Log Returns Research Articles

Forecasting NFTI Index Model: An Univariate Multivariable Regression Approach

This paper proposed a forecasting model of the NFT index (NFTI) in the following year through repeating simulations applied to the univariate multivariable regression model. Beginning by choosing suitable predictors for the regression model which might affect NFTI through the best subset regression method, the team creates the multivariate regression model consisting of four dependent variables which are the log return of BTC, BTC/NFTI, NFTI spread, and NFTI volume/spread with respect to the independent variable log return of NFTI. Application of the regression model to the simulations based on the historical data generates 1000 pairs of data of log return of NFTI and log return of BTC as well as the corresponding predicted price of NFTI and BTC which are moderately correlated. Results are summarized in the cross-tabulation to quantitatively analyze the relationship between two variables which provides information for the investors about how they should formulate their own investment strategy. The results suggest that NFTI outperforms BTC unless NFTI crashes. Therefore, investment strategies can be made depending on the trend of BTC in the following year.

PEMODELAN ARIMA-GARCH UNTUK VOLATILIAS DAN VALUE AT RISK PADA SAHAM PT. GUDANG GARAM TBK

Investment is one of the development factors in economic activity, there are two basic things that investor must know before making investment decisions, namely: returns and risk. One of the statistical methods to calculate the maximum loss in investment is Value at Risk (VaR). this study aims to calculate VaR on the closing stock price data of Pt. Gudang Garam TBK for the daily period starting from 4 January 2021 to 30 December 2021. Log return data is model by ARIMA. The ARIMA model contains a heteroscedasticity effect so it is inadequate for modelling, one of the models that can overcome the heteroscedasticity problem is the ARCH-GARCH model. Forecasting the volatility of the data is done using the ARCH-GARCH model. The results show that the GARCH (1,1) is the best model for predicting volatility. Volatility is predicted for the next 30 days, after the volatility forecasting results are obtained, the VaR calculation can be continued. Based on the results, it shows that volatility increases over time, which means that the risk that investor will accept will be higher and the returns will also be greater

An Empirical Study on the Logarithmic Return of Securities

Objective: Previous studies have shown that the distribution of security returns has the characteristics of peak and fat tail, and it is not realistic to use logarithmic normal distribution to describe security returns. This paper mainly studies the specific form of security returns distribution and conducts empirical research. Methods: We first assume that the security returns follow a logarithmic t-distribution. Then, the maximum likelihood estimation and moment estimation are used to explore the degree of freedom of the distribution. Finally, the goodness of fit test is used to conduct an empirical analysis about Shanghai Securities Composite Index. Results: The specific expression formulas for the estimator of the degree of freedom are obtained. Empirical testing shows that the security returns follow a logarithmic t-distribution. Conclusion: The probability distribution of security returns is unrealistic to assume that the security returns follow the logarithmic normal distribution. It is more practical to use the logarithmic t-distribution to characterize the distribution of security returns. Our results provide theoretical assistance for exploring the pricing of financial derivatives.

Nonparametric estimates of option prices via Hermite basis functions

We consider approximate pricing formulas for European options based on approximating the logarithmic return’s density of the underlying by a linear combination of rescaled Hermite polynomials. The resulting models, that can be seen as perturbations of the classical Black-Scholes one, are nonpararametric in the sense that the distribution of logarithmic returns at fixed times to maturity is only assumed to have a square-integrable density. We extensively investigate the empirical performance, defined in terms of out-of-sample relative pricing error, of this class of approximating models, depending on their order (that is, roughly speaking, the degree of the polynomial expansion) as well as on several ways to calibrate them to observed data. Empirical results suggest that such approximate pricing formulas, when compared with simple nonparametric estimates based on interpolation and extrapolation on the implied volatility curve, perform reasonably well only for options with strike price not too far apart from the strike prices of the observed sample.

