Modeling and Prediction of Great Salt Lake Elevation Time Series Based on ARFIMA

2007 ◽  
Author(s):  
Rongtao Sun ◽  
YangQuan Chen ◽  
Qianru Li
Keyword(s):  
Time Series ◽  
Salt Lake ◽  
Moving Average ◽  
Great Salt Lake ◽  
Estimation Methods ◽  
Arma Models ◽  
Modeling And Prediction ◽  
The People ◽  
Arfima Model ◽  
Parameter Estimation Methods

The elevation of Great Salt Lake (GSL) has a great impact on the people of Utah. The flood of GSL in 1982 has caused a loss of millions of dollars. Therefore, it is very important to predict the GSL levels as precisely as possible. This paper points out the reason why conventional methods failed to describe adequately the rise and fall of the GSL levels — the long-range dependence (LRD) property. The LRD of GSL elevation time series is characterized by some most commonly used Hurst parameter estimation methods in this paper. Then, according to the revealed LRD, the autoregressive fractional integrated moving average (ARFIMA) model is applied to analyze the data and predict the future levels. We have shown that the prediction results has a better performance compared to the conventional ARMA models.

The Modeling of Great Salt Lake Elevation Time Series Based on ARFIMA With Stable Innovations

2009 ◽  
Author(s):  
Hu Sheng ◽  
YangQuan Chen
Keyword(s):  
Time Series ◽  
Fractional Integral ◽  
Salt Lake ◽  
Moving Average ◽  
Great Salt Lake ◽  
Western Hemisphere ◽  
Conditional Heteroskedasticity ◽  
New Model ◽  
The People ◽  
Auto Regressive

Great Salt Lake (GSL) is the largest salt lake in the western hemisphere, the fourth-largest terminal lake in the world. The elevation of Great Salt Lake has critical effect on the people who live nearby and their properties. It is crucial to build an exact model of GSL elevation time series in order to predict the GSL elevation precisely. Although some models, such as FARIMA or ARFIMA (Auto-Regressive Fractional Integral and Moving Average), GARCH (Generalized Auto-Regressive Conditional Heteroskedasticity) and FIGARCH (Fractional Integral Generalized Auto-Regressive Conditional Heteroskedasticity), have been built to characterize the variation of Great Salt Lake elevation, these models can not characterize it perfectly. Therefore, it became a key point to build a more appropriate model of GSL elevation time series. In this paper a new model based on fractional autoregressive integrated moving average (ARFIMA) with Stable innovations is applied to analyze the data and predict the future levels. From the analysis we can see that the new model can characterize GSL elevation time series more accurately. The new model will be beneficial to predict GSL elevation more precisely.

Great Salt Lake Surface Level Forecasting Using FIGARCH Model

2007 ◽  
Author(s):  
Qianru Li ◽  
Christophe Tricaud ◽  
Rongtao Sun ◽  
YangQuan Chen
Keyword(s):  
Time Series ◽  
Fractional Integral ◽  
Salt Lake ◽  
Moving Average ◽  
Great Salt Lake ◽  
Conditional Heteroskedasticity ◽  
High Volatility ◽  
Auto Regressive ◽  
Figarch Model ◽  
Auto Regression

In this paper, we have examined 4 models for Great Salt Lake level forecasting: ARMA (Auto-Regression and Moving Average), ARFIMA (Auto-Regressive Fractional Integral and Moving Average), GARCH (Generalized Auto-Regressive Conditional Heteroskedasticity) and FIGARCH (Fractional Integral Generalized Auto-Regressive Conditional Heteroskedasticity). Through our empirical data analysis where we divide the time series in two parts (first 2000 measurement points in Part-1 and the rest is Part-2), we found that for Part-2 data, FIGARCH offers best performance indicating that conditional heteroscedasticity should be included in time series with high volatility.

scholarly journals Forecasting of Economic Indicators (Production, Consumption, Population) of Wheat Crop (A Case Study)

2021 ◽  
Vol 8 (6) ◽  
pp. 38-46
Author(s):  
Mohammad Karim Ahmadzai
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Moving Average ◽  
Arima Model ◽  
Wheat Crop ◽  
Series Analysis ◽  
The People ◽  
Self Sufficiency ◽  
Univariate Time Series ◽  
Short Run

