scholarly journals Long memory investigation during demonetization in India

2020 ◽  
Vol 17 (2) ◽  
pp. 297-307
Author(s):  
Bikramaditya Ghosh ◽  
Saleema J. S. ◽  
Aniruddha Oak ◽  
Manu K. S. ◽  
Sangeetha R.
Keyword(s):  
Long Range ◽  
Long Memory ◽  
Moving Average ◽  
Long Range Dependence ◽  
Data Sets ◽  
Herd Behavior ◽  
Tick Data ◽  
Key Factor ◽  
Data Points ◽  
Joseph Effect

Long-range dependence (LRD) in financial markets remains a key factor in determining whether there is market memory, herding traces, or a bubble in the economy. Usually referred to as ‘Long Memory’, LRD has remained a key parameter even today since the mid-1970s. In November 2016, a sudden and drastic demonetization measure took place in the Indian market, aimed at curbing money laundering and terrorist funding. This study is an attempt to identify market behavior using long-range dependence during those few days in demonetization. Besides, it tries to identify nascent traces of bubble and embedded herding during that time. Auto Regressive Fractionally Integrated Moving Average (ARFIMA) is used for three consecutive days around the event. Tick-by-tick data from CNX Nifty High Frequency Trading (CNX Nifty HFT) is used for three consecutive days around demonetization (approximately, 5000 data points from morning trading sessions on each of the three days). The results show a clear and profound presence of herd behavior in all three data sets. The herd intensity remained similar, indicating a unique mixture of both ‘Noah Effect’ and ‘Joseph Effect’, proving a clear regime switch. However, the results on the event day show stable and prominent herding. Mandelbrot’s specified effects were tested on an uncertain and sudden financial event in India and proved to function perfectly.

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

2019 ◽  
Vol 13 (1) ◽  
pp. 29-54 ◽  
Author(s):  
Josephine Dufitinema ◽  
Seppo Pynnönen
Keyword(s):  
Housing Market ◽  
Long Range ◽  
Portfolio Management ◽  
Long Memory ◽  
Moving Average ◽  
House Price ◽  
Price Volatility ◽  
Long Range Dependence ◽  
Content Type ◽  
Fractional Differencing

Purpose The 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/approach For 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. Findings A 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/implications Investigating 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/value To 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.

scholarly journals On nonparametric regression for bivariate circular long-memory time series

2021 ◽  
Author(s):  
Jan Beran ◽  
Britta Steffens ◽  
Sucharita Ghosh
Keyword(s):  
Time Series ◽  
Nonparametric Regression ◽  
Long Range ◽  
Long Memory ◽  
Regression Function ◽  
Confidence Bands ◽  
Long Range Dependence ◽  
Asymptotic Results ◽  
Memory Time ◽  
Circular Time Series

AbstractWe consider nonparametric regression for bivariate circular time series with long-range dependence. Asymptotic results for circular Nadaraya–Watson estimators are derived. Due to long-range dependence, a range of asymptotically optimal bandwidths can be found where the asymptotic rate of convergence does not depend on the bandwidth. The result can be used for obtaining simple confidence bands for the regression function. The method is illustrated by an application to wind direction data.

Power-law correlations, related models for long-range dependence and their simulation

2000 ◽  
Vol 37 (04) ◽  
pp. 1104-1109 ◽  
Author(s):  
Tilmann Gneiting
Keyword(s):  
Long Range ◽  
Power Law ◽  
Long Memory ◽  
Stationary Time Series ◽  
Long Range Dependence ◽  
Short Term ◽  
Permissible Range ◽  
Simultaneous Fitting ◽  
Straightforward Proof

Martin and Walker ((1997) J. Appl. Prob. 34, 657–670) proposed the power-law ρ(v) = c|v|-β, |v| ≥ 1, as a correlation model for stationary time series with long-memory dependence. A straightforward proof of their conjecture on the permissible range of c is given, and various other models for long-range dependence are discussed. In particular, the Cauchy family ρ(v) = (1 + |v/c|α)-β/α allows for the simultaneous fitting of both the long-term and short-term correlation structure within a simple analytical model. The note closes with hints at the fast and exact simulation of fractional Gaussian noise and related processes.

scholarly journals Aggregation of a random-coefficient ar(1) process with infinite variance and idiosyncratic innovations

