Time Series: Theory and Methods

By Peter J. Brockwell, Richard A. Davis. 2013

7,383 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability, Time-Series & Forecasting

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Statistics and Probability

In Time-Series & Forecasting

Citations in the corpus

The Arrow of Time in Multivariate Time Series (2016, background): “A way to check if a time series is causal is given by the following suﬃcient criterion: Lemma 1 (Causality criterion, Theorem 11.3.1 in (Brockwell and Davis, 1991)) where the matrices { Ψ j } j 0 have absolutely summable components and are uniquely determined by In this work, we require yet another…”
Telling cause from effect in deterministic linear dynamical systems (2015, background): “Assuming X is a zero mean stationary process (in this paper, stationary will always stand for weakly or wide-sense stationary [5]), we will denote by Cxx(τ) = E[XtXt+τ ] the autocovariance function of the process and assume it is absolutely summable.”
The Tourism Forecasting Competition (2011, background): “To ensure causality and invertibility, it is assumed that φ(z) and θ (z) have no roots for |z| 1 (Brockwell and Davis, 1991).”
Automatic Time Series Forecasting: The forecast Package for R (2008, background): “To ensure causality and invertibility, it is assumed that ϕ ( z ) and θ ( z ) have no roots for ♣ z ♣ 1 (Brockwell and Davis 1991).”
Fast online deconvolution of calcium imaging data (2016, methodology): “g activity. Given c 1 = v 1 the ﬂuorescence values c tfor t= 1;:::;l 1 are then given by dt 1c 1 with decay variable d= 1 2 ( 1 + q 2 1 + 4 2) (S8) as well known in the AR / linear systems literature [51]. The ﬁrst pool is merged with the second one whenever the constraint v 2 dl 1v 1 is violated. S”
Statistical Analysis in Climate Research (2000, neutral): “See Brillinger [66] or Brockwell and Davis [68] for details.”
Low-Frequency Econometrics (2015, background): “In traditional spectral analysis (see, for instance, Priestley (1981) or Brockwell and Davis (1991)), the periodogram is the starting point to learn about the spectral properties of a time series.”
Deep Factors with Gaussian Processes for Forecasting (2018, methodology): “Classical time series methods, such as Autoregressive Integrated Moving Average (ARIMA) [3], exponential smoothing [4] and general Bayesian time series [5], excel at modeling the complex dynamics of individual time series of sufficiently long history.”
Spectral Filtering for General Linear Dynamical Systems (2018, methodology): “This technique is well-established in the context of autoregressive models for time-series prediction that have been extensively studied in the learning and signal-processing literature, see e.g. [Ham94, BJR94, BD09, KM16, AHMS13, MW07].”
Fractional) Beta Convergence (2000, background): “ned in (6) is called an ARFIMA(0; d; 0) process and more in general when vt is an (inverted) ARMA(p; q) we obtain an ARFIMA(p; d; q) process.”