Presence Of Long Memory Research Articles

Stochastic Models for Radon Daily Time Series: Seasonality, Stationarity, and Long-Range Dependence Detection

In this paper, the presence of seasonality, stationarity, and long-range memory structures are detected in daily radon measurements in a permanent monitoring station in central Italy. The transient dynamics and the seasonality structure are identified by power spectral analysis based on the continuous wavelet transformation and a clear 1-year periodicity emerges. The stationarity in the data is assessed with the Dickey Fuller test; the decay of the estimated autocorrelation function and the estimated Hurst exponent indicate the presence of long-range dependence. All the main characteristics of the data have been properly included in a modelling structure. In particular, an autoregressive fractionally integrated moving average (ARFIMA) model is estimated and compared with the classical ARMA and ARIMA models in terms of goodness of fit and, secondarily, of forecast evaluation. An autoregressive model with a non-integer values of the differencing parameter ($d=0.278$) resulted to be the most appropriate on the basis of Akaike Information Criterion, the diagnostic on the residuals, and the Root Mean Squared Error. The results suggest that there is statistically-significant evidence for not rejecting the presence of long memory in the radon concentration. The radon measurements are better characterised as being stationary, but with long memory and so the statistical dependence decays more slowly than an exponential decay.

Revisiting the Long Memory in Global Stock Market Returns: An Empirical Analysis

We present a multifarious view on the presence of long memory across 33 countries, subsampled as developed, emerging and frontier economies for the period 2000–2018. We employ the classical rescaled range test, and two semi-parametric tests proposed by Geweke Porter-Hudak (1983) and the frequency domain test proposed by Robinson (1995) to decipher the presence of long memory. The results confirm that while there exists no long-range dependence for developed countries, the return series in the emerging and the frontier countries display long memory characteristics. The rationale for such result emerges from market quality parameters such as size, liquidity, trading and settlement mechanism or sound regulatory framework. These results are of importance for the global investor community for asset allocation, risk management and portfolio diversification purposes.

Multifractal Analysis of Movement Behavior in Association Football

Research in football has been embracing the complex systems paradigm in order to identify different insights about key determinants of performance. The present study explored the multifractal properties of several football-related scenarios, as a candidate method to describe movement dynamics. The sample consisted of five footballers that were engaged in six different training situations (jogging, high intensity interval protocol, running circuit, 5 vs. 5, 8 vs. 8 and a 10 vs. 10 small-sided game). All kinematic measures were collected using a 100 Hz wireless and wearable inertial measurement unit (WIMUPRO©). Data were processed using a discrete wavelet leader transform in order to obtain a spectrum of singularities that could best describe the movement dynamics. The Holder exponent for each of all six conditions revealed mean values h < 0.5 indicating presence of long memory with anti-correlated behavior. A strong trend was found between the width of the multifractal spectrum and the type of task performed, with jogging showing the weakest multifractality ∆h = 0.215 ± 0.020, whereas, 10 vs. 10 small-sided game revealed the strongest ∆h = 0.992 ± 0.104. The Hausdorff dimension indicates that a maximal fluctuation rate occurs with a higher probability than that of the minimal fluctuation rate for all tasks, with the exception of the high intensity interval protocol. Moreover, the spectrum asymmetry values of jogging, running circuit, 5 vs. 5, 8 vs. 8 and 10 vs. 10 small-sided games reveal their multifractal structures are more sensitive to the local fluctuations with small magnitudes. The multifractal analysis has shown a potential to systematically elucidate the dynamics and variability structure over time for the training situations.

Forecasting of Price of Rice in India Using Long-Memory Time-Series Model

Price forecasting of agricultural commodities plays an important role in efficient planning and formulation of executive decisions. In this study, an attempt has been made to apply autoregressive fractionally integrated moving average (ARFIMA) model to the daily all India maximum, minimum and modal wholesale price data of rice in order to capture the observed long-run persistency. The price series under consideration are stationary, but there is a significant presence of long memory in the price data. Accordingly, ARFIMA model is applied to obtain the forecasts and window-based evaluation of forecasting is carried out with the help of relative mean absolute percentage error, root mean square error and mean absolute error. To this end, a comparative study has also been made between the best fitted ARFIMA model and the best fitted ARIMA model and it is observed that ARFIMA model outperforms the usual ARIMA model.

