Time Series: Theory and Methods (2nd ed,)

By Eric R. Ziegel. 2012

410 citations recorded by the source corpus.

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Citations in the corpus

Trend analysis of climate time series: A review of methods (2019, background): “The AR(1) model has an exponentially (i.e., fast) decaying autocorrelation function (Brockwell and Davis, 1991; Priestley, 1981).”
A Dual-Stage Attention-Based Recurrent Neural Network for Time Series Prediction (2017, methodology): “Although the well-known autoregressive moving average (ARMA) model [Whittle, 1951] and its variants [As-teriou and Hall, 2011; Brockwell and Davis, 2009] have shown their effectiveness for various real world applications, they cannot model nonlinear relationships and do not differentiate among the…”
DEPENDENT FUNCTIONAL LINEAR MODELS WITH APPLICATIONS TO MONITORING STRUCTURAL CHANGE (2014, unknown): “For further information on lag-window estimators and specific examples, such as the Bartlett estimator and the flat-top kernel, we refer to Section 10.4 of Brockwell and Davis (1991).”
Covariance matrix estimation and linear process bootstrap for multivariate time series of possibly increasing dimension (2015, background): “…density estimates in Section 4, we have to assume unconditional CLTs in (A5) and (A6), which are satisfied also under certain mixing conditions [cf. Doukhan (1994), Brillinger (1981)], linearity [cf. Brockwell and Davis (1991), Hannan (1970)] or weak dependence [cf. Dedecker et al. (2007)].”
Uniform change point tests in high dimension (2015, background): “[11]) provides many potential candidates to estimate σ 2 h .”
Modeling and forecasting electricity spot prices: A functional data perspective (2013, methodology): “…subsets of the learning sample and the final model selection is done by the AIC.2 As usual, the days ahead forecasts β̂TL,1( ) and β̂TL,2( ) are given by the conditional expectations of β̂TL+ ,1 and β̂TL+ ,2 given the data from the learning sample; see, for example, Brockwell and Davis (1991).”
Prediction of functional ARMA processes with an application to traffic data (2016, methodology): “We follow the lines of the proof of Proposition 3.1.1 of Brockwell and Davis [2] and Theorem 3.1 in [3].”
Bayesian inference on structural impulse response functions (2019, background): “15 That is, if and only if Θ(L) −1 is a one-sided lag polynomial, so that the SVAR representation Θ(L) −1 y t = ε t obtains (Brockwell & Davis, 1991, −1 is not well-defined in the knife-edge case det(Θ(1)) = det( q =0 Θ ) = 0. ε t = ∞ =0 (−Θ 1 ) y t− , so it can be recovered using current and past…”
TFT-bootstrap: Resampling time series in the frequency domain to obtain replicates in the time domain (2011, background): “1 in Brockwell and Davis [5] yield assertions (b) and (c).”
On the Marčenko-Pastur law for linear time series (2013, background): “, Chapter 10 of [7]), and let for the real case X̃ = UA1(Z + A1ZL̃)U.”
A functional limit theorem for dependent sequences with infinite variance stable limits (2010, result): “Then (Xn)n satisfies the strong mixing condition with geometric rate (see Davis and Mikosch [15]).”
Multivariate CARMA processes, continuous-time state space models and complete regularity of the innovations of the sampled processes (2012, methodology): “4) can be conveniently computed by using the Kalman recursions ([8], Section 12.”
A robust approach for estimating change-points in the mean of an AR(1) process (2014, unknown): “1 of [10], we get that ∑n i=1(yi−1 −E(yi−1)) i = OP ( √ n).”
Locally Stationary Processes (2011, unknown): “With the above form of the spectrum fη(u, λ) (cf.(5)) and Kolmogorov’s formula, (cf. Brockwell and Davis, 1991, Theorem 5.8.1) we obtain with R̂T (uj) and r̂T (uj) as defined in (7) after some straightforward calculations LBWT (η) = 1 2 1 M M∑ j=1 [ log 4π2σ2η(uj) + 1 σ2η(uj) ( ĉT (uj , 0)− r̂T…”
SPLIDHOM: A Method for Homogenization of Daily Temperature Observations (2011, methodology): “according to a classical additive model (Brockwell and Davis 2006).”