Decomposing cryptocurrency high-frequency price dynamics into recurring and noisy components

This paper investigates the temporal patterns of activity in the cryptocurrency market with a focus on Bitcoin, Ethereum, Dogecoin, and WINkLink from January 2020 to December 2022. Market activity measures—logarithmic returns, volume, and transaction number, sampled every 10 s, were divided into intraday and intraweek periods and then further decomposed into recurring and noise components via correlation matrix formalism. The key findings include the distinctive market behavior from traditional stock markets due to the nonexistence of trade opening and closing. This was manifested in three enhanced-activity phases aligning with Asian, European, and U.S. trading sessions. An intriguing pattern of activity surge in 15-min intervals, particularly at full hours, was also noticed, implying the potential role of algorithmic trading. Most notably, recurring bursts of activity in bitcoin and ether were identified to coincide with the release times of significant U.S. macroeconomic reports, such as Nonfarm payrolls, Consumer Price Index data, and Federal Reserve statements. The most correlated daily patterns of activity occurred in 2022, possibly reflecting the documented correlations with U.S. stock indices in the same period. Factors that are external to the inner market dynamics are found to be responsible for the repeatable components of the market dynamics, while the internal factors appear to be substantially random, which manifests itself in a good agreement between the empirical eigenvalue distributions in their bulk and the random-matrix theory predictions expressed by the Marchenko–Pastur distribution. The findings reported support the growing integration of cryptocurrencies into the global financial markets.

Model-based clustering using a new multivariate skew distribution

Quite often real data exhibit non-normal features, such as asymmetry and heavy tails, and present a latent group structure. In this paper, we first propose the multivariate skew shifted exponential normal distribution that can account for these non-normal characteristics. Then, we use this distribution in a finite mixture modeling framework. An EM algorithm is illustrated for maximum-likelihood parameter estimation. We provide a simulation study that compares the fitting performance of our model with those of several alternative models. The comparison is also conducted on a real dataset concerning the log returns of four cryptocurrencies.

Pricing ratchet equity index annuity with mortality risk by complex Fourier series method

In this paper, we consider the pricing of the ratchet equity-indexed annuity with the incorporation of mortality risk by an efficient and accurate method under the general time-changed Lévy processes. The pricing of the contract is a two-dimensional problem: we apply the complex Fourier series method to the log return dimension of the asset and high-order quadrature approximation to the other dimensions. Depending on the subordinating dynamic of the volatility, we use the time-changed Lévy process to model stochastic volatility via the random time change in the Lévy process, which compensates for limitations in the common Lévy process. By combining the recursive algorithm and complex Fourier series method, we obtain the approximate price of the contract. Error analysis proves that the total error can achieve an exponential convergence rate, and numerical examples demonstrate the accuracy and efficiency of the complex Fourier series expansion method.

An Empirical Study on The Calendar Effect of The Shanghai Index in China

The premise of traditional financial theory is efficient market theory and rational man hypothesis, while the market anomaly which can not be explained by traditional financial theory such as the calendar effect poses a great challenge to traditional financial theory. This paper uses the daily closing price data of the Shanghai Composite Index from December 19, 1999, to May 6, 2022, to investigate the calendar effect of the logarithmic return of the Shanghai Composite Index. The research results show that China's Shenzhen stock market is inefficient and has a negative Tuesday effect, which empirically proves the non-efficiency of China's stock market and the calendar effect in behavioral finance in China's stock market.

Investors’ reactions on the publication of integrated reports. Evidence from European stock markets

The last decades brought to stock market investors’ attention several key issues regarding companies’ activity, besides the financial statements. These issues, such as environmental, social, or corporate governance policies are nowadays included in integrated reports issued by many listed companies worldwide. Although these topics seem to currently attract a high interest in the media, our study’s aim is to determine whether the listed firms’ release of Integrated Reports has any bearing on the issuers’ performance on the capital market as assessed by market value, return, and risk. In this respect, we analysed three different stock market time series’ reactions – daily close prices, daily logarithmic returns, and risk measured by the Expected Shortfall – to the publication of integrated reports, for a sample of 48 companies, listed on various European stock markets. In order to identify any sudden changes in the analysed time series behaviour, immediately after the publication date, we used the Bai-Perron multiple structural breaks test. Our results show that no consistent, significant reactions occur within the analysed time series immediately after the publication of integrated reports, but only isolated, circumstantial reactions seem to appear. Moreover, it seems that the markets show common significant reactions to certain events, marked by major structural breaks, but none of these events could be related to the publication of integrated reports. Within this context, our paper manages to prove that although it currently constitutes a hot topic worldwide, integrated reporting is not a key feature in the investors’ short-term decisionmaking process.