Examining the Impact of Structural Breaks on Long Memory of Stock Returns: Evidence from Bombay Stock Exchange of India Long Memory

This study examines the presence of long memory of Stock Returns in India with reference to structural breaks. The study used the Hurst Exponent in Rescaled Range Analysis as proposed by Lo (1991) to measure the presence of long memory on daily stock returns of the Bombay Stock Exchange Indices from January 2000 to December 2017. The analysis indicates that all indices show long memory effects. It is also evident that all indices exhibit long memory effect in the pre and post subprime crisis period. These findings are consistent with Bhattacharya and Bhattacharya (2018), Jha et al.(2018), Goudarzi (2010) and Lillo and Farmer (2004). KEYWORDS: Long Memory, Hurst exponent, Market Efficiency. Structural Breaks

On long memory origins and forecast horizons

AbstractMost long memory forecasting studies assume that long memory is generated by the fractional difference operator. We argue that the most cited theoretical arguments for the presence of long memory do not imply the fractional difference operator and assess the performance of the autoregressive fractionally integrated moving average (ARFIMA) model when forecasting series with long memory generated by nonfractional models. We find that ARFIMA models dominate in forecast performance regardless of the long memory generating mechanism and forecast horizon. Nonetheless, forecasting uncertainty at the shortest forecast horizon could make short memory models provide suitable forecast performance, particularly for smaller degrees of memory. Additionally, we analyze the forecasting performance of the heterogeneous autoregressive (HAR) model, which imposes restrictions on high‐order AR models. We find that the structure imposed by the HAR model produces better short and medium horizon forecasts than unconstrained AR models of the same order. Our results have implications for, among others, climate econometrics and financial econometrics models dealing with long memory series at different forecast horizons.

Прогнозирование суточных цен на ОРЭМ РФ с помощью модели ARFIMA

The long memory phenomenon in time series of daily spot prices in the Russian electricity market is investigated. The forecasting performance of the ARFIMA model is assessed by cross-validation. The empirical results confirmed the presence of long memory in electricity prices and the best prediction accuracy of the ARFIMA model.

Long-range dependence in the returns and volatility of the Finnish housing market

PurposeThe purpose of this paper is to examine the evidence of long-range dependence behaviour in both house price returns and volatility for fifteen main regions in Finland over the period of 1988:Q1 to 2018:Q4. These regions are divided geographically into 45 cities and sub-areas according to their postcode numbers. The studied type of dwellings is apartments (block of flats) divided into one-room, two-rooms, and more than three rooms apartments types.Design/methodology/approachFor each house price return series, both parametric and semiparametric long memory approaches are used to estimate the fractional differencing parameter d in an autoregressive fractional integrated moving average [ARFIMA (p, d,q)] process. Moreover, for cities and sub-areas with significant clustering effects (autoregressive conditional heteroscedasticity [ARCH] effects), the semiparametric long memory method is used to analyse the degree of persistence in the volatility by estimating the fractional differencing parameter d in both squared and absolute price returns.FindingsA higher degree of predictability was found in all three apartments types price returns with the estimates of the long memory parameter constrained in the stationary and invertible interval, implying that the returns of the studied types of dwellings are long-term dependent. This high level of persistence in the house price indices differs from other assets, such as stocks and commodities. Furthermore, the evidence of long-range dependence was discovered in the house price volatility with more than half of the studied samples exhibiting long memory behaviour.Research limitations/implicationsInvestigating the long memory behaviour in both returns and volatility of the house prices is crucial for investment, risk and portfolio management. One reason is that the evidence of long-range dependence in the housing market returns suggests a high degree of predictability of the asset. The other reason is that the presence of long memory in the housing market volatility aids in the development of appropriate time series volatility forecasting models in this market. The study outcomes will be used in modelling and forecasting the volatility dynamics of the studied types of dwellings. The quality of the data limits the analysis and the results of the study.Originality/valueTo the best of the authors’ knowledge, this is the first research that assesses the long memory behaviour in the Finnish housing market. Also, it is the first study that evaluates the volatility of the Finnish housing market using data on both municipal and geographical level.

Comparing two nonparametric regression curves in the presence of long memory in covariates and errors

This paper discusses the problem of testing the equality of two nonparametric regression functions against two-sided alternatives in the presence of long memory in the common covariate and errors. The proposed test is based on a marked empirical process of the differences between the response variables. We discuss asymptotic null distribution of this process and consistency of the test for a class of general alternatives. We also conduct a Monte Carlo simulation study to evaluate the finite sample level and power behavior of the test at some alternatives.

