Searcharxiv⌕ Search

arXiv subjects

Md Nurujjaman

Publications and source records attributed to Md Nurujjaman.

10 recordsLinked to original sources
arXiv2026

Detecting Regime Transitions in Dynamical Systems via the Mixup Euler Characteristic Profile

We develop a framework for detecting regime transitions in dynamical systems using the Mixup Euler Characteristic Profile (Mixup ECP) -- the Euler characteristic of the geometric intersection of ball unions around adjacent delay-embedded trajectory segments, viewed as a function of filtration scale. The Mixup ECP provides a detection statistic with a built-in null and guaranteed stability. We formalize regime detection as a low-side-permutation test, establish its validity and consistency, and introduce a multi-delay extension that automatically selects the most informative dynamical timescale. Complementing the topological signal with Complexity Variance, Higuchi fractal dimension, and a rolling mean baseline, the four-signal combined method achieves $9.50$ days MAE on Indian monsoon onset (Nepal target) -- a $32\%$ improvement over the rolling mean baseline and $9\%$ over CUSUM. Validated on the Lorenz system, logistic map, and three monsoon systems spanning both hemispheres (Indian/Nepal, Indian/Kerala, Western North Pacific), plus ENSO and a synthetic EEG dataset, the framework adds value precisely when the transition is gradual or obscured by noise.

math.DS↗
arXiv2026

Core-Periphery Dynamics in Market-Conditioned Financial Networks: A Conditional P-Threshold Mutual Information Approach

This study investigates how financial market structure reorganizes during the COVID-19 crash using a conditional p-threshold mutual information (MI) based Minimum Spanning Tree (MST) framework. We analyze nonlinear dependencies among the largest stocks from four diverse QUAD countries: the US, Japan, Australia, and India. Crashes are identified using the Hellinger distance and Hilbert spectrum; a crash occurs when HD = mu\_H + 2*sigma\_H, segmenting data into pre-crash, crash, and post-crash periods. Conditional p-threshold MI filters out common market effects and applies permutation-based significance testing. Resulting validated dependencies are used to construct MST networks for comparison across periods. Networks become more integrated during the crash, with shorter path lengths, higher centrality, and lower algebraic connectivity, indicating fragility. Core-periphery structure declines, with increased periphery vulnerability, and disassortative mixing facilitates shock transmission. Post-crash networks show only partial recovery. Aftershock analysis using the Gutenberg-Richter law indicates higher relative frequency of large volatility events following the crash. Results are consistent across all markets, highlighting the conditional p-threshold MI framework for capturing nonlinear interdependencies and systemic vulnerability.

q-fin.ST↗
arXiv2024

Complex network analysis of cryptocurrency market during crashes

This paper identifies the cryptocurrency market crashes and analyses its dynamics using the complex network. We identify three distinct crashes during 2017-20, and the analysis is carried out by dividing the time series into pre-crash, crash, and post-crash periods. Partial correlation based complex network analysis is carried out to study the crashes. Degree density ($ρ_D$), average path length ($\bar{l}$), and average clustering coefficient ($\overline{cc}$) are estimated from these networks. We find that both $ρ_D$ and $\overline{cc}$ are smallest during the pre-crash period, and spike during the crash suggesting the network is dense during a crash. Although $ρ_D$ and $\overline{cc}$ decrease in the post-crash period, they remain higher than pre-crash levels for the 2017-18 and 2018-19 crashes suggesting a market attempt to return to normalcy. We get $\bar{l}$ is minimal during the crash period, suggesting a rapid flow of information. A dense network and rapid information flow suggest that during a crash uninformed synchronized panic sell-off happens. However, during the 2019-20 crash, the values of $ρ_D$, $\overline{cc}$, and $\bar{l}$ did not vary significantly, indicating minimal change in dynamics compared to other crashes. The findings of this study may guide investors in making decisions during market crashes.

q-fin.ST↗
arXiv2023

Detection and Forecasting of Extreme event in Stock Price Triggered by Fundamental, Technical, and External Factors

The sporadic large fluctuations are seen in the stock market due to changes in fundamental parameters, technical setups, and external factors. These large fluctuations are termed as Extreme Events (EE). The EEs may be positive or negative depending on the impact of these factors. During such events, the stock price time series is found to be nonstationary. Hence, the Hilbert-Huang transformation (HHT) is used to identify EEs based on their high instantaneous energy ($IE$) concentration. The analysis shows that the $IE$ concentration in the stock price is very high during both positive and negative EE with $IE>E_μ+4σ,$ where $E_μ$ and $σ$ are the mean energy and standard deviation of energy, respectively. Further, support vector regression is used to predict the stock price during an EE, with the close price being the most helpful input than the open-high-low-close (OHLC) inputs. The maximum prediction accuracy for one step using close price and OHLC prices are 95.98\% and 95.64\% respectively. Whereas, for the two steps prediction, the accuracies are 94.09\% and 93.58\% respectively. The EEs found from the predicted time series shows similar statistical characteristics that were obtained from the original data. The analysis emphasizes the importance of monitoring factors that lead to EEs for a compelling entry or exit strategy as investors can gain or lose significant amounts of capital due to these events.

q-fin.ST↗
arXiv2021

Statistical properties of the aftershocks of stock market crashes revisited: Analysis based on the 1987 crash, financial-crisis-2008 and COVID-19 pandemic