Wheat is the most important food crop in Afghanistan, whether consumed by the bulk of the people or used in various sectors. The problem is that Afghanistan has a significant shortfall of wheat between domestic production and consumption. Thus, the present study looks at the issue of meeting self-sufficiency for the whole population due to wheat shortages. To do so, we employ time series analysis, which can produce a highly exact short-run prediction for a significant quantity of data on the variables in question. The ARIMA models are versatile and widely utilised in univariate time series analysis. The ARIMA model combines three processes: I the auto-regressive (AR) process, (ii) the differencing process, and (iii) the moving average (MA) process. These processes are referred to as primary univariate time series models in statistical literature and are widely employed in various applications. Where predicting future wheat requirements is one of the most important tools that decision-makers may use to assess wheat requirements and then design measures to close the gap between supply and consumption. The present study seeks to forecast Production, Consumption, and Population for the period 2002-2017 and estimate the values of these variables between 2002 and 2017. (2018-2030).  

COGARCH Models

2020 ◽  
pp. 79-97
Author(s):  
Yakup Arı
Keyword(s):  
Differential Equation ◽  
Time Series ◽  
Continuous Time ◽  
Likelihood Method ◽  
Estimation Methods ◽  
Unequally Spaced ◽  
Parameter Estimation Methods ◽  
Pseudo Maximum Likelihood ◽  
Gamma Processes ◽  
Methods Of Moments

In this chapter, the features of a continuous time GARCH (COGARCH) process is discussed since the process can be applied as an explicit solution for the stochastic differential equation which is defined for the volatility of unequally spaced time series. COGARCH process driven by a Lévy process is an analogue of discrete time GARCH process and is further generalized to solutions of Lévy driven stochastic differential equations. The Compound Poisson and Variance Gamma processes are defined and used to derive the increments for the COGARCH process. Although there are various parameter estimation methods introduced for COGARCH, this study is focused on two methods which are Pseudo Maximum Likelihood Method and General Methods of Moments. Furthermore, an example is given to illustrate the findings.

scholarly journals A Fuzzy Set-Valued Autoregressive Moving Average Model and Its Applications

Symmetry ◽  
2018 ◽  
Vol 10 (8) ◽  
pp. 324 ◽  
Author(s):  
Dabuxilatu Wang ◽  
Liang Zhang
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Empirical Analysis ◽  
Moving Average ◽  
Arma Model ◽  
Autoregressive Moving Average ◽  
Complex Data ◽  
Arma Models ◽  
Linguistic Data ◽  
Series Analysis

Autoregressive moving average (ARMA) models are important in many fields and applications, although they are most widely applied in time series analysis. Expanding the ARMA models to the case of various complex data is arguably one of the more challenging problems in time series analysis and mathematical statistics. In this study, we extended the ARMA model to the case of linguistic data that can be modeled by some symmetric fuzzy sets, and where the relations between the linguistic data of the time series can be considered as the ordinary stochastic correlation rather than fuzzy logical relations. Therefore, the concepts of set-valued or interval-valued random variables can be employed, and the notions of Aumann expectation, Fréchet variance, and covariance, as well as standardized process, were used to construct the ARMA model. We firstly determined that the estimators from the least square estimation of the ARMA (1,1) model under some L2 distance between two sets are weakly consistent. Moreover, the justified linguistic data-valued ARMA model was applied to forecast the linguistic monthly Hang Seng Index (HSI) as an empirical analysis. The obtained results from the empirical analysis indicate that the accuracy of the prediction produced from the proposed model is better than that produced from the classical one-order, two-order, three-order autoregressive (AR(1), AR(2), AR(3)) models, as well as the (1,1)-order autoregressive moving average (ARMA(1,1)) model.

scholarly journals Multi-scale CO2

2021 ◽  
Author(s):  
Xiaomeng Gu ◽  
Andrew Viggo Metcalfe ◽  
Gary Glonek
Keyword(s):  
Time Series ◽  
Seasonal Variation ◽  
Industrial Revolution ◽  
Moving Average ◽  
Arima Models ◽  
Arma Models ◽  
Deterministic Models ◽  
Increasing Trend ◽  
Exponential Trend ◽  
Sampling Intervals

