arXiv 13 Aug 2026 · Econometrics
arXiv:2608.13224 · PDF · Extracted main text
I consider an AR($p$) process that is observed every $q$ periods, either as a snapshot (stock variable) or as a sum over the sampling interval (flow variable). Under fairly mild assumptions, I derive the identified set for general lag lengths $p \in \mathbb{N}$ and sampling frequencies $q \in \mathbb{N}$, I bound its cardinality, and I provide a recipe to compute all candidate points and determine their membership in the identified set. My analysis supports the following conjecture: (i) the error term-variance is point-identified, (ii) under temporal aggregation, the autoregressive parameters are point-identified, and (iii) under discrete sampling they are point-identified for odd sampling frequencies and identified up to alternating sign for even sampling frequencies. I prove this conjecture in some settings and verify it numerically more broadly.
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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 | Palm, F. C. and T. E. Nijman (1984) Missing Observations in the Dynamic Regression Model | 1.000 | 17 | 4 | 100% |
| 2 | Nijman, T. E. and F. C. Palm (1990) a): Parameter Identification in Arma Processes in the Presence of Regular but Incomplete Sampling | 1.000 | 8 | 3 | 100% |
| 3 | Nijman, T. E. and F. C. Palm (1985) Séries temporelles incomplètes en modélisation macroéconomique | 1.000 | 5 | 3 | 100% |
| 4 | Telser, L. G (1967) Discrete Samples and Moving Sums in Stationary Stochastic Processes | 0.874 | 11 | 2 | 100% |
| 5 | Amemiya, T. and R. Y. Wu (1972) The Effect of Aggregation on Prediction in the Autoregressive Model | 0.874 | 8 | 2 | 100% |
| 6 | Brockwell, P. J. and R. A. Davis (1991) Time Series: Theory and Methods | 0.874 | 5 | 2 | 100% |
| 7 | Brewer, K (1973) Some consequences of temporal aggregation and systematic sampling for ARMA and ARMAX models | 0.843 | 3 | 3 | 100% |
| 8 | Weiss, A. A (1984) Systematic sampling and temporal aggregation in time series models | 0.811 | 4 | 2 | 100% |
| 9 | Phillips, P (1973) The problem of identification in finite parameter continuous time models | 0.644 | 4 | 1 | 100% |
| 10 | Marcellino, M (1999) Some Consequences of Temporal Aggregation in Empirical Analysis | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 25 scored citations.