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2013, Review of Economics and Finance
This paper investigates the nonlinearities in the behavior of jet fuel prices and air carrier yields as measured by revenue passenger miles(RPMs), where one RPM is defined as one passenger flown one mile in revenue traffic. It indicates that previous research might have overlooked the possibilities of nonlinear dynamics between these two series. Drawing on existing tests of nonlinearities and chaos, this paper first investigates the existence of chaotic behavior as the source of nonlinearities in the monthly prices of jet fuel and RPMs. The findings show strong evidence that the two series exhibit nonlinear dependencies. Evidence is found, however, that this behavior may be inconsistent with chaotic structure. We propose and estimate bivariate GARCH(1,1) and bivariate EGARCH(1,1) models to ascertain the flow of information between jet fuel prices and revenue passenger miles. Estimation results of the bivariate GARCH models offer evidence that the shock transmission between the two series is mainly asymmetric, that is that positive and negative shocks impart degree of volatility differently. It is shown that the positive shocks to jet fuel prices show a substantially higher reaction from the revenue passenger miles. The conclusion is that, RPMs are quite responsive to upward volatility in prices of jet fuel, while falling jet fuel prices may not translate into efficiency gains.
Transportation Research Part E: Logistics and Transportation Review, 2001
This paper examines the behavior of the US airline industry's service demand. Monthly aggregate data for the industry are analyzed. While we ®nd strong evidence of nonlinear dependence in the air transport service time series, the evidence is not consistent with chaos. We also show that GARCH models successfully explain the nonlinear structures in the US airline industry's service series. Finally, within-sample forecasts of air transport demand from the GARCH models outperform those of simple autoregressive models.
2010
The behaviour of different financial or economic time series is captured mainly by nonlinear models. The present study investigates the underlying process of the stock price returns time series of the oil sector taking as an example the case of Hellenic Petroleum SA. The data used are daily for over a 13year period. Nonlinearities are detected with different univariate tests that survey the independence and nonlinear deterministic structure of the time series studied. The data employed for these tests are the closing prices of Hellenic Petroleum SA. All the tests confirm the existence of nonlinearities in the time series studied. Furthermore, we employ a Layapunov test to detect the chaotic behaviour of the stock prices. Finally, we estimate the noisy Mackey-Glass model, which is an equation with errors that follow an F-GARCH (p, q) process. This model is structured in order to enable us to interpret the volatility clustering as an endogenous phenomenon.
Petroleum Science
This paper has two aims. The first one is to investigate the existence of chaotic structures in the oil prices, expectations of investors and stock returns by combining the Lyapunov exponent and Kolmogorov entropy, and the second one is to analyze the dependence behavior of oil prices, expectations of investors and stock returns from January 02, 1990, to June 06, 2017. Lyapunov exponents and Kolmogorov entropy determined that the oil price and the stock return series exhibited chaotic behavior. TAR-TR-GARCH and TAR-TR-TGARCH copula methods were applied to study the co-movement among the selected variables. The results showed significant evidence of nonlinear tail dependence between the volatility of the oil prices, the expectations of investors and the stock returns. Further, upper and lower tail dependence and comovement between the analyzed series could not be rejected. Moreover, the TAR-TR-GARCH and TAR-TR-TGARCH copula methods revealed that the volatility of oil price had crucial effects on the stock returns and on the expectations of investors in the long run.
Qalaai Zanist Scientific Journal, 2019
The paper aims to compare the performance of several univariate symmetric and asymmetric GARCH volatility models in modeling and forecasting the volatility of daily Gasoline prices in Erbil city. This paper chooses the GARCH, GARCH-M, TGARCH, E-GARCH and Power GARCH model to analyze the daily return of Gasoline under three different error distributions: normal distribution, student-t distribution and generalized error distribution and then compare the results and choose the appropriate model to forecast the volatility. The sample is divided into two subsamples. The first subsample is called insample data set (Training sample) used to estimate the ARMA-GARCH models for underlying data and the second subsample is called out-sample data set (Testing sample) used to investigate the performance of volatility forecasting. As a result of analyses, we conclude that the best model fits the volatility of Gasoline returns series is AR(2)-Power GARCH(
The study aims to extend the GARCH type volatility models to their nonlinear TAR (Tong, 1990) and STAR-based (Terasvirta, 1994) counter parts where both the conditional mean and the conditional variance processes follow TAR and STAR nonlinearity. The paper further investigates the models under their fractional integration and asymmetric power variants. The STAR-based models are LSTAR-LST-GARCH, LSTAR-LST-FIGARCH, LSTAR-LST-FIPGARCH and LSTAR-LST-FIAPGARCH models, which may be easily applied to model and forecast various financial time series. In the empirical section, an application is provided to model the daily returns in WTI crude oil prices considering the regime shifts the crude oil prices were subject to during history. Models are evaluated in terms of their out-of-sample forecasting capabilities with equal forecast accuracy tests and also in terms of various error criteria. The results suggest that volatility clustering, asymmetry and nonlinearity characteristics are modeled more efficiently as compared to their single regime variants, such as the GARCH, FIGARCH and FIAPGARCH models. Further, the outof-sample results suggest that the LSTAR-LST-FIAPGARCH model provides the best forecasting accuracy in terms of RMSE and MSE error criteria.
