Dissertations / Theses on the topic 'ARMA-GARCH Model'

This study creates a model to predict short-term exchange rates as a combination of the relative purchasing power parity model (Grossman and Simpson 2011) and the interest power parity model. I then use the statistical techniques ARMA and GARCH to account for the variance of the terms. Previous works considered the effects of these models individually, but mine consider them in unison. I consider both in-sample and out-of-sample tests. I use data on five major exchange rates (JPY/USD, CAD/USD, CHF/USD, GBP/USD, and AUD/USD) sampled at a monthly frequency from 1989-2013. My model statistically significantly predicts these exchange rates over the January 2012 to January 2013 period.

This report is for MA575: Market and Credit Risk Models and Management, given by Professor Marcel Blais. In this project, three different methods for estimating Value at Risk (VaR) and Expected Shortfall (ES) are used, examined, and compared to gain insightful information about the strength and weakness of each method. In the first part of this project, a portfolio of underlying assets and vanilla options were formed in an Interactive Broker paper trading account. Value at Risk was calculated and updated weekly to measure the risk of the entire portfolio. In the second part of this project, Value at Risk was calculated using semi-parametric model. Then the weekly losses of the stock portfolio and the daily losses of the entire portfolio were both fitted into ARMA(1,1)-GARCH(1,1), and the estimated parameters were used to find their conditional value at risks (CVaR) and the conditional expected shortfalls (CES).

This thesis has used the Fama and French five-factor model (FF5M) and proposed an alternative model. The proposed model is named the Fama and French five-factor heteroscedastic student's model (FF5HSM). The model utilises an ARMA model for the returns with the FF5M factors incorporated and a GARCH(1,1) model for the volatility. The FF5HSM uses returns data from the FF5M's portfolio construction for the Japanese stock market and the five risk factors. The portfolio's capture different levels of market capitalisation, and the factors capture market risk. The ARMA modelling is used to address the autocorrelation present in the data. To deal with the heteroscedasticity in daily returns of stocks, a GARCH(1,1) model has been used. The order of the GARCH-model has been concluded to be reasonable in academic literature for this type of data. Another finding in earlier research is that asset returns do not follow the assumption of normality that a regular regression model assumes. Therefore, the skewed student's t-distribution has been assumed for the error terms. The result of the data indicates that the FF5HSM has a better in-sample fit than the FF5M. The FF5HSM addresses heteroscedasticity and autocorrelation in the data and minimises them depending on the portfolio. Regardingforecasting, both the FF5HSM and the FF5M are accurate models depending on what portfolio the model is applied on.

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A proposta do estudo é aplicar ao Ibovespa, modelo paramétrico de VaR de 1 dia, com distribuição dos retornos dinâmica, que procura apreciar características empíricas comumente apresentadas por séries financeiras, como clusters de volatilidade e leptocurtose. O processo de retornos é modelado como um ARMA com erros GARCH que seguem distribuição t assimétrica. A metodologia foi comparada com o RiskMetrics e com modelos ARMA-GARCH com distribuição dos erros normal e t. Os modelos foram estimados diariamente usando uma janela móvel de 1008 dias. Foi verificado pelos backtests de Christoffersen e de Diebold, Gunther e Tay que dentre os modelos testados, o ARMA(2,2)- GARCH(2,1) com distribuição t assimétrica apresentou os melhores resultados.
The proposal of the study is to apply to Ibovespa a 1 day VaR parametric model, with dynamic distribution of returns, that aims to address empirical features usually seen in financial series, such as volatility clustering and leptocurtosis. The returns process is modeled as an ARMA with GARCH residuals that follow a skewed t distribution. The methodology was compared to RiskMetrics and to ARMA-GARCH with normal and t distributed residuals. The models were estimated every daily period using a window of 1008 days. By the backtests of Christoffersen and Diebold, Gunther and Tay, among the tested models, the ARMA(2,2)-GARCH(2,1) with skewed t distribution has given the best results.

