arXiv 20 Aug 2021 · Mathematics — Statistics Theory
arXiv:2108.09083 · PDF · DOI · OpenAlex · Extracted main text
The higher dimensional autoregressive models would describe some of the econometric processes relatively generically if they incorporate the heterogeneity in dependence on times. This paper analyzes the stationarity of an autoregressive process of dimension $k>1$ having a sequence of coefficients $\beta$ multiplied by successively increasing powers of $0<\delta<1$. The theorem gives the conditions of stationarity in simple relations between the coefficients and $k$ in terms of $\delta$. Computationally, the evidence of stationarity depends on the parameters. The choice of $\delta$ sets the bounds on $\beta$ and the number of time lags for prediction of the model.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | E.I. Im, D. L. Hammes and D.T. Wills, Stationarity Condition for an… (2006) 22, 164-168 | 0.811 | 4 | 2 | 100% |
| 2 | A.C Chiang and K. Wainwright, Fundamental Methods of Mathematical Ec… (1980) | 0.644 | 2 | 2 | 100% |
| 3 | P. A. Samuelson, Conditions that the Roots of a Polynomials be Less… (1941) 12, 360-364 | 0.644 | 2 | 2 | 100% |
| 4 | G. E. Box, G. M. Jenkins, G.C. Reinsel and G. M. Ljung, Time series… (2010) | 0.405 | 1 | 1 | 100% |
| 5 | G. G. Judge, W.E. Griffiths, R.C. Hill, H. Lutkepohl and T.C. Lee, I… (1989) | 0.405 | 1 | 1 | 100% |
| 6 | H. Akaike, Fitting autoregressive models for prediction, Ann. Inst.… (1969) 21, 243-247 | 0.405 | 1 | 1 | 100% |
| 7 | R.D. Carmichael, Elementary Inequalities for the Roots of an Algebra… (1918) 24, 286-296 | 0.405 | 1 | 1 | 100% |
Showing the top 7 of 7 scored citations.