Forecasting bitcoin volatility: exploring the potential of deep learning

This study aims to evaluate forecasting properties of classic methodologies (ARCH and GARCH models) in comparison with deep learning methodologies (MLP, RNN, and LSTM architectures) for predicting Bitcoin's volatility. As a new asset class with unique characteristics, Bitcoin's high volatility and structural breaks make forecasting challenging. Based on 2753 observations from 08-09-2014 to 01-05-2022, this study focuses on Bitcoin logarithmic returns. Results show that deep learning methodologies have advantages in terms of forecast quality, although significant computational costs are required. Although both MLP and RNN models produce smoother forecasts with less fluctuation, they fail to capture large spikes. The LSTM architecture, on the other hand, reacts strongly to such movements and tries to adjust its forecast accordingly. To compare forecasting accuracy at different horizons MAPE, MAE metrics are used. Diebold–Mariano tests were conducted to compare the forecast, confirming the superiority of deep learning methodologies. Overall, this study suggests that deep learning methodologies could provide a promising tool for forecasting Bitcoin returns (and therefore volatility), especially for short-term horizons.

GARCHNet: Value-at-Risk Forecasting with GARCH Models Based on Neural Networks

This paper proposes a new GARCH specification that adapts the architecture of a long-term short memory neural network (LSTM). It is shown that classical GARCH models generally give good results in financial modeling, where high volatility can be observed. In particular, their high value is often praised in Value-at-Risk. However, the lack of nonlinear structure in most approaches means that conditional variance is not adequately represented in the model. On the contrary, the recent rapid development of deep learning methods is able to describe any nonlinear relationship in a clear way. We propose GARCHNet, a nonlinear approach to conditional variance that combines LSTM neural networks with maximum likelihood estimators in GARCH. The variance distributions considered in the paper are normal, t and skewed t, but the approach allows extension to other distributions. To evaluate our model, we conducted an empirical study on the logarithmic returns of the WIG 20 (Warsaw Stock Exchange Index), S&P 500 (Standard & Poor’s 500) and FTSE 100 (Financial Times Stock Exchange) indices over four different time periods from 2005 to 2021 with different levels of observed volatility. Our results confirm the validity of the solution, but we provide some directions for its further development.

THE EFFECTS OF COVID-19 ON MULTIFRACTALITY AND LONG-MEMORY IN ETHEREUM’S RETURNS

The global COVID-19 pandemic has shaken the global economy, not sparing the cryptocurrency market. In this paper, we investigate the impact of the COVID-19 pandemic on the dynamics of log returns of the Ethereum. The observed period is divided into three parts: the pre-pandemic period, the pandemic-induced shock, and the period after the pandemic-induced shock on the cryptocurrency market. The research focuses on the impact of the pandemic on the degree of non-linearity and multifractality of log returns. To assess the degree of non-linearity, we used the BDS test and the value of the largest Lyapunov exponent. For multifractality, long-range correlations and information efficiency, we used MF-DFA (Multifractal Detrended Fluctuation Analysis). The research results show that all observed periods have a pronounced non-linearity, but that there is no evidence of the existence of low-dimension chaos. Also, based on the results of the MF-DFA analysis, we conclude that the COVID-19 pandemic has significantly affected the long memory of the log returns of the Ethereum; however, their dynamics and characteristics are returning to the trends present before the pandemic.

