Estimators of Long-Memory: Fourier versus Wavelets

There have been a number of papers written on semi-parametric estimation methods of the long-memory exponent of a time series, some applied, others theoretical. Some using Fourier methods, others using a wavelet-based technique. In this paper, we compare the Fourier and wavelet approaches to the local regression method and to the local Whittle method. We provide an overview of these methods, describe what has been done, indicate the available results and the conditions under which they hold. We discuss their relative strengths and weaknesses both from a practical and a theoretical perspective. We also include a simulation-based comparison. The software written to support this work is available on demand and we illustrate its use at the end of the paper

Forecasting Stock Market Volatility Using Wavelet Transformation Algorithm Of Garch Model

Kemeruapan pasaran saham adalah perkara penting terutamanya kepada dua pihak berkepentingan. Pengamal melalui kanta mata sendiri melihat pandangan tentang kesan kelakuan harga aset dan risiko Stock market volatility is of essential concern, particularly to two major stake-holder

The connectedness and hedging between gold and Islamic securities in the short, medium and long term

This paper investigates the dynamic connectedness between gold, sukuk and Islamic equities at multiple investment horizons, it also computes optimal hedge ratios and portfolio weights for these assets. Our findings suggest that gold hedges the risk of sukuk in the short and medium terms. We find also that gold plays an average but stable role in hedging and diversifying Islamic equities across all investment horizons. Moreover, we find that gold–Islamic assets portfolio provided a better risk diversification in the short term. These empirical findings are important as they highlight the role of gold in diversifying and managing the risks of portfolios that invest in Islamic assets

The CAPM and value at risk at different time scales

Abstract Wavelet analysis, a refinement of Fourier analysis that was developed in the late 1980's, is a powerful tool for decomposing time series data into orthogonal components with different frequencies. Each frequency is localized in the time domain, which makes it possible to quantify correlations between time series at different time horizons. In this article, we focus on the estimation of the capital asset pricing model (CAPM) at different time scales for Chile's stock market. Our sample is comprised of twenty four stocks that were actively traded on the Santiago Stock Exchange over 1997-2002. We find evidence in support of the CAPM at a medium-term horizon. We extend the literature in this area to analyze the impact of time scaling on the computation of value at risk. We conclude that risk is concentrated at the higher frequencies of the data. JEL: C22, G1

The characterisation of international stock markets using signal processing techniques.

Investors are constantly asking whether beating the market on a consistent basis is possible. There is probably no definitive answer to the question of how to make a guaranteed profit (or return) because index prices can fluctuate at any time. The aim of most investors, therefore, is to predict the stock market return and the volatility, (a measure of investment nsk) and this requires an understanding of stock market behaviour. In this research, diierent techniques, both previously existing and newly developed here (and associated specifically with the discrete wavelet transform (DWT)), are applied to study the behav~our of global stock market indices We consider type of memory, mterrelationships between stock markets, market reaction to crashes and events, and the best indicators of market types (short-term, long-term or mixed). The unifylng aim is to provide a baseline set of characteristic features which typify behaviors of given market type Principal remarks include the fact that the DWT, alone or with other methods, can succeed in providing an in-depth view of these data, in particular when confronted with non-stationary, non-normal and noisy characteristics. The approach provides an important method for the aualysis and interpretation of financial market time series. Our principal findings on volatility measures, moreover, show strong evidence of long-term memory effects, which are not evident in the returns themselves. Emerging and Mature markets are found to deal differently with crashes and events with the latter taking a shorter time to recover from crises on average, compared to the former. Furthermore, we conclude that this binary classification is too simple and stock markets can now be demonstrated to fall into more than two groups, with the designation L'emerging" ("developing") and "mature" ("developed") proving imprecise. Additionally, and in the context of the global market, from Chapter 5, we note that international co-movements and volatility (or nsk) have increased markedly since the middle of the 20th century and that cloclnuzse transmtssion between global stock markets is observed, i.e from Asaa to h o p e to Amerzca back to Asia). The combination of ~nternadl ependencies and external influences provide the impacts for stock market volatility. The ultimate goal, of course, would be to anticipate these Impacts to be able to make the rlght investment decision

Uncovering hidden information and relations in time series data with wavelet analysis: three case studies in finance

