scholarly journals CONSTRUCTION OF MODELS FOR BOUNDED PRICE PROCESSES: THE CASE OF THE HKD EXCHANGE RATE

2015 ◽  
Vol 10 (02) ◽  
pp. 1550011
Author(s):  
HONG BEN YEE ◽  
NIKOLAI DOKUCHAEV
Keyword(s):  
Time Series ◽  
Exchange Rate ◽  
Financial Time Series ◽  
Two Dimensional ◽  
One Dimensional ◽  
Financial Time ◽  
Ergodic Properties ◽  
1D Model ◽  
Weak Side ◽  
2D Model

This paper discusses construction of evolution models for financial time series evolving within a given interval. We calibrated a model for the case of the USD/HKD exchange rate after the separation of strong and weak side convertibility undertakings, in which the rate is confined to a specified corridor. This process represents an interesting example of a tradable bounded process. A one-dimensional (1D) model was able to replicate the bounded distribution of the process, but a two-dimensional (2D) model better captured dynamics as measured by the volatility without losing features of the 1D model. We briefly consider the ergodic properties of these models.

scholarly journals Searching for histogram patterns in USD/ZAR foreign exchange financial time series

2009 ◽  
Vol 6 (4) ◽  
pp. 575-584
Author(s):  
JH Van Rooyen
Keyword(s):  
Time Series ◽  
Exchange Rate ◽  
High Frequency ◽  
Financial Risk ◽  
Pattern Analysis ◽  
Financial Time Series ◽  
Rate Data ◽  
Data Set ◽  
Frequency Distributions ◽  
Financial Time

This study aims to investigate whether the phenomena found by Shnoll et al. when applying histogram pattern analysis techniques to stochastic processes from chemistry and physics are also present in financial time series, particularly exchange rate data. The phenomena are related to fine structure of non-smoothed frequency distributions drawn from tick high frequency currency exchange rates over a period of one week. Shnoll et al. use the notion of macroscopic fluctuations (MF) to explain the behaviour of sequences of histograms. Histogram patterns in time adhere to several laws that could not be detected when using time series analysis methods. In this study, which is a follow up of research by Van ZylBulitta, VH, Otte, R and Van Rooyen, JH, special emphasis is placed on the histogram pattern analysis of high frequency exchange rate data set. Following previous studies of the Shnoll phenomena from other fields, different steps of the histogram sequence analysis are carried out to determine whether the findings of Shnoll et al. could also be applied to financial market data. The findings presented here widen the understanding of time varying volatility and can aid in financial risk measurement and management. Outcomes of the study include an investigation of time series characteristics, more specifically the formation of discrete states and the repetition of histogram patterns

scholarly journals Fractional Laplace motion

2006 ◽  
Vol 38 (02) ◽  
pp. 451-464 ◽  
Author(s):  
T. J. Kozubowski ◽  
M. M. Meerschaert ◽  
K. Podgórski
Keyword(s):  
Time Series ◽  
Brownian Motion ◽  
Hydraulic Conductivity ◽  
Fractional Brownian Motion ◽  
Long Range ◽  
Financial Time Series ◽  
Long Range Dependence ◽  
Self Similarity ◽  
One Dimensional ◽  
Financial Time

Fractional Laplace motion is obtained by subordinating fractional Brownian motion to a gamma process. Used recently to model hydraulic conductivity fields in geophysics, it might also prove useful in modeling financial time series. Its one-dimensional distributions are scale mixtures of normal laws, where the stochastic variance has the generalized gamma distribution. These one-dimensional distributions are more peaked at the mode than is a Gaussian distribution, and their tails are heavier. In this paper we derive the basic properties of the process, including a new property called stochastic self-similarity. We also study the corresponding fractional Laplace noise, which may exhibit long-range dependence. Finally, we discuss practical methods for simulation.

scholarly journals Fractional Laplace motion

2006 ◽  
Vol 38 (2) ◽  
pp. 451-464 ◽  
Author(s):  
T. J. Kozubowski ◽  
M. M. Meerschaert ◽  
K. Podgórski
Keyword(s):  
Time Series ◽  
Brownian Motion ◽  
Hydraulic Conductivity ◽  
Fractional Brownian Motion ◽  
Long Range ◽  
Financial Time Series ◽  
Long Range Dependence ◽  
Self Similarity ◽  
One Dimensional ◽  
Financial Time

Fractional Laplace motion is obtained by subordinating fractional Brownian motion to a gamma process. Used recently to model hydraulic conductivity fields in geophysics, it might also prove useful in modeling financial time series. Its one-dimensional distributions are scale mixtures of normal laws, where the stochastic variance has the generalized gamma distribution. These one-dimensional distributions are more peaked at the mode than is a Gaussian distribution, and their tails are heavier. In this paper we derive the basic properties of the process, including a new property called stochastic self-similarity. We also study the corresponding fractional Laplace noise, which may exhibit long-range dependence. Finally, we discuss practical methods for simulation.

