scholarly journals Average crossing time: An alternative characterization of mean aversion and reversion

2021 ◽  
Vol 12 (3) ◽  
pp. 903-944 ◽  
Author(s):  
John B. Donaldson ◽  
Rajnish Mehra
Keyword(s):  
Time Series ◽  
Financial Time Series ◽  
Mean Reversion ◽  
Statistical Characteristics ◽  
Alternative Measure ◽  
Financial Time ◽  
Asset Pricing Models ◽  
Crossing Time ◽  
Alternative Characterization

This study compares and contrasts the multiple characterizations of mean reversion in financial time series as regards the restrictions they imply. This is accomplished by translating them into statements about an alternative measure, the “Average Crossing Time” or ACT. We argue that the ACT measure, per se, provides not only a useful benchmark for the degree of mean reversion/aversion, but also an intuitive, and easily quantified sense of one time series being “more strongly mean‐reverting/averting” than another. We conclude our discussion by deriving the ACT measure for a wide class of stochastic processes and detailing its statistical characteristics. Our analysis is principally undertaken within a class of well‐understood production based asset pricing models.

scholarly journals On the Connection between the GEP Performances and the Time Series Properties

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1853
Author(s):  
Alina Bărbulescu ◽  
Cristian Ștefan Dumitriu
Keyword(s):  
Time Series ◽  
Goodness Of Fit ◽  
Functional Form ◽  
Financial Time Series ◽  
Gene Expression Programming ◽  
Parametric Models ◽  
Statistical Characteristics ◽  
Data Series ◽  
Financial Time ◽  
Data Generating Process

Artificial intelligence (AI) methods are interesting alternatives to classical approaches for modeling financial time series since they relax the assumptions imposed on the data generating process by the parametric models and do not impose any constraint on the model’s functional form. Even if many studies employed these techniques for modeling financial time series, the connection of the models’ performances with the statistical characteristics of the data series has not yet been investigated. Therefore, this research aims to study the performances of Gene Expression Programming (GEP) for modeling monthly and weekly financial series that present trend and/or seasonality and after the removal of each component. It is shown that series normality and homoskedasticity do not influence the models’ quality. The trend removal increases the models’ performance, whereas the seasonality elimination results in diminishing the goodness of fit. Comparisons with ARIMA models built are also provided.

scholarly journals Análise de propriedades das séries temporais dos ativos que compõem o índice IBOVESPA

2021 ◽  
Vol 9 (2) ◽  
pp. 5-35
Author(s):  
César Daltoé Berci ◽  
Ceslo Pascoli Bottura
Keyword(s):  
Time Series ◽  
Financial Time Series ◽  
Statistical Properties ◽  
Point Of View ◽  
Financial Time ◽  
Analysis Tools ◽  
Financial Transactions ◽  
Computing Capacity

Several characteristics of financial time series are of interest both from an academic point of view, which is intended to analyze the dynamics of the data and its numerical properties, as well as from investors point of view, who use this knowledge to generate profit in their financial transactions. By applying several analysis tools and using a massive computing capacity, the numerical and statistical properties of the assets that compose the IBOVESPA index were evaluated. Given the relevance and scope of the analyzed time series, the results obtained from this analysis can serve as a basis for the characterization of financial time series

scholarly journals HURST EXPONENTS AND DELAMPERTIZED FRACTIONAL BROWNIAN MOTIONS

2019 ◽  
Vol 22 (05) ◽  
pp. 1950024
Author(s):  
MATTHIEU GARCIN
Keyword(s):  
Time Series ◽  
High Frequency ◽  
Hurst Exponent ◽  
Stationary Process ◽  
Financial Time Series ◽  
Mean Reversion ◽  
Foreign Exchange Rates ◽  
Medium Term ◽  
Fractional Brownian Motions ◽  
Financial Time

The inverse Lamperti transform of a fractional Brownian motion (fBm) is a stationary process. We determine the empirical Hurst exponent of such a composite process with the help of a regression of the log absolute moments of its increments, at various scales, on the corresponding log scales. This perceived Hurst exponent underestimates the Hurst exponent of the underlying fBm. We thus encounter some time series having a perceived Hurst exponent lower than [Formula: see text], but an underlying Hurst exponent higher than [Formula: see text]. This paves the way for short- and medium-term forecasting. Indeed, in such series, mean reversion predominates at high scales, whereas persistence is overriding at lower scales. We propose a way to characterize the Hurst horizon, namely a limit scale between these opposite behaviors. We show that the delampertized fBm, which mixes persistence and mean reversion, is relevant for financial time series, in particular for high-frequency foreign exchange rates. In our sample, the empirical Hurst horizon is always above 1[Formula: see text]h and 23[Formula: see text]min.

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