Xuanling Yang, Dong Li, Ting Zhang
arXiv 13 Jan 2024 · Mathematics — Statistics Theory · publishedStatistica Sinica (2026)
arXiv:2401.07038 · PDF · DOI · OpenAlex · Extracted main text
Economic and financial time series can feature locally explosive behavior when a bubble is formed. The economic or financial bubble, especially its dynamics, is an intriguing topic that has been attracting longstanding attention. To illustrate the dynamics of the local explosion itself, the paper presents a novel, simple, yet useful time series model, called the stochastic nonlinear autoregressive model, which is always strictly stationary and geometrically ergodic and can create long swings or persistence observed in many macroeconomic variables. When a nonlinear autoregressive coefficient is outside of a certain range, the model has periodically explosive behaviors and can then be used to portray the bubble dynamics. Further, the quasi-maximum likelihood estimation (QMLE) of our model is considered, and its strong consistency and asymptotic normality are established under minimal assumptions on innovation. A new model diagnostic checking statistic is developed for model fitting adequacy. In addition, two methods for bubble tagging are proposed, one from the residual perspective and the other from the null-state perspective. Monte Carlo simulation studies are conducted to assess the performances of the QMLE and the two bubble tagging methods in finite samples. Finally, the usefulness of the model is illustrated by an empirical application to the monthly Hang Seng Index.
appendix boundary found by appendix_command · 72% of the source is main text. Read the extracted text to check this.
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 | Phillips, Shi \ Yu (2015) `Testing for multiple bubbles: Limit theory of real-time detectors', Internat | 0.874 | 7 | 2 | 100% |
| 2 | Blasques, Koopman \ Nientker (2022) `A time-varying parameter model for local explosions', J | 0.811 | 4 | 2 | 100% |
| 3 | Phillips \ Yu (2011) `Dating the timeline of financial bubbles during the subprime crisis', Quant | 0.737 | 3 | 2 | 100% |
| 4 | Phillips, Shi \ Yu (2015) `Testing for multiple bubbles: Historical episodes of exuberance and collapse in the S&P 500', Internat | 0.737 | 3 | 2 | 100% |
| 5 | Kurozumi \ Skrobotov (2023) `On the asymptotic behavior of bubble date estimators', J | 0.644 | 2 | 2 | 100% |
| 6 | Meyn \ Tweedie (2009) Markov Chains and Stochastic Stability, 2nd edn, Cambridge University Press | 0.511 | 3 | 2 | 33% |
| 7 | Blanchard \ Watson (1982) `Bubbles, rational expectations and financial markets', NBER working paper p. no | 0.511 | 2 | 1 | 100% |
| 8 | Evans (1991) `Pitfalls in testing for explosive bubbles in asset prices', Am | 0.511 | 2 | 1 | 100% |
| 9 | Ling (2005) `Self-weighted least absolute deviation estimation for infinite variance autoregressive models', J | 0.511 | 2 | 1 | 100% |
| 10 | Ling (2007) `Self-weighted and local quasi-maximum likelihood estimators for ARMA-GARCH/IGARCH models', J | 0.511 | 2 | 1 | 100% |
Showing the top 10 of 35 scored citations.