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- W4290687598 abstract "Inspired by the question of identifying the start time $tau$ of financial bubbles, we address the calibration of time series in which the inception of the latest regime of interest is unknown. By taking into account the tendency of a given model to overfit data, we introduce the Lagrange regularisation of the normalised sum of the squared residuals, $chi^{2}_{np}(Phi)$, to endogenously detect the optimal fitting window size := $w^* in [tau:bar{t}_2]$ that should be used for calibration purposes for a fixed pseudo present time $bar{t}_2$. The performance of the Lagrange regularisation of $chi^{2}_{np}(Phi)$ defined as $chi^{2}_{lambda (Phi)}$ is exemplified on a simple Linear Regression problem with a change point and compared against the Residual Sum of Squares (RSS) := $chi^{2}(Phi)$ and RSS/(N-p):= $chi^{2}_{np}(Phi)$, where $N$ is the sample size and p is the number of degrees of freedom. Applied to synthetic models of financial bubbles with a well-defined transition regime and to a number of financial time series (US S&P500, Brazil IBovespa and China SSEC Indices), the Lagrange regularisation of $chi^{2}_{lambda}(Phi)$ is found to provide well-defined reasonable determinations of the starting times for major bubbles such as the bubbles ending with the 1987 Black-Monday, the 2008 Sub-prime crisis and minor speculative bubbles on other Indexes, without any further exogenous information. It thus allows one to endogenise the determination of the beginning time of bubbles, a problem that had not received previously a systematic objective solution." @default.
- W4290687598 created "2022-08-08" @default.
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- W4290687598 date "2017-07-22" @default.
- W4290687598 modified "2023-10-17" @default.
- W4290687598 title "Lagrange regularisation approach to compare nested data sets and determine objectively financial bubbles' inceptions" @default.
- W4290687598 doi "https://doi.org/10.48550/arxiv.1707.07162" @default.
- W4290687598 hasPublicationYear "2017" @default.
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