Romanian Journal of Economic Forecasting, 2014
The study aims to extend the GARCH type volatility models to their nonlinear TAR (Tong, 1990) and STAR-based (Terasvirta, 1994) counter parts where both the conditional mean and the conditional variance processes follow TAR and STAR nonlinearity. The paper further investigates the models under their fractional integration and asymmetric power variants. The STAR-based models are LSTARLST- GARCH, LSTAR-LST-FIGARCH, LSTAR-LST-FIPGARCH and LSTAR-LSTFIAPGARCH models, which may be easily applied to model and forecast various financial time series. In the empirical section, an application is provided to model the daily returns in WTI crude oil prices considering the regime shifts the crude oil prices were subject to during history. Models are evaluated in terms of their out-of-sample forecasting capabilities with equal forecast accuracy tests and also in terms of various error criteria. The results suggest that volatility clustering, asymmetry and nonlinearity characteristics are modeled m...
Brazilian Review of Econometrics, 2001
In this paper we examine certain properties of the Dow Jones and the Nikkey indices, investigating the existence of stochastic and deterministic non linear structures. Using the detrended fluctuation analysis, we construct a local measurement of randomness which identifies some extreme events and their im pact on the randomness of the systems. Our results suggest no evidence of chaos in the data. In fact, GARCH processes explain most of the nonlinear dependence in the Dow Jones daily returns and the estimated Kolmogorov entropy for the Nikkey index diverges, conversely to what one would expect if the data fo llowed a chaotic dynamics. Resurno o artigo investiga algumas propriedades dos indices de a�oes Nikkey e Dow Jones, tais como a existencia de estruturas nao-lineares deterministicas e es tocasticas. Usando 0 metoda "detrended fluctuation analysis" , construimos uma medida local de aleatoriedade que identifica alguns eventos extremos e seus im pactos na aleatoriedade dos sistemas em estudo. Os resultados nao sugerem evidencia de caos nos cl ades. De fato, processes GARCH explicam a maior parte da dependencia nao-linear nes retornos diaries do Dow Jenes enquanto que a entropia de Kolmogorov estimada para ° indice Nikkey diverge, evidenciando assirn urn sistema estocastico para este indice.
Energy Economics, 2001
We test for the presence of low-dimensional chaotic structure in crude oil, heating oil, and unleaded gasoline futures prices from the early 1980s. Evidence on chaos will have important implications for regulators and short-term trading strategies. While we find strong evidence of non-linear dependencies, the evidence is not consistent with chaos. Our test results indicate that ARCH-type processes, with controls for seasonal variation in prices, generally explain the non-linearities in the data. We also demonstrate that employing seasonally adjusted price series contributes to obtaining robust results via the existing tests for chaotic structure. Maximum likelihood methodologies, that are robust to the non-linear dynamics, lend support for Samuelson's hypothesis on contract-maturity effects in futures price-changes. However, the tests for chaos are not found to be sensitive to the maturity effects in the futures contracts. The results are robust to controls for the oil shocks of 1986 and 1991. ᮊ A. Chatrath . 0140-9883r01r$ -see front matter ᮊ 2001 Elsevier Science B.V. All rights reserved. Ž . PII: S 0 1 4 0 -9 8 8 3 0 0 0 0 0 7 9 -7 ( )
The Financial Review, 1998
By using recently developed statistical tools designed to overcome some of the limitations often associated with financial data, this study attempts to detect low-dimensional deterministic chaos in five major European stock markets and the United States. Country indexes exhibiting low-dimensional deterministic chaos may contain some informational inefficiency; thus, it may be possible to use nonlinear dynamics to predict future stock returns. The results do not provide evidence of the existence of low-dimensional chaotic systems in any of the examined indexes. As such, the notion of market efficiency in the examined indexes is not threatened by the findings of this study.
Mathematics and computers …, 1999
Academic and applied researchers in economics have, in the last 10 years, become increasingly interested in the topic of chaotic dynamics. In this paper we undertake non-linear dynamical analysis of one representative time series taken from financial markets, namely the Standard and Poor's (S&P) Composite Price Index. The data is based upon (adjusted) daily data from 1928 to 1987 comprising 16 127 observations. The results in the paper, based on the Grassberger–Procaccia (GP) correlation dimension measurement in conjunction with non-linear noise filtering and the surrogate technique, show strong evidence of chaos in one of these series, the S&P 500. The analysis shows that the accuracy of results improves with the increase in the number of recording points and the length of the time series, 5000 data points being sufficient to identify deterministic dynamics.