Empirical analysis of the effectiveness and liquidity of the European carbon emission rights futures market

Global warming from greenhouse gas emissions is a worldwide concern and the European Emissions Trading System (EU ETS) is the largest market in the world and has a model role. Some researchers have argued that the carbon emissions futures market was not weakly effective at the beginning of its establishment, but there is a lack of sufficient research on the effectiveness of the market in recent years. Therefore, this study analyses market effectiveness and liquidity by using positions, trading volumes and settlement prices for carbon futures from 2 January 2014 to 23 November 2022, and calculates log returns from settlement prices to construct an ARIMA model for verifying the market efficiency. The analysis finds that the carbon futures market satisfies weak form validity and that the market's macro liquidity and micro liquidity are gradually increasing, and the ARIMA model finds that there is a large seasonality factor in the market. This is mainly related to the maturity of the market, the improvement of the trading mechanism and the global consensus, providing constructive reference for the improvement of the carbon emission rights futures trading market and trading mechanism in China.

2T-POT Hawkes model for left- and right-tail conditional quantile forecasts of financial log returns: Out-of-sample comparison of conditional EVT models

Conditional extreme value theory (EVT) methods promise enhanced forecasting of the extreme tail events that often dominate systemic risk. We present an improved two-tailed peaks-over-threshold (2T-POT) Hawkes model that is adapted for conditional quantile forecasting in both the left and right tails of a univariate time series. This is applied to the daily log returns of six large-cap indices. We also take the unique step of fitting the model at multiple exceedance thresholds (from the 1.25% to 25.00% mirrored quantiles). Quantitatively similar asymmetries in Hawkes parameters are found across all six indices, adding further empirical support to a temporal leverage effect in financial price time series in which the impact of losses is not only larger but also more immediate. Out-of-sample backtests find that our 2T-POT Hawkes model is more reliably accurate than the GARCH-EVT model when forecasting (mirrored) value at risk and expected shortfall at the 5% coverage level and below. This suggests that asymmetric Hawkes-type arrival dynamics are a better approximation of the true generating process for extreme daily log returns than GARCH-type conditional volatility. Our 2T-POT Hawkes model therefore presents a better-performing alternative for financial risk modelling.

Agricultural policy uncertainty and its impact on commodity markets

AbstractWe construct an agricultural policy uncertainty (APU) index from leading national and local newspapers in major agricultural states in the United States from January 1999 to September 2021. Our analysis shows that economic policy uncertainty Granger causes APU linearly in the short run, but the relationship is nonlinear and bidirectional in the long run. When economic policy uncertainty is considered, APU significantly reduces hedgers' net short positions and speculators' net long positions (except for corn hedgers) in the corn and soybean markets. APU also has a significant positive impact on the log returns of corn and soybean futures prices, consistent with the theory of storage where commodity returns and volatility are positively correlated.

Simplified calculus for semimartingales: Multiplicative compensators and changes of measure

The paper develops multiplicative compensation for complex-valued semimartingales and studies some of its consequences. It is shown that the stochastic exponential of any complex-valued semimartingale with independent increments becomes a true martingale after multiplicative compensation when such compensation is meaningful. This generalization of the Lévy–Khintchin formula fills an existing gap in the literature. It allows, for example, the computation of the Mellin transform of a signed stochastic exponential, which in turn has practical applications in mean–variance portfolio theory. Girsanov-type results based on multiplicatively compensated semimartingales simplify treatment of absolutely continuous measure changes. As an example, we obtain the characteristic function of log returns for a popular class of minimax measures in a Lévy setting.

Research on properties of Bitcoin Based on GARCH model

Cryptocurrencies have become a world-class phenomenon, with governments, companies and investors facing huge challenges and opportunities. Bitcoin is the one of most widely known cryptocurrencies. People prefer to use Bitcoin as an asset to invest for profit and hedge risk than for its payment function. This is the reason for the study of bitcoin market is so important. Many scholars had used daily data on bitcoin to construct different GARCH models to analyse the volatility of its returns. This research builds a GARCH model for the logarithmic return series of the bitcoin price to understand the volatility of the bitcoin price over the experimental time horizon. The experimental results show that the price of bitcoin is more volatile and vulnerable to external shocks. The analysis suggests that Bitcoin is more clearly a speculative financial instrument and that the price of Bitcoin is highly frothy.

