arXiv 28 Aug 2026 · Econometrics
arXiv:2608.28115 · PDF · Extracted main text
In this paper, we study causal non-causal state space models to model time series characterised by a local explosive increase followed by a sharp decrease such as stock prices. To motivate the use of causal non-causal state space models, we show that the causal non-causal convolution autoregressive model introduced by Gourieroux and Zakoian (2017) can be consistent with the rational expectations stock price model. As in a causal state space model, a central question is how to perform state and parameter inference in the causal non-causal state space model, which we discuss in the paper. We also study the causal non-causal convolution autoregressive model in more detail, providing some new results for the model. To illustrate the usefulness of causal non-causal state space models, we use the causal non-causal convolution autoregressive model to estimate the size of the dot-com bubble in both real time and a posteriori with the stable non-causal autoregressive model considered also by Gourieroux and Zakoian (2017) as a benchmark.
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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 | C. Gouriéroux and J.-M. Zakoän (2017) Local explosion modelling by non-causal process | 1.000 | 14 | 4 | 100% |
| 2 | J. L. Knight and J. Yu (2002) Empirical characteristic function in time series estimation | 1.000 | 9 | 3 | 100% |
| 3 | C. Gouriéroux, J. Jasiak, and M. Tong (2021) Convolution-based filtering and forecasting: An application to wti crude oil prices | 1.000 | 5 | 3 | 100% |
| 4 | P. C. Phillips, Y. Wu, and J. Yu (2011) Explosive behavior in the 1990s nasdaq: When did exuberance escalate asset values? | 0.811 | 4 | 2 | 100% |
| 5 | P. J. Brockwell and R. A. Davis (1991) Time series: theory and methods | 0.737 | 3 | 3 | 67% |
| 6 | G. Samorodnitsky and M. S. Taqqu (1994) Stable Non-Gaussian Random Processes | 0.737 | 3 | 3 | 67% |
| 7 | N. J. Gordon, D. J. Salmond, and A. F. Smith (1993) Novel approach to nonlinear/non-gaussian bayesian state estimation | 0.737 | 3 | 2 | 100% |
| 8 | M. Klaas, M. Briers, N. De Freitas, A. Doucet, S. Maskell, and D. Lang (2006) Fast particle smoothing: If i had a million particles | 0.737 | 3 | 2 | 100% |
| 9 | N. Chopin, O. Papaspiliopoulos, et al (2020) An introduction to sequential Monte Carlo, volume 4 | 0.693 | 6 | 1 | 100% |
| 10 | S. Cambanis and I. Fakhre-Zakeri (1995) On prediction of heavy-tailed autoregressive sequences: forward versus reversed time | 0.644 | 3 | 2 | 67% |
Showing the top 10 of 47 scored citations.