Long Memory, Realized Volatility and Heterogeneous Autoregressive Models

The presence of long memory in realized volatility (RV) is a widespread stylized fact. The origins of long memory in RV have been attributed to jumps, structural breaks, contemporaneous aggregation, nonlinearities, or pure long memory. An important development has been the heterogeneous autoregressive (HAR) model and its extensions. This article assesses the separate roles of fractionally integrated long memory models, extended HAR models and time varying parameter HAR models. We find that the presence of the long memory parameter is often important in addition to the HAR models.

Evaluation of Long Memory on the Malaysia Exchange Rate Market

This research evaluates the presence of long memory or long-term dependence on the Malaysian exchange rate. Daily, weekly and monthly data are evaluated against the US dollar (USD) covering from January 2005 to March 2018. Evaluation of long memory is based on the Geweke and Porter-Hudak estimation and the Maximum Likelihood Estimation. The result suggests the presence of long memory on all the daily, weekly and monthly data. Results show that shock on the Malaysian exchange rate persist longer than expected. The forecast capability also concludes that addition of the long memory presence from ARIMA model to ARFIMA model could improve the model forecast.

Long Memory of NSE Indices

Long range memory in share indices show temporal dependence between observations spaced by long intervals of time and has distinct non-periodic cycles. This paper examines the presence of long memory of various indices of National Stock Exchange (NSE). The data consists of closing values of indices over different periods of time. The tests applied to examine long memory are Hurst exponent, Manderbolt-Hurst exponent, Lo’s rescaled-range analysis and Geweke and Porter-Hudak (GPH) test. The results of the estimated Hurst exponent, Manderbolt-Hurst exponent and GPH test show that invariably all NSE indices series have long memory. However, the results of Lo’s rescaled-range analysis indicate the absence of long memory for all indices. Key words: Long memory, rescaled range analysis, fractional dimension, Hurst exponent, GPH test, NSE indices

Statistical modelling for forecasting volatility in potato prices using ARFIMA-FIGARCH model

This paper investigates the presence of long memory both in mean and volatility in the potato prices in Agra and Amritsar markets of India, using the Autoregressive fractionally integrated moving average (ARFIMA) and Fractionally integrated generalized autoregressive conditional heteroscedastic (FIGARCH) models. Long memory tests are carried out both for the returns and squared return series. The results of GPH estimator indicate the existence of long memory in the price data.The ARFIMA model with error following FIGARCH process is fitted to return prices of potato for each of the two markets. At the end, the forecasting performance of fitted ARFIMA-FIGARCH models are carried out in terms of RMAPE and RMSE and the residuals are also examined to check adequacy of the fitted models.

Volatility is rough

Estimating volatility from recent high frequency data, we revisit the question of the smoothness of the volatility process. Our main result is that log-volatility behaves essentially as a fractional Brownian motion with Hurst exponent H of order 0.1, at any reasonable timescale. This leads us to adopt the fractional stochastic volatility (FSV) model of Comte and Renault [Long memory in continuous-time stochastic volatility models. Math. Finance, 1998, 8(4), 291–323]. We call our model Rough FSV (RFSV) to underline that, in contrast to FSV, . We demonstrate that our RFSV model is remarkably consistent with financial time series data; one application is that it enables us to obtain improved forecasts of realized volatility. Furthermore, we find that although volatility is not a long memory process in the RFSV model, classical statistical procedures aiming at detecting volatility persistence tend to conclude the presence of long memory in data generated from it. This sheds light on why long memory of volatility has been widely accepted as a stylized fact.

How Long Memory Affects True Dependence Structure? Evidence From the Dow Jones Islamic Sub-indexes

Long memory is a stylized fact found in most financial return series. In this paper, we seek to examine the impact of the presence of long memory on the dependence structure. First, we fit the multivariate dependence structure using R-vine copulas for pairs of raw and filtered returns. Second, we discuss whether or not changes in the fitted dependence may be driven by long memory. Based on the comparison results, we found that filtered returns of Dow Jones sub-indexes capture higher dependence in the conditional dependence structure. However, they capture lower dependence in bivariate dependence. Thus, the true degree of dependence is masked and such information is crucial for hedging and portfolios management.

The Comparative Dynamics of Developed and Emerging Stock Markets: A Long Memory Perspective

The paper explores the difference in efficiency between developed and emerging stock market from a long memory perspective for the period 2000 to 2015. Ten developed, and ten emerging countries were selected for the study based on Morgan Stanley Capital International’s classification. We used both rescaled range and detrended fluctuation analysis and supplemented the findings with estimates of the fractionally integrated parameter for stock market return, its volatility as well as its absolute return using spectral regression. Findings are supportive of the absence of long memory in returns but support presence of long memory in absolute returns and volatility. We conclude that co-movement and spillover between stock markets have affected the market efficiencies and the efficiency of the emerging stock markets is no longer very different from that of the developed stock markets.

