Analysis of Financial Time-Series Using Fourier and Wavelet Methods

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This paper presents a set of tools, which allow gathering information about the frequency components of a time-series. We focus on the concepts rather than giving too much weight to mathematical technicalities.

In a first step, we discuss spectral analysis and filtering methods. Spectral analysis can be used to identify and to quantify the different frequency components of a data series. Filters permit to capture specific components (e.g. trends, cycles, seasonalities) of the original time-series. Both spectral analysis and standard filtering methods have two main drawbacks: (i) they impose strong restrictions regarding the possible processes underlying the dynamics of the series (e.g. stationarity), and, (ii) they lead to a pure frequency-domain representation of the data, i.e. all information from the time-domain representation is lost in the operation.

In a second step, we introduce wavelets, which are relatively new tools in economics and finance. They take their roots from filtering methods and Fourier analysis. But they overcome most of the limitations of these two methods. Indeed their principal advantages are the following: (1) they combine information from both time-domain and frequency-domain and, (2) they are also very flexible and do not make strong assumptions concerning the data generating process for the series under investigation.


Sutte Indicator: A Technical Indicator in Stock Market

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This study aims at development of the technical indicator in Stock Market as Sutte indicator. Sutte indicator in stock trading that will assist in the investment decision-making process which is to buy or sell stocks. This study took data from PT. Astra Agro Lestari Tbk. Which is listed in the Indonesia stock exchange in the period of 5 April 2001 - 20 September 2016. To find out the performance of Sutte indicator, two other technical analysis are used as a comparison, they are simple moving average (SMA) and moving average convergence/divergence (MACD). The mean of square error (MSE), mean absolute deviation (MAD), and mean absolute percentage error (MAPE) are used to fnd out a comparison of the level of reliability in predicting the stock data. The results of this study are Sutte indicator could be used as a reference in predicting stock movements. Sutte indicator have a better level of reliability compared to two other indicators method SMA and MACD based on the MSE, MAD and MAPE.

The Relationship between Interest Rate, Exchange Rate and Stock Price: A Wavelet Analysis

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This paper examines the multi-scale relationship between the interest rate, exchange rate and stock price using a wavelet transform. In particular, we apply the maximum overlap discrete wavelet transform (MODWT) to the interest rate, exchange rate and stock price in US over the period from january 1990 to december 2008 and using the definitions of wavelet variance, wavelet correlation and cross-correlations to analyze the association as well as the lead/lag relationship between these series at the different time scales. Our results show that the relationship between interest rate and exchange rate is not significantly different from zero at all scales. On the other hand, the relationship between interest rate returns and stock index returns is significantly different from zero only at the highest scales. The exchange rate returns and stock index returns have a bidirectional relationship in this period at longer horizons.


Optimal Trend Following Trading Rules

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We develop an optimal trend following trading rule in a bull-bear switching market, where the drift of the stock price switches between two parameters corresponding to an uptrend (bull market) and a downtrend (bear market) according to an unobservable Markov chain. We consider a finite horizon investment problem and aim to maximize the expected return of the terminal wealth. We start by restricting to allowing flat and long positions only and describe the trading decisions using a sequence of stopping times indicating the time of entering and exiting long positions. Assuming trading all available funds, we show that the optimal trading strategy is a trend following system characterized by the conditional probability in the uptrend crossing two threshold curves. The thresholds can be obtained by solving the associated HJB equations. In addition, we examine trading strategies with short selling in terms of an approximation. Simulations and empirical experiments are conducted and reported.

The Meaning of Market Efficiency

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The Meaning of Market Efficiency wrote:Fama (1970) defined an efficient market as one in which prices always “fully reflect” available information. This paper formalizes this definition and provides various characterizations relating to equilibrium models, profitable trading strategies, and equivalent martingale measures. These various characterizations facilitate new insights and theorems relating to efficient markets. In particular, we overcome a well known limitation in tests for market efficiency, i.e., the need to assume a particular equilibrium asset pricing model, called the joint-hypothesis or bad-model problem. Indeed, we show that an efficient market is completely characterized by the absence of both arbitrage opportunities and dominated securities, an insight that provides tests for efficiency that are devoid of the bad-model problem. Other theorems useful for both the testing of market efficiency and the pricing of derivatives are also provided.

Momentum Investing and Asset Allocation

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This paper highlights the use of a new strategic approach within a quantitative investment methodology in the context of making prudent asset allocation decisions. Three asset classes will frame the dynamic asset allocation discussion: Equities, Fixed Income, and Hedge Funds. The quantitative methodology used is an evolution of J. Welles Wilder’s Relative Strength Index (RSI) first published in New Concepts in Technical Trading Systems . The sample portfolio that was analyzed over several market cycles has demonstrated greater compound returns with less volatility. The result is a set of strategies that yield better risk-adjusted returns to the broad equity markets, broad bond markets, and broad returns of hedge funds. In fact, the portfolios we analyzed delivered significantly higher risk adjusted returns across multiple market cycles.

Can Fuzzy Logic Make Technical Analysis 20/20?

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One of the most challenging areas in technical analysis is the automatic detection of technical patterns that would be similarly detected by the eyes of experts. In this study, cognitive uncertainty was incorporated in technical analysis by using a fuzzy logic-based approach. The results show that the algorithm can detect subtle differences in a clearly defined pattern. Significant postpattern abnormal returns were found that varied directly with the fuzziness of a pattern. This approach can be valuable for investors as a way to incorporate human cognition into historical trading statistics so as to form future winning strategies.


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