Effectiveness of non-pharmaceutical interventions in nine fields of activity to decrease SARS-CoV-2 transmission (Spain, September 2020-May 2021).

We estimated the association between the level of restriction in nine different fields of activity and SARS-CoV-2 transmissibility in Spain, from 15 September 2020 to 9 May 2021. A stringency index (0-1) was created for each Spanish province (n = 50) daily. A hierarchical multiplicative model was fitted. The median of coefficients across provinces (95% bootstrap confidence intervals) quantified the effect of increasing one standard deviation in the stringency index over the logarithmic return of the weekly percentage variation of the 7-days SARS-CoV-2 cumulative incidence, lagged 12 days. Overall, increasing restrictions reduced SARS-CoV-2 transmission by 22% (RR = 0.78; one-sided 95%CI: 0, 0.82) in 1 week, with highest effects for culture and leisure 14% (0.86; 0, 0.98), social distancing 13% (0.87; 0, 0.95), indoor restaurants 10% (0.90; 0, 0.95) and indoor sports 6% (0.94; 0, 0.98). In a reduced model with seven fields, culture and leisure no longer had a significant effect while ceremonies decreased transmission by 5% (0.95; 0, 0.96). Models R 2 was around 70%. Increased restrictions decreased COVID-19 transmission. Limitations include remaining collinearity between fields, and somewhat artificial quantification of qualitative restrictions, so the exact attribution of the effect to specific areas must be done with caution.

Modelling Volatility of Size Indices Through Garch and Tgarch Models: Evidence from India

Purpose: The objective of this study was to select the best model for modelling the volatility of log return series of four size indices taken from the Indian stock markets. Theoretical framework: Stock markets throughout the world have been designing various kinds of indices depending upon the requirements of the investors. Accordingly, BSE launched some indices, categorized as size indices, depending upon the market capitalization of the stocks listed on their exchange. Such categorization helps the investors in appropriate decision making. Research on these specific indices is scarce and therefore the aim of the present study. Design/methodology/approach: We analyzed the log return series of four indices, namely S&P BSE Sensex, S&P BSE Large cap index, S&P BSE Mid cap Select index and the S&P BSE Small cap index, by fitting the GARCH (1,1) and the TGARCH (1,1) models for the period from 1 Januray 2018 to 31 December 2022. Findings: The research on modelling volatility is voluminous with varied results as per the various assets and datasets utilized for the purpose. Present study confirms the results from previous study that to model the volatility of size indices a GARCH (1,1) model should suffice and there is no betterment achieved by implementing a TAGARCH (1,1) model. Research, Practical & Social implications: We suggest the implementation of a simple GARCH (1,1) model for all those investors who want to invest in Indian size indices in order to model volatility of these indices. Originality/value: Present study is one of its kinds, investigating size indices specifically, through the two of the most popular GARCH-family models in the Indian context.

Stock Index Return Volatility Forecast via Excitatory and Inhibitory Neuronal Synapse Unit with Modified MF-ADCCA

Financial prediction persists a strenuous task in Fintech research. This paper introduces a multifractal asymmetric detrended cross-correlation analysis (MF-ADCCA)-based deep learning forecasting model to predict a succeeding day log return via excitatory and inhibitory neuronal synapse unit (EINS) using asymmetric Hurst exponent as input features, with return and volatility increment of Shanghai Stock Exchanges Composite Index (SSECI) from 2014 to 2020 as proxies for analysis. Experimental results revealed that multifractal elements by MF-ADCCA method as input features are applicable to time series forecasting in deep learning than multifractal detrended fluctuation analysis (MF-DFA) method. Further, the proposed biologically inspired EINS model achieved satisfactory performances in effectiveness and reliability in time series prediction compared with prevalent recurrent neural networks (RNNs) such as LSTM and GRU. The contributions of this paper are to (1) introduce a moving-window MF-ADCCA method to obtain asymmetric Hurst exponent sequences used directly as an input feature for deep learning prediction and (2) evaluate performances of various asymmetric multifractal approaches for deep learning time series forecasting.