Statistical Analysis of Time Series

By Tomás Cipra. 2010

633 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Control and Systems Engineering, Signal Processing

View Paper: https://www.semanticscholar.org/paper/48ad8c3057e3aec7fb1ee18aca302771b768b2ab

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Citations in the corpus

Representation of Cointegrated Autoregressive Processes with Application to Fractional Processes (2008, positive): “In case ′1 ∑t i=1 ′Xi + ′2Xt were stationary, we would have ′1 ′C ∗ + ′2C = 0 Multiplying by , we get 0 = ′1 ′C ∗ = − ′1, so that 1 = 0 For details, see Engsted and Johansen (1999).”
Machine Learning Strategies for Time Series Forecasting (2012, background): “is a specific realization of a random process, where the randomness arises from many independent degrees of freedom interacting linearly [4].”
Fourier analysis of stationary time series in function space (2013, background): “Adding more structure, for example, in the context of linear processes, one can focus on extending weaker conditions requiring finite fourth moments and summable coefficients [Hannan (1970), Anderson (1994)].”
The MVGC multivariate Granger causality toolbox: a new approach to Granger-causal inference. (2014, methodology): “Standard theory (Anderson, 1971) yields that a rather general class of covariance-stationary multivariate process—including many nonlinear processes—may be modelled as VARs, albeit of theoretically inﬁnite order (see also the next Section).”
Understanding the Lomb–Scargle Periodogram (2017, background): “…extensions (including the Lomb-Scargle we will discuss momentarily) are not consistent estimators of the power spectrum: that is, the periodogram has unavoidable intrinsic variance, even in the limit of an infinite number of observations (for a detailed discussion, see Chp 8.4 of Anderson 1971).”
Time Series Analysis (2003, neutral): “The variance and covariances of the estimated autocovariances are derived, inter alia, by Hannan (1960), and Anderson (1971). As T , both tend to zero, as the estimates are asymptotically uncorrelated and consistent.”
OPENING THE BLACK BOX: STRUCTURAL FACTOR MODELS WITH LARGE CROSS SECTIONS (2009, background): “For a general result see Anderson and Deistler (2008). The proof of their Proposition 1 can be adapted to show that for a generic rational K (L), with given maxima for the orders of numerator and denominator polynomials, if n > q ≥ 1, then rank(K (z)) = q for all complex numbers z (no matter whether”
From moments of sum to moments of product (2008, neutral): “Examples of these include the sample autocovariances and the sample autocorrelation coefficients are discussed in Anderson [1].”
Batch means and spectral variance estimators in Markov chain Monte Carlo (2008, methodology): “One could use the sum of the γn(s) to estimate σ2 g , though this turns out to be a poor estimator; see Anderson (1994) and Bratley et al.”
ASYMPTOTICS OF SPECTRAL DENSITY ESTIMATES (2009, background): “(1.5) Properties of spectral density estimates have been explored in many classical textbooks on time series; see, for example, Anderson (1971), Brillinger (1975), Brockwell and Davis (1991), Grenander and Rosenblatt (1957), Priestley (1981), and Rosenblatt (1985), among others.”
Consideration of Trends in Time Series (2011, background): “Anderson (1971): ... a slowly moving function of time, which is often called a trend, particularly by economists, and is exempli ed by a polynomial of fairly low degree .”
Asymptotic normality of the principal components of functional time series (2013, positive): “[1], convergence of the sample covariance matrices is established by imposing summability conditions on the impulse response coefficients.”
Banks' risk assessment of Swedish SMEs (2008, background): “The size of the Z-values indicates the importance of the factor; in other words, the higher the Z-value, the more important the factor (Andersen 1971).”
Asymptotic theory for stationary processes (2011, methodology): “Properties of spectral density estimates have been discussed in many classical textbooks on time series; see Anderson (1971), Brillinger (1975), Brockwell and Davis (1991), Grenander and Rosenblatt (1984), Priestley (1981) and Rosenblatt (1985) among others.”
Asymptotic properties of the efficient estimators for cointegrating regression models with serially dependent errors (2009, methodology): “hFMR = ⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨ ⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩ [ 1 cB1·2(1) 1 c ∫ 1 0 B2(r)dB1·2(r) ] , MN → ∞, ⎡ ⎢⎣ 1 c ( B1(1) −B′ 2(1)Ω 22 ω21κ ) [ 1 c (∫ 1 0 B2(r)dB1(r) − ∫ 1 0 B2(r)dB ′ 2(r)Ω −1 22 ω21κ ) +1c (1 − κ)ω21 ] ⎤ ⎥⎦ , MN → dM , [ 1 cB1(1) 1 c (∫ 1 0 B2(r)dB1(r) + ω21 ) ] , MN → 0,”