El siguiente proyecto de tesis pretende mostrar y verificar cómo las redes neuronales, en concreto, la red backpropagation son una alternativa para la predicción de la volatilidad condicional frente a los modelos econométricos clásicos de la familia GARCH. El estudio se realiza para diferentes índices bursátilies de diferentes tamaños y zonas geográficas, así como para datos tanto diarios como de alta frecuencia utilizando para la comparativa uno de los modelos más extendidos para el estudio de la volatildiad condicional en índices bursátiles como el EGARCH, dada la existencia comprobada de asimetrías en la volatildiad de dichos índices. La elección de la red neuronal backpropagation viene motivada por ser una de las redes neuronales más extendidas en su uso en finanzas por su capacidad de generalización método de aprendizaje basada en la relga delta generalizada.
Oliver Muncharaz, J. (2014). MODELIZACIÓN DE LA VOLATILIDAD CONDICIONAL EN ÍNDICES BURSÁTILES : COMPARATIVA MODELO EGARCH VERSUS RED NEURONAL BACKPROPAGATION [Tesis doctoral]. Editorial Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/35803
Alfresco

碩士
清雲科技大學
經營管理研究所
95
Mainland China keep reducing the currency under the standard value since its economical development intermediate stage. Because China is the export country under the weak monetary policy, the exporting product price is more competitive which is similar to the export oriented policy. Due to the advantage of Mainland China export trade continues to grow, Driving Taiwan’s the hot money goes to China .The favorable balance of trade keep increasing, however Taiwan and the mainland mutually dependent highly. No matter Taiwanese businessman, who is trading with mainland China in Taiwan, or directly trading in the mainland, the Renminbi exchange rate will impact on their business. Therefore grasping the change of the Renminbi exchange rate becomes urgent. This paper discusses exchange rate statistical characteristics and its econometrics by reading the Renminbi exchange rate path and using the ARMA-GARCH to establish exchange rate model. We discovered the Renminbi exchange rate presents continues small revaluation. Further we can forecast the trend of the Renminbi exchange rate and the undulation in the short term. Renminbi exchange rate by using ones differencing estimated parameters is significant。Using estimated models to simulate the tendency of the characteristics of the Renminbi sequence, and all there models present good export forecast performance.

碩士
國立高雄第一科技大學
風險管理與保險研究所
100
Using the five mines TAIEX intra-day high frequency data and closing price from 2001 to 2011, this paper empirically tests the trading strategies according to the moving average approach. This paper applies three variation GARCH-type volatility models: GARCH, GJR and EGARCH models with normal and Student’ t distributions to forecast TAIEX prices. Based on the moving average of the forecast prices, this paper constructs the relevant trading strategies and empirically tests their performance for investors’ reference. From the empirical results, this paper demonstrates that the moving average trading strategies according to GARCH-normal model provides a better performance.

碩士
中原大學
應用數學研究所
97
Time series analysis has a good many applications on all kinds of fields. Especially,GARCH models have been a tool to explain the leptokurtosis and the volatility clusteringphenomenon commonly seen in financial data. In the literature, Harvey and Shephard (1993) and Harvey (1994) used the quasi-maximum likelihood to estimate the parameters of GARCH models. So (1997) and Shephard (1994) applied the EM algorithm. Shephard (1993), Jacquier (1994), Pitt (1997), Pitt and Shephard (1999), Kim (1998) and So (1998) employed the Bayesian approaches. Some information criterion are the traditional ways to check the model fitting problems, such as AIC, BIC, Consistent AIC, Consistent AIC with Fisher information. On the other hand, Green (1995) provided the reversible jump Markoc Chain Monte Carlo (RJMCMC) method that viewed the model as an other parameter,and updated all parameters, including models themselves in different dimension. We continue the works of Hsu (2005), Chen (2006), and Hsu (2007), and extend the study to the ARMA-GARCH models. Simulation studies show that our method successfully estimate the parameters of ARMA parts. Although we only consider 11 targeted models in simulation studies, our method can accurately identify the correct model from possibly infinitely many models. Finally, this method is applied to the Texas oil data (2000-2009).