2010 ◽  
Vol 42 (2) ◽  
pp. 509-527 ◽  
Author(s):  
Donata Puplinskaitė ◽  
Donatas Surgailis
Keyword(s):  
Long Memory ◽  
Moving Average ◽  
Domain Of Attraction ◽  
Random Coefficient ◽  
Partial Sums ◽  
Long Range Dependence ◽  
Infinite Variance ◽  
Stable Law ◽  
Slope Coefficient ◽  
Finite Dimensional

Contemporaneous aggregation ofNindependent copies of a random-coefficient AR(1) process with random coefficienta∈ (−1, 1) and independent and identically distributed innovations belonging to the domain of attraction of an α-stable law (0 < α < 2) is discussed. We show that, under the normalizationN1/α, the limit aggregate exists, in the sense of weak convergence of finite-dimensional distributions, and is a mixed stable moving average as studied in Surgailis, Rosiński, Mandrekar and Cambanis (1993). We focus on the case where the slope coefficientahas probability density vanishing regularly ata= 1 with exponentb∈ (0, α − 1) for α ∈ (1, 2). We show that in this case, the limit aggregate {X̅t} exhibits long memory. In particular, for {X̅t}, we investigate the decay of the codifference, the limit of partial sums, and the long-range dependence (sample Allen variance) property of Heyde and Yang (1997).

scholarly journals Variability and Confidence Intervals for the Mean of Climate Data with Short- and Long-Range Dependence

2018 ◽  
Vol 31 (15) ◽  
pp. 6135-6156 ◽  
Author(s):  
Matthew C. Bowers ◽  
Wen-wen Tung
Keyword(s):  
Confidence Intervals ◽  
Long Range ◽  
Long Memory ◽  
Long Range Dependence ◽  
Climate Data ◽  
Temperature State ◽  
Correlation Structures ◽  
The Mean ◽  
Error Bars ◽  
Mean State

This paper presents an adaptive procedure for estimating the variability and determining error bars as confidence intervals for climate mean states by accounting for both short- and long-range dependence. While the prevailing methods for quantifying the variability of climate means account for short-range dependence, they ignore long memory, which is demonstrated to lead to underestimated variability and hence artificially narrow confidence intervals. To capture both short- and long-range correlation structures, climate data are modeled as fractionally integrated autoregressive moving-average processes. The preferred model can be selected adaptively via an information criterion and a diagnostic visualization, and the estimated variability of the climate mean state can be computed directly from the chosen model. The procedure was demonstrated by determining error bars for four 30-yr means of surface temperatures observed at Potsdam, Germany, from 1896 to 2015. These error bars are roughly twice the width as those obtained using prevailing methods, which disregard long memory, leading to a substantive reinterpretation of differences among mean states of this particular dataset. Despite their increased width, the new error bars still suggest that a significant increase occurred in the mean temperature state of Potsdam from the 1896–1925 period to the most recent period, 1986–2015. The new wider error bars, therefore, communicate greater uncertainty in the mean state yet present even stronger evidence of a significant temperature increase. These results corroborate a need for more meticulous consideration of the correlation structures of climate data—especially of their long-memory properties—in assessing the variability and determining confidence intervals for their mean states.

scholarly journals Aggregation of a random-coefficient ar(1) process with infinite variance and idiosyncratic innovations

2010 ◽  
Vol 42 (02) ◽  
pp. 509-527 ◽  
Author(s):  
Donata Puplinskaitė ◽  
Donatas Surgailis
Keyword(s):  
Long Memory ◽  
Moving Average ◽  
Domain Of Attraction ◽  
Random Coefficient ◽  
Partial Sums ◽  
Long Range Dependence ◽  
Infinite Variance ◽  
Stable Law ◽  
Slope Coefficient ◽  
Finite Dimensional

Contemporaneous aggregation of N independent copies of a random-coefficient AR(1) process with random coefficient a ∈ (−1, 1) and independent and identically distributed innovations belonging to the domain of attraction of an α-stable law (0 &lt; α &lt; 2) is discussed. We show that, under the normalization N 1/α, the limit aggregate exists, in the sense of weak convergence of finite-dimensional distributions, and is a mixed stable moving average as studied in Surgailis, Rosiński, Mandrekar and Cambanis (1993). We focus on the case where the slope coefficient a has probability density vanishing regularly at a = 1 with exponent b ∈ (0, α − 1) for α ∈ (1, 2). We show that in this case, the limit aggregate {X̅ t } exhibits long memory. In particular, for {X̅ t }, we investigate the decay of the codifference, the limit of partial sums, and the long-range dependence (sample Allen variance) property of Heyde and Yang (1997).