During any unique crisis, panic sell-off leads to a massive stock market crash that may continue for more than a day, termed as mainshock. The effect of a mainshock in the form of aftershocks can be felt throughout the recovery phase of stock price. As the market remains in stress during recovery, any small perturbation leads to a relatively smaller aftershock. The duration of the recovery phase has been estimated using structural break analysis. We have carried out statistical analyses of the 1987 stock market crash, 2008 financial crisis and 2020 COVID-19 pandemic considering the actual crash-times of the mainshock and aftershocks. Earlier, such analyses were done considering an absolute one-day return, which cannot capture a crash properly. The results show that the mainshock and aftershock in the stock market follow the Gutenberg-Richter (GR) power law. Further, we obtained a higher $β$ value for the COVID-19 crash compared to the financial-crisis-2008 from the GR law. This implies that the recovery of stock price during COVID-19 may be faster than the financial-crisis-2008. The result is consistent with the present recovery of the market from the COVID-19 pandemic. The analysis shows that the high magnitude aftershocks are rare, and low magnitude aftershocks are frequent during the recovery phase. The analysis also shows that the distribution $P(τ_i)$ follows the generalized Pareto distribution, i.e., $\displaystyle~P(τ_i)\propto\frac{1}{\{1+λ(q-1)τ_i\}^{\frac{1}{(q-1)}}}$, where $λ$ and $q$ are constants and $τ_i$ is the inter-occurrence time. This analysis may help investors to restructure their portfolios during a market crash.

q-fin.ST↗
arXiv2020

Modeling and analysis of the effect of COVID-19 on the stock price: V and L-shape recovery

The emergence of the COVID-19 pandemic, a new and novel risk factor, leads to the stock price crash due to the investors' rapid and synchronous sell-off. However, within a short period, the quality sectors start recovering from the bottom. A stock price model has been developed during such crises based on the net-fund-flow ($Ψ_t$) due to institutional investors, and financial antifragility ($ϕ$) of a company. We assume that during the crash, the stock price fall is independent of the $ϕ$. We study the effects of shock lengths and $ϕ$ on the stock price during the crises period using the $Ψ_t$ obtained from synthetic and real fund flow data. We observed that the possibility of recovery of stock with $ϕ>0$, termed as quality stock, decreases with an increase in shock-length beyond a specific period. A quality stock with higher $ϕ$ shows V-shape recovery and outperform others. The shock length and recovery period of quality stock are almost equal that is seen in the Indian market. Financially stressed stocks, i.e., the stocks with $ϕ<0$, show L-shape recovery during the pandemic. The stock data and model analysis shows that the investors, in uncertainty like COVID-19, invest in quality stocks to restructure their portfolio to reduce the risk. The study may help the investors to make the right investment decision during a crisis.

q-fin.ST↗
arXiv2019

Identification of short-term and long-term time scales in stock markets and effect of structural break

The paper presents the comparative study of the nature of stock markets in short-term and long-term time scales with and without structural break in the stock data. Structural break point has been identified by applying Zivot and Andrews structural trend break model to break the original time series (TSO) into time series before structural break (TSB) and time series after structural break (TSA). The empirical mode decomposition based Hurst exponent and variance techniques have been applied to the TSO, TSB and TSA to identify the time scales in short-term and long-term from the decomposed intrinsic mode functions. We found that for TSO, TSB and TSA the short-term time scales and long-term time scales are within the range of few days to 3 months and greater than 5 months respectively, which indicates that the short-term and long-term time scales are present in the stock market. The Hurst exponent is $\sim 0.5$ and $\geq 0.75$ for TSO, TSB and TSA in short-term and long-term respectively, which indicates that the market is random in short-term and strongly correlated in long-term. The identification of time scales at short-term and long-term investment horizon will be useful for investors to design investment and trading strategies.

q-fin.ST↗
arXiv2019

Time scales in stock markets

Different investment strategies are adopted in short-term and long-term depending on the time scales, even though time scales are adhoc in nature. Empirical mode decomposition based Hurst exponent analysis and variance technique have been applied to identify the time scales for short-term and long-term investment from the decomposed intrinsic mode functions(IMF). Hurst exponent ($H$) is around 0.5 for the IMFs with time scales from few days to 3 months, and $H\geq0.75$ for the IMFs with the time scales $\geq5$ months. Short term time series [$X_{ST}(t)$] with time scales from few days to 3 months and $H~0.5$ and long term time series [$X_{LT}(t)$] with time scales $\geq5$ and $H\geq0.75$, which represent the dynamics of the market, are constructed from the IMFs. The $X_{ST}(t)$ and $X_{LT}(t)$ show that the market is random in short-term and correlated in long term. The study also show that the $X_{LT}(t)$ is correlated with fundamentals of the company. The analysis will be useful for investors to design the investment and trading strategy.

q-fin.ST↗
arXiv2017

Stochastic and Vibrational Resonances in a Uni-junction Transistor Relaxation Oscillator

The effects of perturbation of a weak periodic signal (WPS) assisted by noise or a high frequency signal (HFS) respectively on an excitable uni-junction transistor relaxation oscillator (UJT-RO) is presented here. When the perturbation by a WPS modulated with the noise is optimum, the UJT-RO has been observed to produce regular dynamics that mimics the WPS maximum, which is termed as stochastic resonance (SR). Interestingly, when the noise component is replaced by a HFS, the system shows the same SR kind of behavior, which is called vibrational resonance (VR). Here the system produces the dynamics that mimics the WPS resembling the SR assisted by the optimum level of HFS. Both SR and VR have been confirmed through PSPICE simulation. The results show that the regular dynamics that mimics the WPS in case of HFS modulation is better than the noise perturbation.

nlin.AO↗