Tang Him John.
Thesis (M.Phil.)--Chinese University of Hong Kong, 2003.
Includes bibliographical references (leaves 76-80).
Abstracts in English and Chinese.
Abstract --- p.i
Acknowledgment --- p.iii
Chapter 1 --- Introduction --- p.1
Chapter 1.1 --- Background --- p.2
Chapter 1.1.1 --- Linear Time Series --- p.2
Chapter 1.1.2 --- Mixture Models --- p.3
Chapter 1.1.3 --- EM algorithm --- p.6
Chapter 1.1.4 --- Model Selection --- p.6
Chapter 1.2 --- Main Objectives --- p.7
Chapter 1.3 --- Outline of this thesis --- p.7
Chapter 2 --- Finite Gaussian Mixture ARMA-GARCH Model --- p.9
Chapter 2.1 --- Introduction --- p.9
Chapter 2.1.1 --- "AR, MA, and ARMA" --- p.10
Chapter 2.1.2 --- Stationarity --- p.11
Chapter 2.1.3 --- ARCH and GARCH --- p.12
Chapter 2.1.4 --- Gaussian mixture --- p.13
Chapter 2.1.5 --- EM and GEM algorithms --- p.14
Chapter 2.2 --- Finite Gaussian Mixture ARMA-GARCH Model --- p.16
Chapter 2.3 --- Estimation of Gaussian mixture ARMA-GARCH model --- p.17
Chapter 2.3.1 --- Autocorrelation and Stationarity --- p.20
Chapter 2.3.2 --- Model Selection --- p.24
Chapter 2.4 --- Experiments: First Step Prediction --- p.26
Chapter 2.5 --- Chapter Summary --- p.28
Chapter 2.6 --- Notations and Terminologies --- p.30
Chapter 2.6.1 --- White Noise Time Series --- p.30
Chapter 2.6.2 --- Lag Operator --- p.30
Chapter 2.6.3 --- Covariance Stationarity --- p.31
Chapter 2.6.4 --- Wold's Theorem --- p.31
Chapter 2.6.5 --- Multivariate Gaussian Density function --- p.32
Chapter 3 --- Finite Mixture-of-Expert ARMA-GARCH Model --- p.33
Chapter 3.1 --- Introduction --- p.33
Chapter 3.1.1 --- Mixture-of-Expert --- p.34
Chapter 3.1.2 --- Alternative Mixture-of-Expert --- p.35
Chapter 3.2 --- ARMA-GARCH Finite Mixture-of-Expert Model --- p.36
Chapter 3.3 --- Estimation of Mixture-of-Expert ARMA-GARCH Model --- p.37
Chapter 3.3.1 --- Model Selection --- p.38
Chapter 3.4 --- Experiments: First Step Prediction --- p.41
Chapter 3.5 --- Second Step and Third Step Prediction --- p.44
Chapter 3.5.1 --- Calculating Second Step Prediction --- p.44
Chapter 3.5.2 --- Calculating Third Step Prediction --- p.45
Chapter 3.5.3 --- Experiments: Second Step and Third Step Prediction . --- p.46
Chapter 3.6 --- Comparison with Other Models --- p.50
Chapter 3.7 --- Chapter Summary --- p.57
Chapter 4 --- Stable Estimation Algorithms --- p.58
Chapter 4.1 --- Stable AR(1) estimation algorithm --- p.59
Chapter 4.2 --- Stable AR(2) Estimation Algorithm --- p.60
Chapter 4.2.1 --- Real p1 and p2 --- p.61
Chapter 4.2.2 --- Complex p1 and p2 --- p.61
Chapter 4.2.3 --- Experiments for AR(2) --- p.63
Chapter 4.3 --- Experiment with Real Data --- p.64
Chapter 4.4 --- Chapter Summary --- p.65
Chapter 5 --- Conclusion --- p.66
Chapter 5.1 --- Further Research --- p.69
Chapter A --- Equation Derivation --- p.70
Chapter A.1 --- First Derivatives for Gaussian Mixture ARMA-GARCH Esti- mation --- p.70
Chapter A.2 --- First Derivatives for Mixture-of-Expert ARMA-GARCH Esti- mation --- p.71
Chapter A.3 --- First Derivatives for BYY Harmony Function --- p.72
Chapter A.4 --- First Derivatives for stable estimation algorithms --- p.73
Chapter A.4.1 --- AR(1) --- p.74
Chapter A.4.2 --- AR(2) --- p.74
Bibliography --- p.80

