scholarly journals The Optimal Bandwidth Parameter Selection in GPH Estimation

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Weijie Zhou ◽  
Huihui Tao ◽  
Feifei Wang ◽  
Weiqiang Pan
Keyword(s):  
Time Series ◽  
Long Memory ◽  
Financial Time Series ◽  
Optimal Choice ◽  
Estimation Accuracy ◽  
Optimal Bandwidth ◽  
Bandwidth Parameter ◽  
High Level ◽  
The Impact ◽  
Memory Parameter

In this paper, the optimal bandwidth parameter is investigated in the GPH algorithm. Firstly, combining with the stylized facts of financial time series, we generate long memory sequences by using the ARFIMA (1, d, 1) process. Secondly, we use the Monte Carlo method to study the impact of the GPH algorithm on existence test, persistence or antipersistence judgment of long memory, and the estimation accuracy of the long memory parameter. The results show that the accuracy of above three factors in the long memory test reached a relatively high level within the bandwidth parameter interval of 0.5 < a < 0.7. For different lengths of time series, bandwidth parameter a = 0.6 can be used as the optimal choice of the GPH estimation. Furthermore, we give the calculation accuracy of the GPH algorithm on existence, persistence or antipersistence of long memory, and long memory parameter d when a = 0.6.

Estimating the memory parameter for potentially non-linear and non-Gaussian time series with wavelets

2022 ◽  
Author(s):  
Chen Xu ◽  
Ye Zhang
Keyword(s):  
Time Series ◽  
Long Memory ◽  
Asymptotic Theory ◽  
Financial Time Series ◽  
Non Linear ◽  
Long Memory Processes ◽  
Non Gaussian ◽  
Gaussian Time ◽  
Gaussian Time Series ◽  
Memory Parameter

Abstract The asymptotic theory for the memory-parameter estimator constructed from the log-regression with wavelets is incomplete for 1/$f$ processes that are not necessarily Gaussian or linear. Having a complete version of this theory is necessary because of the importance of non-Gaussian and non-linear long-memory models in describing financial time series. To bridge this gap, we prove that, under some mild assumptions, a newly designed memory estimator, named LRMW in this paper, is asymptotically consistent. The performances of LRMW in three simulated long-memory processes indicate the efficiency of this new estimator.

scholarly journals Searching for long memory effects in time series of central Europe stock market indices

2008 ◽  
Vol 56 (3) ◽  
pp. 187-200
Author(s):  
Luboš Střelec
Keyword(s):  
Time Series ◽  
Stock Market ◽  
Central Europe ◽  
Long Memory ◽  
Hurst Exponent ◽  
Financial Time Series ◽  
Memory Effects ◽  
Stock Index ◽  
Source Data ◽  
Independent Process

This article deals with one of the important parts of applying chaos theory to financial and capital markets – namely searching for long memory effects in time series of financial instruments. Source data are daily closing prices of Central Europe stock market indices – Bratislava stock index (SAX), Budapest stock index (BUX), Prague stock index (PX) and Vienna stock index (ATX) – in the period from January 1998 to September 2007. For analysed data R/S analysis is used to calculate the Hurst exponent. On the basis of the Hurst exponent is characterized formation and behaviour of analysed financial time series. Computed Hurst exponent is also statistical compared with his expected value signalling independent process. It is also operated with 5-day returns (i.e. weekly returns) for the purposes of comparison and identification nonperiodic cycles.

Influence of some ARFIMA model parameters on the accuracy of financial time series forecasting

2021 ◽  
Vol 62 ◽  
pp. 85-100
Author(s):  
Robert Garafutdinov ◽  
Keyword(s):  
Time Series ◽  
Long Memory ◽  
Financial Time Series ◽  
Time Series Forecasting ◽  
Model Parameters ◽  
Memory Length ◽  
Financial Time ◽  
True Value ◽  
Arfima Model ◽  
Practical Recommendations

The influence of ARFIMA model parameters on the accuracy of financial time series forecasting on the example of artificially generated long memory series and daily log returns of RTS index is investigated. The investigated parameters are deviation of the integration order value from its «true» value, as well as the memory «length» considered by the model. Based on the research results, some practical recommendations for modeling using ARFIMA have been formulated.

