EconBase
← All papers

Causal Non-causal State Space Models and the Modelling of Financial Bubbles

Frederik Bjerg Krabbe

arXiv 28 Aug 2026 · Econometrics

arXiv:2608.28115 · PDF · Extracted main text

Abstract

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.

Citation extraction

47
references
96
in-text mentions
47
distinct cited
0
self-citations
12,763
main-text words

appendix boundary found by appendix_command · 55% of the source is main text. Read the extracted text to check this.

Most heavily cited references

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.

ReferenceIntensityMentionsSectionsMain text
1C. Gouriéroux and J.-M. Zakoän (2017) Local explosion modelling by non-causal process1.000144100%
2J. L. Knight and J. Yu (2002) Empirical characteristic function in time series estimation1.00093100%
3C. Gouriéroux, J. Jasiak, and M. Tong (2021) Convolution-based filtering and forecasting: An application to wti crude oil prices1.00053100%
4P. C. Phillips, Y. Wu, and J. Yu (2011) Explosive behavior in the 1990s nasdaq: When did exuberance escalate asset values?0.81142100%
5P. J. Brockwell and R. A. Davis (1991) Time series: theory and methods0.7373367%
6G. Samorodnitsky and M. S. Taqqu (1994) Stable Non-Gaussian Random Processes0.7373367%
7N. J. Gordon, D. J. Salmond, and A. F. Smith (1993) Novel approach to nonlinear/non-gaussian bayesian state estimation0.73732100%
8M. Klaas, M. Briers, N. De Freitas, A. Doucet, S. Maskell, and D. Lang (2006) Fast particle smoothing: If i had a million particles0.73732100%
9N. Chopin, O. Papaspiliopoulos, et al (2020) An introduction to sequential Monte Carlo, volume 40.69361100%
10S. Cambanis and I. Fakhre-Zakeri (1995) On prediction of heavy-tailed autoregressive sequences: forward versus reversed time0.6443267%

Showing the top 10 of 47 scored citations.