By Wai Keung Li, David A. Stanford, Hao Yu
This quantity experiences and summarizes a few of A. I. McLeod's major contributions to time sequence research. It additionally comprises unique contributions to the sector and to comparable parts through members of the festschrift held in June 2014 and neighbors of Dr. McLeod. overlaying a various diversity of state of the art issues, this quantity good balances utilized and theoretical study throughout fourteen contributions by means of specialists within the box. will probably be of curiosity to researchers and practitioners in time sequence, econometricians, and graduate scholars in time sequence or econometrics, in addition to environmental statisticians, info scientists, statisticians drawn to graphical types, and researchers in quantitative possibility management.
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This quantity studies and summarizes a few of A. I. McLeod's major contributions to time sequence research. It additionally comprises unique contributions to the sector and to comparable parts via members of the festschrift held in June 2014 and acquaintances of Dr. McLeod. overlaying a various diversity of cutting-edge themes, this quantity good balances utilized and theoretical study throughout fourteen contributions via specialists within the box.
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Additional info for Advances in Time Series Methods and Applications : The A. Ian McLeod Festschrift
Kock, A. B. (2012). On the oracle property of the adaptive lasso in stationary and nonstationary autoregressions. CREATES research papers 2012-05, Aarhus University. 21. Kock, A. , & Callot, L. A. F. (2012). Oracle inequalities for high dimensional vector autoregressions. CREATES research paper 2012-12, Aarhus University. 22. Liu, Z. Z. (2014). The doubly adaptive LASSO methods for time series analysis. University of Western Ontario - Electronic Thesis and Dissertation Repository. Paper 2321. 23.
Da L γ Theorem 2 (Oracle properties of φˆ T ) Let aT = T min |φ˜l |γ1 Al 2 and bT = l∈S √ γ γ γ T maxc |φ˜l |γ1 Al 2 , where |φ˜l |γ1 Al 2 corresponds to |φ˜ (i j,k) |γ1 Ak 2 by the bijecl∈S da L P tive function (11). If λT = o p (aT ) and λT /bT − → ∞, then under A0–A3, φˆ T must satisfy: (i) Selection Consistency: P Sˆ T = S (ii) Identification consistency: P √ (iii) Asymptotic Normality: T as T → ∞. − → 1, pˆ Tda L = p da L φˆ Sˆ T − φ ∗S − → 1, and D −→ N 0, (Γ SS )−1 ⊗ Σε , The Doubly Adaptive LASSO for Vector Autoregressive Models 31 da L Theorem 2 regards the asymptotic properties of φˆ Sˆ T , the nonzero subvector of da L da L φˆ T .
For each data set, we use grid-search method and the BIC criteria to find an approximately optimal combination of γ0 , γ1 , and γ2 . 25 . The same 3-dimensional grid G is used for all 1000 replicates. Z. Liu et al. Z. Liu et al. 3⎠ . 1 The results are consistent with what we got from the bivariate case. Interested readers may obtain the results from authors through emails. 7 Real Data Analysis We use the data of quarterly West German investment, income, and consumption data (1960–1982) from Lütkepohl [23, pp.
Advances in Time Series Methods and Applications : The A. Ian McLeod Festschrift by Wai Keung Li, David A. Stanford, Hao Yu