PERFORMANCE OF MULTIPLE LINEAR REGRESSION AND AUTOREGRESSIVE INTEGRATED MOVING AVERAGE MODELS IN PREDICTING ANNUAL TEMPERATURES OF OGUN STATE, NIGERIA

The performance of Autoregressive Moving Average and Multiple Linear Regression Models in predicting minimum and maximum temperatures of Ogun State is herein reported. Maximum and Minimum temperatures data covering a period of 29 years (1982 -2009) obtained from the Nigerian Meteorological Agency (NiMet), Abeokuta office, Nigeria, were used for the analyses. The data were first processed and aggregated into annual time series. Mann-Kendal non-parametric test and spectral analysis were carried out to detect whether there is trend, seasonal pattern, and either short or long memory in the time series. Mann-Kendal Z-values obtained are –0.47 and –2.03 for minimum and maximum temperatures respectively, indicating no trend, though the plot shows a slight change. The Lo’s R/S Q(N,q) values for minimum and maximum temperatures are 3.67 and 4.43, which are not within the range 0.809 and 1.862, thus signifying presence of long memory. The data was divided into two and the first 20 years data was used for model development, while the remaining was used for validation. Autoregressive Moving Average (ARMA) model of order (5, 3) and Autoregressive (AR) model of order 2 are found best for predicting minimum and maximum temperatures respectively. Multiple Linear Regression (MLR) model with 4 features (moving average, exponential moving average, rate of change and oscillator) were fitted for both temperatures. The ARMA and AR models were found to perform better with Mean Absolute Percentage Error (MAPE) values of -2.89 and -1.37 for minimum and maximum temperatures, compared with the Multiple Linear Regression Models with MAPE values of 141 and 876 respectively. Results of ARMA model can be relied on in generating forecast of temperature of the study area because of their minimal error values. However, it is recommended other climatic elements that were not captured in this paper due to unavailability of information be considered too in order to see which model is best for them.

Some stylized facts of the Bitcoin market

In recent years a new type of tradable assets appeared, generically known as cryptocurrencies. Among them, the most widespread is Bitcoin. Given its novelty, this paper investigates some statistical properties of the Bitcoin market. This study compares Bitcoin and standard currencies dynamics and focuses on the analysis of returns at different time scales. We test the presence of long memory in return time series from 2011 to 2017, using transaction data from one Bitcoin platform. We compute the Hurst exponent by means of the Detrended Fluctuation Analysis method, using a sliding window in order to measure long range dependence. We detect that Hurst exponents changes significantly during the first years of existence of Bitcoin, tending to stabilize in recent times. Additionally, multiscale analysis shows a similar behavior of the Hurst exponent, implying a self-similar process.

Long memory behavior in Singapore's tourism market

AbstractUsing nonparametric, semiparametric, and parametric estimation techniques, this paper investigates the presence of long memory in tourist arrivals to Singapore from 11 countries and 4 geographical regions. Empirical analysis of the monthly data from 1978 to 2012 shows that tourist arrivals to Singapore from all countries and regions are subject to long memory behavior. Analysis of the impulse response functions derived from an autoregressive fractionally integrated moving average model shows evidence of persistence in tourist arrivals. Our analysis suggests that visitors consider Singapore as a long‐term tourism destination and like to return to Singapore to relive their experiences.

Selecting between autoregressive conditional heteroskedasticity models: An empirical application to the volatility of stock returns in Peru

An extensive family of univariate models of autoregressive conditional heteroskedasticity is applied to Peru’s daily stock market returns for the period January 3, 1992 to March 30, 2012 with four different specifications related to the distribution of the disturbance term. This concerns capturing the asymmetries of the behavior of the volatility, as well as the presence of heavy tails in these time series. Using different statistical tests and different criteria, the results show that: (i) the FIGARCH (1,1)-t is the best model among all symmetric models while the FIEGARCH (1,1)-Sk is selected from the class of asymmetrical models. Also, the model FIAPARCH (1,1)-t is selected from the class of asymmetric power models; (ii) the three models capture well the behavior of the conditional volatility; (iii) however, the empirical distribution of the standardized residuals shows that the behavior of the tails is not well captured by either model; (iv) the three models suggest the presence of long memory with estimates of the fractional parameter close to the region of nonstationarity