Local Whittle estimation of the long-memory parameter

2020 ◽  
Vol 20 (3) ◽  
pp. 565-583
Author(s):  
Christopher F. Baum ◽  
Stan Hurn ◽  
Kenneth Lindsay
Keyword(s):  
Time Series ◽  
Long Memory ◽  
Fractional Integration ◽  
Whittle Estimation ◽  
Memory Parameter

In this article, we describe and implement the local Whittle and exact local Whittle estimators of the order of fractional integration of a time series.

scholarly journals TESTING THE ORDER OF FRACTIONAL INTEGRATION OF A TIME SERIES IN THE POSSIBLE PRESENCE OF A TREND BREAK AT AN UNKNOWN POINT

2018 ◽  
Vol 35 (6) ◽  
pp. 1201-1233 ◽  
Author(s):  
Fabrizio Iacone ◽  
Stephen J. Leybourne ◽  
A.M. Robert Taylor
Keyword(s):  
Time Series ◽  
Power Function ◽  
Long Memory ◽  
Fractional Integration ◽  
Monte Carlo Study ◽  
Local Power ◽  
Finite Sample ◽  
Lm Test ◽  
Unknown Point ◽  
Memory Parameter

We develop a test, based on the Lagrange multiplier [LM] testing principle, for the value of the long memory parameter of a univariate time series that is composed of a fractionally integrated shock around a potentially broken deterministic trend. Our proposed test is constructed from data which are de-trended allowing for a trend break whose (unknown) location is estimated by a standard residual sum of squares estimator applied either to the levels or first differences of the data, depending on the value specified for the long memory parameter under the null hypothesis. We demonstrate that the resulting LM-type statistic has a standard limiting null chi-squared distribution with one degree of freedom, and attains the same asymptotic local power function as an infeasible LM test based on the true shocks. Our proposed test therefore attains the same asymptotic local optimality properties as an oracle LM test in both the trend break and no trend break environments. Moreover, this asymptotic local power function does not alter between the break and no break cases and so there is no loss in asymptotic local power from allowing for a trend break at an unknown point in the sample, even in the case where no break is present. We also report the results from a Monte Carlo study into the finite-sample behaviour of our proposed test.

Modeling the risk-return characteristics of the SB1 Mexican private pension fund index

2016 ◽  
Vol 5 (2) ◽  
pp. 70
Author(s):  
Roberto J. Santillán- Salgado ◽  
Marissa Martínez Preece ◽  
Francisco López Herrera
Keyword(s):  
Time Series ◽  
Long Memory ◽  
Financial Time Series ◽  
Private Pension ◽  
Long Term Memory ◽  
Investment Funds ◽  
Risk Return ◽  
Time Series Modelling ◽  
Figarch Model

This paper analyzes the returns and variance behavior of the largest specialized private pension investment funds index in Mexico, the SIEFORE Básica 1 (or, SB1). The analysis was carried out with time series techniques to model the returns and volatility of the SB1, using publicly available historical data for SB1. Like many standard financial time series, the SB1 returns show non-normality, volatility clusters and excess kurtosis. The econometric characteristics of the series were initially modeled using three GARCH family models: GARCH (1,1), TGARCH and IGARCH. However, due to the presence of highly persistent volatility, the series modeling was extended using Fractionally Integrated GARCH (FIGARCH) methods. To that end, an extended specification: an ARFIMA (p,d,q) and a FIGARCH model were incorporated. The evidence obtained suggests the presence of long memory effects both in the returns and the volatility of the SB1. Our analysis’ results have important implications for the risk management of the SB1. Keywords: Private Pension Funds, Time Series modelling, GARCH models, Long Term memory series

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