This thesis aims to provide new insights into the importance of decomposing aggregate time series data using the Maximum Overlap Discrete Wavelet Transform. In particular, the analysis throughout this thesis involves decomposing aggregate financial time series data at hand into approximation (low-frequency) and detail (high-frequency) components. Following this, information and hidden relations can be extracted for different investment horizons, as matched with the detail components. The first study examines the ability of different GARCH models to forecast stock return volatility in eight international stock markets. The results demonstrate that de-noising the returns improves the accuracy of volatility forecasts regardless of the statistical test employed. After de-noising, the asymmetric GARCH approach tends to be preferred, although that result is not universal. Furthermore, wavelet de-noising is found to be more important at the key 99% Value-at-Risk level compared to the 95% level. The second study examines the impact of fourteen macroeconomic news announcements on the stock and bond return dynamic correlation in the U.S. from the day of the announcement up to sixteen days afterwards. Results conducted over the full sample offer very little evidence that macroeconomic news announcements affect the stock-bond return dynamic correlation. However, after controlling for the financial crisis of 2007-2008 several announcements become significant both on the announcement day and afterwards. Furthermore, the study observes that news released early in the day, i.e. before 12 pm, and in the first half of the month, exhibit a slower effect on the dynamic correlation than those released later in the month or later in the day. While several announcements exhibit significance in the 2008 crisis period, only CPI and Housing Starts show significant and consistent effects on the correlation outside the 2001, 2008 and 2011 crises periods. The final study investigates whether recent returns and the time-scaled return can predict the subsequent trading in ten stock markets. The study finds little evidence that recent returns do predict the subsequent trading, though this predictability is observed more over the long-run horizon. The study also finds a statistical relation between trading and return over the long-time investment horizons of [8-16] and [16-32] day periods. Yet, this relation is mostly a negative one, only being positive for developing countries. It also tends to be economically stronger during bull-periods

Advanced Sensing, Fault Diagnostics, and Structural Health Management

Advanced sensing, fault diagnosis, and structural health management are important parts of the maintenance strategy of modern industries. With the advancement of science and technology, modern structural and mechanical systems are becoming more and more complex. Due to the continuous nature of operation and utilization, modern systems are heavily susceptible to faults. Hence, the operational reliability and safety of the systems can be greatly enhanced by using the multifaced strategy of designing novel sensing technologies and advanced intelligent algorithms and constructing modern data acquisition systems and structural health monitoring techniques. As a result, this research domain has been receiving a significant amount of attention from researchers in recent years. Furthermore, the research findings have been successfully applied in a wide range of fields such as aerospace, manufacturing, transportation and processes

Fast, Scalable, and Accurate Algorithms for Time-Series Analysis

Time is a critical element for the understanding of natural processes (e.g., earthquakes and weather) or human-made artifacts (e.g., stock market and speech signals). The analysis of time series, the result of sequentially collecting observations of such processes and artifacts, is becoming increasingly prevalent across scientific and industrial applications. The extraction of non-trivial features (e.g., patterns, correlations, and trends) in time series is a critical step for devising effective time-series mining methods for real-world problems and the subject of active research for decades. In this dissertation, we address this fundamental problem by studying and presenting computational methods for efficient unsupervised learning of robust feature representations from time series. Our objective is to (i) simplify and unify the design of scalable and accurate time-series mining algorithms; and (ii) provide a set of readily available tools for effective time-series analysis. We focus on applications operating solely over time-series collections and on applications where the analysis of time series complements the analysis of other types of data, such as text and graphs. For applications operating solely over time-series collections, we propose a generic computational framework, GRAIL, to learn low-dimensional representations that natively preserve the invariances offered by a given time-series comparison method. GRAIL represents a departure from classic approaches in the time-series literature where representation methods are agnostic to the similarity function used in subsequent learning processes. GRAIL relies on the attractive idea that once we construct the data-to-data similarity matrix most time-series mining tasks can be trivially solved. To overcome scalability issues associated with approaches relying on such matrices, GRAIL exploits time-series clustering to construct a small set of landmark time series and learns representations to reduce the data-to-data matrix to a data-to-landmark points matrix. To demonstrate the effectiveness of GRAIL, we first present domain-independent, highly accurate, and scalable time-series clustering methods to facilitate exploration and summarization of time-series collections. Then, we show that GRAIL representations, when combined with suitable methods, significantly outperform, in terms of efficiency and accuracy, state-of-the-art methods in major time-series mining tasks, such as querying, clustering, classification, sampling, and visualization. Overall, GRAIL rises as a new primitive for highly accurate, yet scalable, time-series analysis. For applications where the analysis of time series complements the analysis of other types of data, such as text and graphs, we propose generic, simple, and lightweight methodologies to learn features from time-varying measurements. Such applications often organize operations over different types of data in a pipeline such that one operation provides input---in the form of feature vectors---to subsequent operations. To reason about the temporal patterns and trends in the underlying features, we need to (i) track the evolution of features over different time periods; and (ii) transform these time-varying features into actionable knowledge (e.g., forecasting an outcome). To address this challenging problem, we propose principled approaches to model time-varying features and study two large-scale, real-world, applications. Specifically, we first study the problem of predicting the impact of scientific concepts through temporal analysis of characteristics extracted from the metadata and full text of scientific articles. Then, we explore the promise of harnessing temporal patterns in behavioral signals extracted from web search engine logs for early detection of devastating diseases. In both applications, combinations of features with time-series relevant features yielded the greatest impact than any other indicator considered in our analysis. We believe that our simple methodology, along with the interesting domain-specific findings that our work revealed, will motivate new studies across different scientific and industrial settings