Using Empirical Recurrence Rates Ratio For Time Series Data Similarity

Several methods exist in classification literature to quantify the similarity between two time series data sets. Applications of these methods range from the traditional Euclidean type metric to the more advanced Dynamic Time Warping metric. Most of these adequately address structural similarity but fail in meeting goals outside it. For example, a tool that could be excellent to identify the seasonal similarity between two time series vectors might prove inadequate in the presence of outliers. In this paper, we have proposed a unifying measure for binary classification that performed well while embracing several aspects of dissimilarity. This statistic is gaining prominence in various fields, such as geology and finance, and is crucial in time series database formation and clustering studies

Bi-Directional Testing for Change Point Detection in Poisson Processes

Point processes often serve as a natural language to chronicle an event\u27s temporal evolution, and significant changes in the flow, synonymous with non-stationarity, are usually triggered by assignable and frequently preventable causes, often heralding devastating ramifications. Examples include amplified restlessness of a volcano, increased frequencies of airplane crashes, hurricanes, mining mishaps, among others. Guessing these time points of changes, therefore, merits utmost care. Switching the way time traditionally propagates, we posit a new genre of bidirectional tests which, despite a frugal construct, prove to be exceedingly efficient in culling out non-stationarity under a wide spectrum of environments. A journey surveying a lavish class of intensities, ranging from the tralatitious power laws to the deucedly germane rough steps, tracks the established unidirectional forward and backward test\u27s evolution into a p-value induced dual bidirectional test, the best member of the proffered category. Niched within a hospitable Poissonian framework, this dissertation, through a prudent harnessing of the bidirectional category\u27s classification prowess, incites a refreshing alternative to estimating changes plaguing a soporific flow, by conducting a sequence of tests. Validation tools, predominantly graphical, rid the structure of forbidding technicalities, aggrandizing the swath of applicability. Extensive simulations, conducted especially under hostile premises of hard non-stationarity detection, document minimal estimation error and reveal the algorithm\u27s obstinate versatility at its most unerring

Beyond Cumulative Sum Charting in Non-Stationarity Detection and Estimation

In computer science, stochastic processes, and industrial engineering, stationarity is often taken to imply a stable, predictable flow of events and non-stationarity, consequently, a departure from such a flow. Efficient detection and accurate estimation of non-stationarity are crucial in understanding the evolution of the governing dynamics. Pragmatic considerations include protecting human lives and property in the context of devastating processes such as earthquakes or hurricanes. Cumulative Sum (CUSUM) charting, the prevalent technique to weed out such non-stationarities, suffers from assumptions on a priori knowledge of the pre and post-change process parameters and constructs such as time discretization. In this paper, we have proposed two new ways in which non-stationarity may enter an evolving system - an easily detectable way, which we term strong corruption, where the post-change probability distribution is deterministically governed, and an imperceptible way which we term hard detection, where the post-change distribution is a probabilistic mixture of several densities. In addition, by combining the ordinary and switched trend of incoming observations, we develop a new trend ratio statistic in order to detect whether a stationary environment has changed. Surveying a variety of distance metrics, we examine several parametric and non-parametric options in addition to the established CUSUM and find that the trend ratio statistic performs better under the especially difficult scenarios of hard detection. Simulations (both from deterministic and mixed inter-event time densities), sensitivity-specificity type analyses, and estimated time of change distributions enable us to track the ideal detection candidate under various non-stationarities. Applications on two real data sets sampled from volcanology and weather science demonstrate how the estimated change points are in agreement with those obtained in some of our previous works, using different methods. Incidentally, this study sheds light on the inverse nature of dependence between the Hawaiian volcanoes Kilauea and Mauna Loa and demonstrates how inhabitants of the now-restless Kilauea may be relocated to Mauna Loa to minimize the loss of lives and moving costs

Spotting the stock and crypto markets’ rings of fire: measuring change proximities among spillover dependencies within inter and intra-market asset classes

Abstract Crypto assets have lately become the chief interest of investors around the world. The excitement around, along with the promise of the nascent technology led to enormous speculation by impulsive investors. Despite a shaky understanding of the backbone technology, the price mechanism, and the business model, investors’ risk appetites pushed crypto market values to record highs. In addition, pricings are largely based on the perception of the market, making crypto assets naturally embedded with extreme volatility. Perhaps unsurprisingly, the new asset class has become an integral part of the investor’s portfolio, which traditionally consists of stock, commodities, forex, or any type of derivative. Therefore, it is critical to unearth possible connections between crypto currencies and traditional asset classes, scrutinizing correlational upheavals. Numerous research studies have focused on connectedness issues among the stock market, commodities, or other traditional asset classes. Scant attention has been paid, however, to similar issues when cryptos join the mix. We fill this void by studying the connectedness of the two biggest crypto assets to the stock market, both in terms of returns and volatility, through the Diebold Francis spillover model. In addition, through a novel bidirectional algorithm that is gaining currency in statistical inference, we locate times around which the nature of such connectedness alters. Subsequently, using Hausdorff-type metrics on such estimated changes, we cluster spillover patterns to describe changes in the dependencies between which two assets are evidenced to correlate with those between which other two. Creating an induced network from the cluster, we highlight which specific dependencies function as crucial hubs, how the impacts of drastic changes such as COVID-19 ripple through the networks—the Rings of Fire—of spillover dependencies

Change detection in non-stationary Hawkes processes through sequential testing

Detecting changes in an incoming data flow is immensely crucial for understanding inherent dependencies, formulating new or adapting existing policies, and anticipating further changes. Distinct modeling constructs have triggered varied ways of detecting such changes, almost every one of which gives in to certain shortcomings. Parametric models based on time series objects, for instance, work well under distributional assumptions or when change detection in specific properties - such as mean, variance, trend, etc. are of interest. Others rely heavily on the “at most one change-point” assumption, and implementing binary segmentation to discover subsequent changes comes at a hefty computational cost. This work offers an alternative that remains both versatile and untethered to such stifling constraints. Detection is done through a sequence of tests with variations to certain trend permuted statistics. We study non-stationary Hawkes patterns which, with an underlying stochastic intensity, imply a natural branching process structure. Our proposals are shown to estimate changes efficiently in both the immigrant and the offspring intensity without sounding too many false positives. Comparisons with established competitors reveal smaller Hausdorff-based estimation errors, desirable inferential properties such as asymptotic consistency and narrower bootstrapped margins. Four real data sets on NASDAQ price movements, crude oil prices, tsunami occurrences, and COVID-19 infections have been analyzed. Forecasting methods are also touched upon