1,552 research outputs found

    Time series forecasting with the WARIMAX-GARCH method

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    It is well-known that causal forecasting methods that include appropriately chosen Exogenous Variables (EVs) very often present improved forecasting performances over univariate methods. However, in practice, EVs are usually difficult to obtain and in many cases are not available at all. In this paper, a new causal forecasting approach, called Wavelet Auto-Regressive Integrated Moving Average with eXogenous variables and Generalized Auto-Regressive Conditional Heteroscedasticity (WARIMAX-GARCH) method, is proposed to improve predictive performance and accuracy but also to address, at least in part, the problem of unavailable EVs. Basically, the WARIMAX-GARCH method obtains Wavelet “EVs” (WEVs) from Auto-Regressive Integrated Moving Average with eXogenous variables and Generalized Auto-Regressive Conditional Heteroscedasticity (ARIMAX-GARCH) models applied to Wavelet Components (WCs) that are initially determined from the underlying time series. The WEVs are, in fact, treated by the WARIMAX-GARCH method as if they were conventional EVs. Similarly to GARCH and ARIMA-GARCH models, the WARIMAX-GARCH method is suitable for time series exhibiting non-linear characteristics such as conditional variance that depends on past values of observed data. However, unlike those, it can explicitly model frequency domain patterns in the series to help improve predictive performance. An application to a daily time series of dam displacement in Brazil shows the WARIMAX-GARCH method to remarkably outperform the ARIMA-GARCH method, as well as the (multi-layer perceptron) Artificial Neural Network (ANN) and its wavelet version referred to as Wavelet Artificial Neural Network (WANN) as in [1], on statistical measures for both in-sample and out-of-sample forecasting

    A multi-horizon scale for volatility

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    We decompose volatility of a stock market index both in time and scale using wavelet filters and design a probabilistic indicator for valatilities, analogous to the Richter scale in geophysics. The peak-over-threshold method is used to fit the generalized Pareto probability distribution for the extreme values in the realized variances of wavelet coefficients. The indicator is computed for the daily Dow Jones Industrial Averages index data from 1986 to 2007 and for the intraday CAC 40 data from 1995 to 2006. The results are used for comparison and structural multi-resolution analysis of extreme events on the stock market and for the detection of financial crises.Stock market, volatility, wavelets, multi-resolution analysis, financial crisis.

    Neuro-wavelet Model for price prediction in high-frequency data in the Mexican Stock market

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    With the availability of high frequency data and new techniques for the management of noise in signals, we revisit the question, can we predict financial asset prices? The present work proposes an algorithm for next-step log-return prediction. Data in frequencies from 1 to 15 minutes, for 25 high capitalization assets in the Mexican market were used. The model applied consists on a wavelet followed by a Long Short-Term Memory neural network (LSTM). Application of either wavelets or neural networks in finance are common, the novelty comes from the application of the particular architecture proposed. The results show that, on average, the proposed LSTM neuro-wavelet model outperforms both an ARIMA model and a benchmark dense neural network model. We conclude that, although further research (in other stock markets, at higher frequencies, etc.) is in order, given the ever increasing technical capacity of market participants, the inclusion of the LSTM neuro-wavelet model is a valuable addition to the market participant toolkit, and might pose an advantage to traditional predictive tools.Modelo de neuro-onda para predicción de precios en datos de alta frecuencia en el Mercado Bursátil MexicanoCon la disponibilidad de datos de alta frecuencia y nuevas técnicas para la filtración de señales, es pertinente preguntarse una vez más ¿podemos predecir los precios de los activos financieros? El presente trabajo propone un algoritmo para la predicción de retorno logarítmico del siguiente periodo. Se usan datos en frecuencias de 1 a 15 minutos, para 25 activos de alta capitalización en el mercado accionario mexicano. El modelo consiste en la aplicación de una wavelet seguida de una red neuronal de tipo Long Short-Term Memory (LSTM). En la literatura comúnmente se encuentra el uso de wavelets o de redes neuronales en aplicaciones financieras, la novedad de nuestro trabajo radica en la arquitectura particular que proponemos. Los resultados muestran que, en promedio, el modelo de neuro-wavelet propuesto supera tanto a un modelo ARIMA como a un modelo de red neuronal densa de referencia. Podemos concluir que, aunque más investigación es necesaria, dada la creciente capacidad técnica actual de los participantes del mercado, la inclusión del modelo LSTM neuro – wavelet al abanico de herramientas disponibles es de mucho valor, pues podría representar una ventaja sobre las herramientas predictivas tradicionales