Abstract Five time series of estimated atmospheric CO 2 with sampling intervals ranging from 0.5 million years to the relatively high frequency of one week are analysed. The yearly series shows a clear increasing trend since the beginning of the first Industrial Revolution around 1760. The weekly series shows a clear increasing trend and also seasonal variation. In both cases, the trend is fitted by a conceptual model that consists of a baseline value with an exponential trend superimposed. For the weekly series, the seasonal variation is modelled as an exponential of a sum of sine and cosine terms. The deviations from these deterministic models are treated as detrended and deseasonalised time series.Then,threesub-categoriesof autoregressive integrated moving average (ARIMA) models are fitted to the five time series: ARMA models which are stationary; FARIMA models which are stationary but have long memory and are fractal processes, and ARIMA models which are variations on a random walk and so non-stationary in the variance.The FARIMA and ARIMA models provide better fits to the data than the corresponding ARMA models. All the fitted models are close to the boundary of stability, and are consistent with claims that climate change due to an increase in atmospheric CO 2 may not quickly be reversed even if CO 2 emissions are stopped.

scholarly journals Forecasting RMB Exchange Rate Based on a Nonlinear Combination Model of ARFIMA, SVM, and BPNN

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Chi Xie ◽  
Zhou Mao ◽  
Gang-Jin Wang
Keyword(s):  
Time Series ◽  
Exchange Rate ◽  
Financial Time Series ◽  
Moving Average ◽  
Back Propagation ◽  
Back Propagation Neural Network ◽  
Support Vector ◽  
Rmb Exchange Rate ◽  
Combination Model ◽  
Arfima Model

There are various models to predict financial time series like the RMB exchange rate. In this paper, considering the complex characteristics of RMB exchange rate, we build a nonlinear combination model of the autoregressive fractionally integrated moving average (ARFIMA) model, the support vector machine (SVM) model, and the back-propagation neural network (BPNN) model to forecast the RMB exchange rate. The basic idea of the nonlinear combination model (NCM) is to make the prediction more effective by combining different models’ advantages, and the weight of the combination model is determined by a nonlinear weighted mechanism. The RMB exchange rate against US dollar (RMB/USD) and the RMB exchange rate against Euro (RMB/EUR) are used as the empirical examples to evaluate the performance of NCM. The results show that the prediction performance of the nonlinear combination model is better than the single models and the linear combination models, and the nonlinear combination model is suitable for the prediction of the special time series, such as the RMB exchange rate.

scholarly journals An Overview of FIGARCH and Related Time Series Models

2016 ◽  
Vol 41 (3) ◽  
Author(s):  
Maryam Tayefi ◽  
T.V. Ramanathan
Keyword(s):  
Time Series ◽  
Moving Average ◽  
Option Prices ◽  
Market Returns ◽  
Future Directions ◽  
Stock Market Returns ◽  
Inflation Rates ◽  
Modeling Volatility ◽  
Figarch Model ◽  
Arfima Model

This paper reviews the theory and applications related to fractionally integrated generalized autoregressive conditional heteroscedastic (FIGARCH) models, mainly for describing the observed persistence in the volatility of a time series. The long memory nature of FIGARCH models allows to be a better candidate than other conditional heteroscedastic models for modeling volatility in exchange rates, option prices, stock market returns and inflation rates. We discuss some of the important properties of FIGARCH models inthis review. We also compare the FIGARCH with the autoregressive fractionally integrated moving average (ARFIMA) model. Problems related to parameter estimation and forecasting using a FIGARCH model are presented. The application of a FIGARCH model to exchange rate data is discussed. We briefly introduce some other models, that are closely related to FIGARCH models. The paper ends with some concluding remarks and future directions of research.

Volatility Behaviors of Financial Time Series by Percolation System on Sierpinski Carpet Lattice

2015 ◽  
Vol 14 (02) ◽  
pp. 1550015 ◽  
Author(s):  
Anqi Pei ◽  
Jun Wang
Keyword(s):  
Time Series ◽  
Financial Time Series ◽  
Moving Average ◽  
Composite Index ◽  
Stock Index ◽  
Sierpinski Carpet ◽  
Financial Model ◽  
Financial Time ◽  
Arfima Model ◽  
Sierpiński Carpet

The financial time series is simulated and investigated by the percolation system on the Sierpinski carpet lattice, where percolation is usually employed to describe the behavior of connected clusters in a random graph, and the Sierpinski carpet lattice is a graph which corresponds the fractal — Sierpinski carpet. To study the fluctuation behavior of returns for the financial model and the Shanghai Composite Index, we establish a daily volatility measure — multifractal volatility (MFV) measure to obtain MFV series, which have long-range cross-correlations with squared daily return series. The autoregressive fractionally integrated moving average (ARFIMA) model is used to analyze the MFV series, which performs better when compared to other volatility series. By a comparative study of the multifractality and volatility analysis of the data, the simulation data of the proposed model exhibits very similar behaviors to those of the real stock index, which indicates somewhat rationality of the model to the market application.

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