共查询到10条相似文献,搜索用时 101 毫秒
1.
O. D. Anderson 《时间序列分析杂志》1992,13(6):485-500
Abstract. We are primarily interested in relating the partial autocorrelation behaviour of an autoregressive integrated moving-average process of order ( p, d, q ), { Z i } say, with those of its D -differenced processes {(1 - B ) D Z i } ( D = 1, …, d ). To this end, we evaluate the early partial correlations corresponding to serial correlations which initially follow a slow linear decline from unity. These partials, to a first approximation, take a small constant negative value from lag 2 onwards. We also demonstrate a relationship between the theoretical partials π k and π k (Δ) for a once-integrated process { Z i } and its first-differenced process {(1 - B ) Z i } respectively. These results carry over to cases where the non-stationary zeros are at -1, and differencing is replaced by the corresponding 'simplifying' transformation implicit in the operator 1 + B. 相似文献
2.
Abstract. For the SETAR (2; 1,1) model
where {at (i)} are i.i.d. random variables with mean 0 and variance σ2 (i), i = 1,2, and {at (l)} is independent of {at (2)}, we consider estimators of φ1 , φ 2 and r which minimize weighted sums of the sum of squares functions for σ2 (1) and σ2 (2). These include as a special case the usual least squares estimators. It is shown that the usual least squares estimators of φ1 , φ2 and r are consistent. If σ2 (1) ≠σ2 (2) conditions on the weights are found under which the estimators of r and φ1 or φ2 are not consistent. 相似文献
where {a
3.
Abstract. For the strictly stationary AR( k ) process Z t = Λ ( Z t -1 ) + α t , with Λ : R k → R , Z t -1 = [ Z t -1 , Z t -2 ,…, Z t-k ] and { α t } an independent identically distributed white noise process, we partially characterize the Λ for which the stationary distribution of Z t is normal. 相似文献
4.
R. J. Bhansali 《时间序列分析杂志》1997,18(3):213-229
Consider a discrete-time linear process { x t }, a one-sided moving average of independent identically distributed random variables {ε t }, with the common distribution in the domain of attraction of a symmetric stable law of index δ∈ (0, 2) and the moving-average coefficients b ( j ) such that ε t is invertible in terms of the present and possibly infinite past values of { x t }. By treating { x t } as if it is second-order stationary, a normalized spectral density function f (μ) is defined in terms of the b ( j ) and, having observed x 1 , ..., x T , an autoregression of order k is fitted by the well-known Yule–Walker and least squares methods and the normalized autoregressive spectral estimators are constructed. On letting k ←∞ as T ←∞, but sufficiently slowly, these estimators are shown to be uniformly consistent for f (μ), the convergence rate being T −1/φ , φ > δ. The finite sample behaviour is investigated by a simulation study which also examines possible effects of considering 'non-invertible' models. 相似文献
5.
Jií Andl 《时间序列分析杂志》1987,8(4):373-378
Abstract. Let X t = c 0 Y t + c 1 Y t -1 +… be a linear process with known coefficients c k , where Y t is a strict white noise. Let m 1 , …, m 2r be given numbers. A method is presented to determine whether there exists a distribution of Y t such that EX k t = m k for k = 1, …, 2 r . In the positive case, such a distribution of Y t is described. Some explicit formulas for AR(1) and AR(2) models are derived. The results can be used for simulating a process with given moments of its stationary distribution. The procedure also enables proof that some stationary distributions cannot belong to the given linear process. 相似文献
6.
Abstract. Consider a stationary non-negative autoregressive (AR) model given x t = b 1 x t -1, +…+ b p x t-p + e t , where the e t are independent identically distributed non-negative variables and b 1 , …, b p are non-negative parameters, and all the roots of the equation 1 – b 1 u –…– b p u p = 0 are outside the unit circle. The stationary solution of the above AR model is called a stationary non-negative AR process. Let x 1 , x 2 , … x n be an example of a stationary non-negative AR process. Under very general conditions strongly consistent estimators of the AR parameters b 1 , b 2 , …, b p have been studied. In this paper a new procedure is proposed to estimate not only b 1 , b 2 , …, b p but also b o which is the essential lower bound of the variable e t . We shall show that the new estimators obtained using the new procedure are consistent estimators of b o , b 1 , …, b p under the weakest condition which guarantees that the stationary non-negative AR model has a stationary non-degenerative solution. 相似文献
7.
Kamal C. Chanda 《时间序列分析杂志》1987,8(3):283-291
Abstract. Let X 1 , …, X n be a random sample from a population with a distribution function F and let E ( X 1 ) = 0, E ( X 1 2 ) < ∞. Let r 1 =Σ t =1 n -1 X t X t +1 /Σ t =1 n -1 ( X t 2 + X t +1 2 ). We derive a proper Edgeworth type expansion for the sampling distribution of r 1 under the assumption that F is a mixture of Gaussian distributions of one of two given types. The result can easily be extended to the sampling distributions of serial correlations of arbitrary lag s . 相似文献
8.
Abstract. Consider a stationary autoregressive process given by X t = b 1 X t -1 +…+ b p X t-p + Y t , where the Y t are independent identically distributed positive variables and b 1 ,…, b p are non-negative parameters. Let the variables X 1 ,…, X n be given. If p = 1 then it is known that b 1 *= min( X t / X t -1 ) is a strongly consistent estimator for b 1 under very general conditions. In this paper the case p = 2 is analysed in detail. It is proved that min( X t / X t -1 )→ b 1 almost surely (a.s.) and min( X t / X t -2 )→ b 2 + b 1 2 a.s. as n → 8. The convergence is very slow. Denote by b 1 * and b 2 * values of b 1 and b 2 respectively which maximize b 2 + b 2 under the conditions X t - b 1 X t -1 - b 2 X t -2 ≥ 0 for t = 3,…, n . We prove that b 1 * b 1 and b 2 * b 2 a.s. Simulations show that b 1 * and b 2 * are better than the least-squares estimators of the autoregressive coefficients when the distribution of Y t is exponential. 相似文献
9.
Abstract. A generalized autoregressive (GAR) process {Z ( t ) ; t = 0 , ±1, …} is defined to satisfy the recurrence relation Z(t) = Aθ (t)Z (t -l)+ u( t ), where {Aθ (t); t = 0,±1, …} is itself a stochastic process depending on a vector parameter θ and where {u( t ); t = 0, ±1, …} is white noise with Eu 2 ( t ) = a 2 . This paper develops theory and methodology and implementing the class of GAR processes for time series modeling and forecasting. Conditions on the 'parameter process' { A θ ( t ); t = 0, ±1, …} are obtained for the existence of a GAR process; necessary and sufficient conditions on { Aθ ( t ) ; t = 0, ±1, …} for existence of a stationary GAR process are also obtained. Procedures are developed for computing maximum likelihood estimates of the parameters 0 and u2 and for computing the minimum mean squared error forecasts for GAR processes. 相似文献
10.
STATIONARY PROCESSES WITH A FINITE NUMBER OF NON-ZERO CANONICAL CORRELATIONS BETWEEN FUTURE AND PAST
Abstract. The spectral densities f (γ) are determined for stationary random processes X (t) with continuous time which have the property that the number of non-zero canonical correlations between the past X(t) ( t ≤ 0) (more accurately the present and the past) and the future X(t) ( t ≥θ) is finite (equal to N ) at any θ≥τ for some r > 0. A method for finding all the corresponding canonical correlations P1 , …, PN and the canonical variables X 1 - , …, X N - and X 1 + , …, X N + is given. Similar results related to processes X(t) with discrete (integral) time are briefly considered. 相似文献