    Analyzing the forecast performance of S&P 500 Index Options implied volatility

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    Ankara : The Department of Management, İhsan Doğramacı Bilkent University, 2012.Thesis (Master's) -- Bilkent University, 2012.Includes bibliographical references.This study examines the comparative performance of the call and put implied volatility (IV) of at-the-money European-style SPX Index Options on the S&P 500 Price Index as a precursor to the ex-post realized volatility. The results confirm that implied volatility contains valuable information regarding the ex-post realized volatility during the last decade for the S&P 500 market. The empirical findings also indicate that the put implied volatility has a higher forecast performance. Furthermore, from the wavelet estimations it has been concluded that the long-run variation of the implied volatility is consistent and unbiased in explaining the long-run variations of the ex-post realized volatility. Wavelet estimations further reveal that in the long-run put and call implied volatility contain comparable information regarding the realized volatility of the market. However, in the short-run put implied volatility dynamics have better predictive ability.Erdemir, AytaçM.S

    Wavelet Neural Networks: A Practical Guide

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    Wavelet networks (WNs) are a new class of networks which have been used with great success in a wide range of application. However a general accepted framework for applying WNs is missing from the literature. In this study, we present a complete statistical model identification framework in order to apply WNs in various applications. The following subjects were thorough examined: the structure of a WN, training methods, initialization algorithms, variable significance and variable selection algorithms, model selection methods and finally methods to construct confidence and prediction intervals. In addition the complexity of each algorithm is discussed. Our proposed framework was tested in two simulated cases, in one chaotic time series described by the Mackey-Glass equation and in three real datasets described by daily temperatures in Berlin, daily wind speeds in New York and breast cancer classification. Our results have shown that the proposed algorithms produce stable and robust results indicating that our proposed framework can be applied in various applications

    Wavelet Multiresolution Analysis of High-Frequency Asian FX Rates, Summer 1997

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    FX pricing processes are nonstationary and their frequency characteristics are time-dependent. Most do not conform to geometric Brownian motion, since they exhibit a scaling law with a Hurst exponent between zero and 0.5 and fractal dimensions between 1.5 and 2. This paper uses wavelet multiresolution analysis, with Haar wavelets, to analyze the nonstationarity (time-dependence) and self-similarity (scale-dependence) of intra-day Asian currency spot exchange rates. These are the ask and bid quotes of the currencies of eight Asian countries (Japan, Hong Kong, Indonesia, Malaysia, Philippines, Singapore, Taiwan, Thailand), and of Germany for comparison, for the crisis period May 1, 1998 - August 31, 1997, provided by Telerate (U.S. dollar is the numeraire). Their time-scale dependent spectra, which are localized in time, are observed in wavelet based scalograms. The FX increments can be characterized by the irregularity of their singularities. This degrees of irregularity are measured by homogeneous Hurst exponents. These critical exponents are used to identify the fractal dimension, relative stability and long term dependence of each Asian FX series. The invariance of each identified Hurst exponent is tested by comparing it at varying time and scale (frequency) resolutions. It appears that almost all FX markets show anti-persistent pricing behavior. The anchor currencies of the D-mark and Japanese Yen are ultra-efficient in the sense of being most anti-persistent. The Taiwanese dollar is the most persistent, and thus unpredictable, most likely due to administrative control. FX markets exhibit these non- linear, non-Gaussian dynamic structures, long term dependence, high kurtosis, and high degrees of non-informational (noise) trading, possibly because of frequent capital flows induced by non-synchronized regional business cycles, rapidly changing political risks, unexpected informational shocks to investment opportunities, and, in particular, investment strategies synthesizing interregional claims using cash swaps with different duration horizons.foreign exchange markets, anti-persistence, long-term dependence, multi-resolution analysis, wavelets, time-scale analysis, scaling laws, irregularity analysis, randomness, Asia

    Wavelet Multiresolution Analysis of High-Frequency FX Rates, Summer 1997

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    FX pricing processes are nonstationary and their frequency characteristics are time-dependent. Most do not conform to geometric Brownian motion, since they exhibit a scaling law with a Hurst exponent between zero and 0.5 and fractal dimensions between 1.5 and 2. This paper uses wavelet multiresolution analysis, with Haar wavelets, to analyze the nonstationarity (time-dependence) and self-similarity (scale-dependence) of intra-day Asian currency spot exchange rates.foreign exchange, anti-persistence, multi-resolution analysis, wavelets, Asia
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