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Asymptotic inference for a nonstationary double AR(1) model
We investigate the nonstationary double AR(1) model, y t = Φy t-1 + η t √ (ω + αy 2 t-1 ), where ω > 0, a > 0, the η t are independent standard normal random variables and E log |Φ+ η t √α | ≥ 0. We show that the maximum likelihood estimator of (Φ, α) is consistent and asymptotically normal. Combination of this result with that in Ling (2004) for
Ling, Shiqing, Li, Dong
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The polynomial aggregated AR(1) model*
Summary: This paper develops a new kind of aggregation model. We extend the work of \textit{M. Linden} [Econ. Lett. 64, No.~1, 31--36 ( (1999; Zbl 1049.62510) to allow the AR coefficient to be drawn from a polynomial density function. The polynomial density incorporates a wealth of multi-modal density functions as special cases.
Terence Tai-Leung Chong
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Chaotic AR(1) model estimation
2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221), 2002Chaotic signals generated by iterating nonlinear difference equations may be useful models for many natural phenomena. We propose a family of chaotic models for signal processing applications. The chaotic signals generated by this family of first-order difference equations have autocorrelations identical to stochastic first-order autoregressive (AR ...
Carlos Pantaleón +2 more
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Journal of Applied Probability, 1984
We consider the model where φ 1, φ 2 are real coefficients, not necessarily equal, and the at ,'s are a sequence of i.i.d. random variables with mean 0. Necessary and sufficient conditions on the φ 's are given for stationarity of the process.
Petruccelli, Joseph D. +1 more
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We consider the model where φ 1, φ 2 are real coefficients, not necessarily equal, and the at ,'s are a sequence of i.i.d. random variables with mean 0. Necessary and sufficient conditions on the φ 's are given for stationarity of the process.
Petruccelli, Joseph D. +1 more
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CONFIDENCE REGIONS FOR PARAMETERS IN THE AR(1) MODEL
Journal of Time Series Analysis, 1995Abstract.The construction of approximate joint and marginal confidence regions for parameters in the first‐order autoregressive time series model is discussed. These regions are based on the large sample distributions of the likelihood ratio (and approximations to it), of the maximum likelihood estimates and of the score statistics.
Hamilton, David C., Wu, Ka Ho
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A multiple-threshold AR(1) model
Journal of Applied Probability, 1985We consider the modelZt=φ(0,k)+ φ(1,k)Zt–1+at(k) wheneverrk−1<Zt−1≦rk, 1≦k≦l, withr0= –∞ andrl=∞. Here {φ(i, k);i= 0, 1; 1≦k≦l} is a sequence of real constants, not necessarily equal, and, for 1≦k≦l, {at(k),t≧1} is a sequence of i.i.d. random variables with mean 0 and with {at(k),t≧1} independent of {at(j),t≧1} forj≠k.Necessary and sufficient ...
Chan, K. S. +3 more
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TAIL INDEX OF AN AR(1) MODEL WITH ARCH(1) ERRORS
Econometric Theory, 2013Relevant sample quantities such as the sample autocorrelation function and extremes contain useful information about autoregressive time series with heteroskedastic errors. As these quantities usually depend on the tail index of the underlying heteroskedastic time series, estimating the tail index becomes an important task. Since the tail index of such
Chan, Ngai Hang +3 more
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STRUCTURAL CHANGE IN AR(1) MODELS
Econometric Theory, 2001This paper investigates the consistency of the least squares estimators and derives their limiting distributions in an AR(1) model with a single structural break of unknown timing. Let β1 and β2 be the preshift and postshift AR parameter, respectively. Three cases are considered: (i) |β1| < 1 and |β2| < 1; (ii) |β1| < 1 and β2 = 1; and
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An omnibus test for the time series model AR(1)
Journal of Econometrics, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Anderson, T. W. +2 more
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Unit root bootstrap tests for AR (1) models
Biometrika, 1996zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ferretti, Nelida, Romo, Juan
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