The thesis evaluates several hundred one-day-ahead VaR forecasting models in the time period between the years 2004 and 2009 on data from six world stock indices - DJI, GSPC, IXIC, FTSE, GDAXI and N225. The models model mean using the AR and MA processes with up to two lags and variance with one of GARCH, EGARCH or TARCH processes with up to two lags. The models are estimated on the data from the in-sample period and their forecasting ac- curacy is evaluated on the out-of-sample data, which are more volatile. The main aim of the thesis is to test whether a model estimated on data with lower volatility can be used in periods with higher volatility. The evaluation is based on the conditional coverage test and is performed on each stock index sepa- rately. Unlike other works in this eld of study, the thesis does not assume the log-returns to be normally distributed and does not explicitly select a partic- ular conditional volatility process. Moreover, the thesis takes advantage of a less known conditional coverage framework for the measurement of forecasting accuracy.

Value at Risk (VaR) and Expected Shortfall (ES) are methods often used to measure market risk. Inaccurate and unreliable Value at Risk and Expected Shortfall models can lead to underestimation of the market risk that a firm or financial institution is exposed to, and therefore may jeopardize the well-being or survival of the firm or financial institution during adverse markets. The objective of this study is therefore to examine various Value at Risk and Expected Shortfall models, including fatter tail models, in order to analyze the accuracy and reliability of these models. Thirteen VaR and ES models under three main approaches (Parametric, Non-Parametric and Semi-Parametric) are examined in this study. The results of this study show that the proposed model (ARMA(1,1)-GJR-GARCH(1,1)-SGED) gives the most balanced Value at Risk results. The semi-parametric model (Extreme Value Theory, EVT) is the most accurate Value at Risk model in this study for S&P 500.
October 2014

O interesse decorrente do facto do índice PSI-20 constituir o principal benchmark do mercado accionista português e sustentar o novo mercado de produtos derivados em Portugal, domínio particularmente rico de análise da moderna investigação financeira sobretudo a nível da medida do risco e valorização dos produtos derivados, origina que a modelação da volatilidade deste índice se revista de grande importância. O objectivo desta dissertação é modelar a volatilidade do índice PSI-20, compreender como se comporta, à custa da sua informação passada registada entre 31 de Dezembro de 1992 e 28 de Abril de 2000, e analisar os efeitos de calendário que de certa forma o influenciam. Esta modelação será realizada recorrendo aos modelos econométricos do tipo ARMA-GARCH. Utilizando os modelos estimados são realizadas previsões para a volatilidade do índice PSI-20 para prazos até 5 dias. De modo a avaliar a qualidade destas previsões são calculados os valores teóricos do prémio das Opções PSI-20, com datas de vencimento a 19 de Maio e 16 de Junho do ano 2000, e procede-se à sua comparação com os prémios (preços) de mercado reais e ainda com os prémios teóricos utilizando a volatilidade histórica.

Title: Actuarial and Exposure-based Models for Hail Peril Author: Bc. Matúš Drobuliak Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Michal Pešta, Ph.D., Department of Probability and Mathe- matical Statistics Abstract: This thesis covers an introduction to catastrophe modelling and focuses on statistical methods for extreme events. This includes methods of estimating parameters of claim distribution with a focus on probability weighted moments estimation technique. Furthermore, times series modelling, skew t-distribution, and two model clustering techniques are examined as well. This is later utilised in the practical application part of this thesis, which uses real data provided by an insurance company operating in the Czech Republic. Probability distribution fitting of large claims caused by hailstorms and Monte Carlo simulation of future losses are demonstrated later. Keywords: Catastrophe modelling, Hail peril, Probability weighted moments, Extreme events, ARMA-GARCH, Monte Carlo simulation iii