date require specification of the number of autoregressive and moving average coefficients in the model. In this paper we develop a test for unit roots which is based on an approximation of an autoregressive-moving average model by an autoregression. The test statistic is standard output from most regression programs and has a limit distribution whose percentiles have been tabulated. An example is provided.
3,231 citations
TL;DR: In this article, the authors show that if ρ = 1, the limiting distribution of nonlinear least squares regression estimators of the parameters appearing in the preceding model are obtained.
Abstract: Let the time series {Yt : t ∈ (1, 2, …)} satisfy Yt = ρY t-1 + Z t and Zt + Σ p i=1 a i Zt−1 = et + Σ q j=1 β j et-j, where {e t } is a sequence of normal, independently distributed (NID(0, σ2)) random variables, and y 0 = 0. Associated with the Zt process are the characteristic equations mp + Σ p i=1 aimp-i = 0 and mq + Σ q j=1 βjmq-j = 0, the roots of which are assumed to be less than one in absolute value. Thus, using the notation of Box and Jenkins (1976), we would say Yt is an ARIMA(p, 1, q) process if ρ = 1. Under the assumption that ρ = 1, the limiting distributions of nonlinear least squares regression estimators of the parameters appearing in the preceding model are obtained. Regression t-type statistics for testing the hypothesis that ρ = 1 are discussed. Similar results are obtained for models that allow a nonzero mean. An illustrative example is given.
143 citations
TL;DR: In this paper, a test for unit roots in autoregressive, moving-average models containing a linear time trend term is proposed, based on the estimation procedure suggested in Fuller (1976), which is basically a nonlinear type of estimation.
21 citations
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TL;DR: In this article, the authors proposed new tests for detecting the presence of a unit root in quite general time series models, which accommodate models with a fitted drift and a time trend so that they may be used to discriminate between unit root nonstationarity and stationarity about a deterministic trend.
Abstract: SUMMARY This paper proposes new tests for detecting the presence of a unit root in quite general time series models. Our approach is nonparametric with respect to nuisance parameters and thereby allows for a very wide class of weakly dependent and possibly heterogeneously distributed data. The tests accommodate models with a fitted drift and a time trend so that they may be used to discriminate between unit root nonstationarity and stationarity about a deterministic trend. The limiting distributions of the statistics are obtained under both the unit root null and a sequence of local alternatives. The latter noncentral distribution theory yields local asymptotic power functions for the tests and facilitates comparisons with alternative procedures due to Dickey & Fuller. Simulations are reported on the performance of the new tests in finite samples.
16,874 citations
TL;DR: In this article, a unit root test for dynamic heterogeneous panels based on the mean of individual unit root statistics is proposed, which converges in probability to a standard normal variate sequentially with T (the time series dimension) →∞, followed by N (the cross sectional dimension)→∞.
12,838 citations
TL;DR: In this article, the authors consider pooling cross-section time series data for testing the unit root hypothesis, and they show that the power of the panel-based unit root test is dramatically higher, compared to performing a separate unit-root test for each individual time series.
10,792 citations
TL;DR: In this paper, a test of the null hypothesis that an observable series is stationary around a deterministic trend is proposed, where the series is expressed as the sum of deterministic trends, random walks, and stationary error.
10,068 citations
TL;DR: In this paper, the authors consider the null hypothesis that a time series has a unit root with possibly nonzero drift against the alternative that the process is "trend-stationary" and show how standard tests of the unit root hypothesis against trend stationary alternatives cannot reject the unit-root hypothesis if the true data generating mechanism is that of stationary fluctuations around a trend function which contains a one-time break.
Abstract: We consider the null hypothesis that a time series has a unit root with possibly nonzero drift against the alternative that the process is «trend-stationary». The interest is that we allow under both the null and alternative hypotheses for the presence for a one-time change in the level or in the slope of the trend function. We show how standard tests of the unit root hypothesis against trend stationary alternatives cannot reject the unit root hypothesis if the true data generating mechanism is that of stationary fluctuations around a trend function which contains a one-time break
7,471 citations