Foundations of Time Series Analysis and Prediction Theory

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Dynamic factor models with infinite-dimensional factor spaces: One-sided representations (2015, background): “This bears no relationship with the possible non-existence of one-sided representations for finite-dimensional processes, which occurs in particular if their spectral density is singular in a positive-measure subset of [−π π], see e.g. Pourahmadi (2001), Theorem 10.5, p. 361.”
BANDING SAMPLE AUTOCOVARIANCE MATRICES OF STATIONARY PROCESSES (2009, background): “Key words and phrases: Covariance matrix, prediction, regularization, short-range dependence, stationary process.”
On the range of validity of the autoregressive sieve bootstrap (2012, methodology): “For more details of the autoregressive Wold representation (2.3) see Pourahmadi (2001), Lemma 6.4(b), (6.10) and (6.12).”
The asymptotic size and power of the augmented Dickey–Fuller test for a unit root (2018, background): “Furthermore, the coe cients bj are absolutely summable, i.e., ∑∞ j=1 |bj| < ∞ and b(z) = 1 −∑∞ k=1 bjz j 6= 0 for |z| ≤ 1; see Pourahmadi (2001), Lemma 6.4.”
A Course in Time Series Analysis (2001, background): “Whittle (1962) showed that the above criterion is an approximation of the GMLE. The correct proof is quite complicated and uses several matrix approximations due to Grenander and Szegö (1958). Instead we give a heuristic proof which is quite enlightening.”