Parametric modelling of turbulence

1990 ◽  
Vol 332 (1627) ◽  
pp. 439-455 ◽  
Keyword(s):  
Long Range ◽  
Three Dimensional ◽  
Large Data ◽  
Theoretical Work ◽  
Long Range Dependence ◽  
Dependence Structure ◽  
Data Sets ◽  
Parametric Modelling ◽  
First Order ◽  
Log Linear

Some steps are taken towards a parametric statistical model for the velocity and velocity derivative fields in stationary turbulence, building on the background of existing theoretical and empirical knowledge of such fields. While the ultimate goal is a model for the three-dimensional velocity components, and hence for the corresponding velocity derivatives, we concentrate here on the stream wise velocity component. Discrete and continuous time stochastic processes of the first-order autoregressive type and with one-dimensional marginals having log-linear tails are constructed and compared with two large data-sets. It turns out that a first-order autoregression that fits the local correlation structure well is not capable of describing the correlations over longer ranges. A good fit locally as well as at longer ranges is achieved by using a process that is the sum of two independent autoregressions. We study this type of model in some detail. We also consider a model derived from the above-mentioned autoregressions and with dependence structure on the borderline to long-range dependence. This model is obtained by means of a general method for construction of processes with long-range dependence. Some suggestions for future empirical and theoretical work are given.

A study on the variations in long-range dependence of solar energetic particles during different solar cycles

2018 ◽  
Vol 13 (S340) ◽  
pp. 47-48
Author(s):  
V. Vipindas ◽  
Sumesh Gopinath ◽  
T. E. Girish
Keyword(s):  
Long Range ◽  
Long Memory ◽  
Hurst Exponent ◽  
High Energy ◽  
Energetic Particles ◽  
Solar Energetic Particles ◽  
Long Range Dependence ◽  
Solar Cycles ◽  
Self Similarity ◽  
High Energy Particles

AbstractSolar Energetic Particles (SEPs) are high-energy particles ejected by the Sun which consist of protons, electrons and heavy ions having energies in the range of a few tens of keVs to several GeVs. The statistical features of the solar energetic particles (SEPs) during different periods of solar cycles are highly variable. In the present study we try to quantify the long-range dependence (or long-memory) of the solar energetic particles during different periods of solar cycle (SC) 23 and 24. For stochastic processes, long-range dependence or self-similarity is usually quantified by the Hurst exponent. We compare the Hurst exponent of SEP proton fluxes having energies (>1MeV to >100 MeV) for different periods, which include both solar maximum and minimum years, in order to find whether SC-dependent self-similarity exist for SEP flux.

scholarly journals Variance Bound of ACF Estimation of One Block of fGn with LRD

2010 ◽  
Vol 2010 ◽  
pp. 1-14 ◽  
Author(s):  
Ming Li ◽  
Wei Zhao
Keyword(s):  
Long Range ◽  
Autocorrelation Function ◽  
Gaussian Noise ◽  
Block Size ◽  
Long Range Dependence ◽  
Hurst Parameter ◽  
Sample Length ◽  
Fractional Gaussian Noise ◽  
Variance Bound ◽  
Data Points

This paper discusses the estimation of autocorrelation function (ACF) of fractional Gaussian noise (fGn) with long-range dependence (LRD). A variance bound of ACF estimation of one block of fGn with LRD for a given value of the Hurst parameter (H) is given. The present bound provides a guideline to require the block size to guarantee that the variance of ACF estimation of one block of fGn with LRD for a givenHvalue does not exceed the predetermined variance bound regardless of the start point of the block. In addition, the present result implies that the error of ACF estimation of a block of fGn with LRD depends only on the number of data points within the sample and not on the actual sample length in time. For a given block size, the error is found to be larger for fGn with stronger LRD than that with weaker LRD.

Correlation models with long-range dependence

2002 ◽  
Vol 39 (2) ◽  
pp. 370-382 ◽  
Author(s):  
Chunsheng Ma
Keyword(s):  
Time Series ◽  
Long Range ◽  
Long Memory ◽  
Short Range ◽  
Sufficient Conditions ◽  
Long Range Dependence ◽  
Simple Method ◽  
Summable Sequence ◽  
Correlation Models ◽  
Necessary And Sufficient

This paper is concerned with the correlation structure of a stationary discrete time-series with long memory or long-range dependence. Given a sequence of bounded variation, we obtain necessary and sufficient conditions for a function generated from the sequence to be a proper correlation function. These conditions are applied to derive various slowly decaying correlation models. To obtain correlation models with short-range dependence from an absolutely summable sequence, a simple method is introduced.

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