scholarly journals Layer histogram patterns in financial time series

2009 ◽  
Vol 6 (3) ◽  
pp. 137-146
Author(s):  
Verena Helen Van Zyl-Bulitta ◽  
R. Otte ◽  
JH Van Rooyen
Keyword(s):  
Time Series ◽  
Exchange Rate ◽  
Financial Risk ◽  
Pattern Analysis ◽  
Financial Time Series ◽  
Data Set ◽  
Frequency Distributions ◽  
Analysis Techniques ◽  
Financial Time ◽  
Macroscopic Fluctuations

This study aims to investigate whether the phenomena found by Shnoll et al. when applying histogram pattern analysis techniques to stochastic processes from chemistry and physics are also present in financial time series, particularly exchange rate and index data. The phenomena are related to fine structure of non-smoothed frequency distributions drawn from statistically insufficient samples of changes and their patterns in time. Shnoll et al. use the notion of macroscopic fluctuations (MF) to explain the behavior of sequences of histograms. Histogram patterns in time adhere to several laws that could not be detected when using time series analysis methods. In this study special emphasis is placed on the histogram pattern analysis of high frequency exchange rate data set. Following previous studies of the Shnoll phenomena from other fields, different steps of the histogram sequence analysis are carried out to determine whether the findings of Shnoll et al. could also be applied to financial market data. The findings presented here widen the understanding of time varying volatility and can aid in financial risk measurement and management. Outcomes of the study include an investigation of time series characteristics, more specifically the formation of discrete states.

Calibration of a 1D/1D urban flood model using 1D/2D model results in the absence of field data

2011 ◽  
Vol 64 (5) ◽  
pp. 1016-1024 ◽  
Author(s):  
J. Leandro ◽  
S. Djordjević ◽  
A. S. Chen ◽  
D. A. Savić ◽  
M. Stanić
Keyword(s):  
Field Data ◽  
Computational Time ◽  
Necessary Condition ◽  
Two Dimensional ◽  
Time Step ◽  
Urban Flood ◽  
One Dimensional ◽  
1D Model ◽  
Surface Network ◽  
2D Model

Recently increased flood events have been prompting researchers to improve existing coupled flood-models such as one-dimensional (1D)/1D and 1D/two-dimensional (2D) models. While 1D/1D models simulate sewer and surface networks using a one-dimensional approach, 1D/2D models represent the surface network by a two-dimensional surface grid. However their application raises two issues to urban flood modellers: (1) stormwater systems planning/emergency or risk analysis demands for fast models, and the 1D/2D computational time is prohibitive, (2) and the recognized lack of field data (e.g. Hunter et al. (2008)) causes difficulties for the calibration/validation of 1D/1D models. In this paper we propose to overcome these issues by calibrating a 1D/1D model with the results of a 1D/2D model. The flood-inundation results show that: (1) 1D/2D results can be used to calibrate faster 1D/1D models, (2) the 1D/1D model is able to map the 1D/2D flood maximum extent well, and the flooding limits satisfactorily in each time-step, (3) the 1D/1D model major differences are the instantaneous flow propagation and overestimation of the flood-depths within surface-ponds, (4) the agreement in the volume surcharged by both models is a necessary condition for the 1D surface-network validation and (5) the agreement of the manholes discharge shapes measures the fitness of the calibrated 1D surface-network.

Application of Pi-Sigma Neural Networks and Ridge Polynomial Neural Networks to Financial Time Series Prediction

2009 ◽  
pp. 271-293 ◽  
Author(s):  
Rozaida Ghazali ◽  
Dhiya Al-Jumeily
Keyword(s):  
Neural Networks ◽  
Time Series ◽  
Exchange Rate ◽  
Financial Time Series ◽  
Time Series Prediction ◽  
The United States ◽  
Financial Time ◽  
Higher Order Neural Networks ◽  
The Exchange Rate ◽  
Japanese Yen

This chapter discusses the use of two artificial Higher Order Neural Networks (HONNs) models; the Pi- Sigma Neural Networks and the Ridge Polynomial Neural Networks, in financial time series forecasting. The networks were used to forecast the upcoming trends of three noisy financial signals; the exchange rate between the US Dollar and the Euro, the exchange rate between the Japanese Yen and the Euro, and the United States 10-year government bond. In particular, we systematically investigate a method of pre-processing the signals in order to reduce the trends in them. The performance of the networks is benchmarked against the performance of Multilayer Perceptrons. From the simulation results, the predictions clearly demonstrated that HONNs models, particularly Ridge Polynomial Neural Networks generate higher profit returns with fast convergence, therefore show considerable promise as a decision making tool. It is hoped that individual investor could benefit from the use of this forecasting tool.

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