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High-frequency data offers unparalleled insights into market dynamics, facilitating the analysis of statistical properties, dynamic correlations, and scaling behaviours with a precision previously unattainable. These Statistical Properties are essential framework for understanding and modelling the interactions between global financial markets over time. The aim of this study was to investigate the dynamic conditional correlations and scaling behaviour of high-frequency data from January,1 2010 to December 31, 2020. Using the S&P 500, FTSE 100, Nikkei 225, HKEX and DAX as sampled financial markets, the results revealed significant differences in correlation patterns across the markets, as well as fractal-like scaling behaviour. The relationship between the S&P 500-FTSE 100 and S&P 500-DAX supports trend-following strategies, while the Nikkei 225-HKEX and Nikkei 225-FTSE 100 may be closer to random-walk behaviour. This study advances the frontier of knowledge on high-frequency data and offers insights into the temporal relationships and scaling properties between financial markets.

Speculative bubbles are of extreme importance in modern society. They are well known for their dynamics and their dramatic consequences which affect most financial markets. Therefore, many researchers have aimed to fully understand, identify and predict speculative bubbles. However, they still cannot agree on the correct identification and exact prediction of when they will burst ahead. One of the best-known models in this context is the Johansen-Ledoit-Sornette (JLS) model introduced in 1996 and which has then undergone several adjustments over the years. This model states that bubbles are not characterized by exponential growth but rather by faster than exponential growth in prices. This characteristic is due to the imitation and herd behavior of irrational investors which creates positive feedback during the bubble forming period. Thus, this model is mainly based on the log-periodic power law equation (LPPL) which is generally used in physics for the prediction of natural phenomena such as earthquakes. Our contribution through this paper is to examine the ability of standard JLS models as well as its extension to the generalized JLS model to predict the critical time of bubble burst, to measure its size and to calculate the fundamental value of financial assets. Our results are obtained by modeling asset prices of the historical oil bubble of 2008. Indeed, our implemented algorithm is based on a combination between the Levenberg-Marquardt algorithm and the Price Gyration method instead of the Taboo search method. Our obtained results gave rise to precise and correct predictions and the expected characteristics of the JLS model during the bubble period.