Journal of Economic Surveys, 1988
The structure of the relationship between oil prices, gold price, silver price and copper price are not only important for economists but also for policymakers since it contributes to the policy debate on the link between variables and co-movement of the variables. In this paper, the relationship between oil prices and the price of gold and silver was analysed by BDS test, non-linear ARDL approach and two non-linear Granger causality methods for 1973:1-2012:11 period in Turkey. This study complements previous empirical papers. However, it differs from the existing literature with simultaneous use of nonlinear ARDL and two non-linear causality model: Hiemstra and Jones (1994) non-linear causality and augmented granger causality developed by this paper. The main findings of this paper are: (a) the gold price level showed positive asymmetric response to changes in the oil price in the short-and long-run. The gold price probably possesses some market power and it is a means of store of value. Because of the exception of gold, there is a substantial sluggishness in the adaption to changes in demand. In the long run the exception of gold lags and adjustment costs should play a smaller part; b) there is a unique long-term relationship between oil prices and the prices of gold, silver and cooper; and (c) there is a unidirectional Granger causality between oil price and precious metal price.
International Business & Economics Research Journal (IBER), 2010
Employing the daily bilateral exchange rate of the dollar against the Canadian dollar, the Swiss franc and the Japanese yen, we conduct a battery of tests for the presence of low-dimension chaos. The three stationary series are subjected to Correlation Dimension tests, BDS tests, and tests for entropy. While we find strong evidence of nonlinear dependence in the data, the evidence is not consistent with chaos. Our test results indicate that GARCH-type processes explain the nonlinearities in the data. We also show that employing seasonally adjusted index series enhances the robustness of results via the existing tests for chaotic structure.
This study tests for the presence of nonlinear dependence and deterministic chaos in the rate of returns series for six Indian stock market indices. The overall result of our analysis suggests that the returns series do not follow a random walk process. Rather it appears that the daily increments in stock returns are serially correlated and the estimated Hurst exponents are indicative of marginal persistence in equity returns. Result from test of independence on filtered residuals suggests that the existence of nonlinear dependence, at least to some extent, can be attributed to the presence of conditional heteroskedasticity. It appears, therefore, that low order GARCH–type models can adequately explain some, but not all, of the observed nonlinear dependence in the data. The existing nonlinearity in the data appears to be multiplicative in nature. Further, we find very little evidence to support the proposition that returns are generated by a chaotic system. Only in two out of six ca...
Theoretical and Applied Economics, 2015
In recent years, retail fuel prices have raised the question of whether they are anomalous in relation with the crude oil prices. This paper aims to study the price volatility and the response of retail fuel prices to changes in international crude oil prices on the Romanian fuel market and on four other markets, namely Germany, France, Poland and Czech Rep., during the period between 2008 and 2014. By estimating univariate and multivariate GARCH models, as well as applying an MTAR threshold cointegration approach, the study finds similar patterns across the aforementioned markets. Our results show that the conditional volatility reached its peak during the outbreak of the financial crisis, together with an abrupt fall in time-varying correlations, which offer support for the asymmetric transmission hypothesis. Finally, the cointegration analysis detects some signs of asymmetric adjustments, supporting the hypothesis of a faster adjustment above the threshold in most cases.
International Journal of Banking, Risk and Insurance, 2022
Macroeconomic stability is crucial not only for economic growth but also for the living standards and investments in a market economy. The macroeconomic variables like crude oil price, gold price, exchange rate, inflation and stock returns are highly correlated to each other and are highly volatile, and the volatility in one market spills over to other markets. This paper analyses the dynamic causality between crude oil price, exchange rate and BSE Sensex and their volatilities in India. The daily data on macro variables for 14 years between January 2006 to March 2019 is used in the GARCH estimation of causal effects of volatility spillovers. The GARCH estimates show that the volatility and volatility spillover of one market cause volatility and volatility spillovers in other markets in India. The crude oil price and exchange rate volatility and volatility spillovers cause volatility in BSE Sensex. The volatility in BSE Sensex is highly overdone by internal shocks of the stock market itself.
This research finds evidence of noisy chaotic properties in the returns of four Dow Jones indices, based on three tests of non-linearity and chaos. The study uses an average of 24,815 data points to correctly simulate chaos in financial time-series. The data consists of the Dow Jones Industrial Average (29,229 observations); Dow Jones Transportation Average (29,121 observations); Dow Jones Utility Average (21,150 observations) and the Dow Jones Composite Average (19,906 observations). The a) Brock, Dechert, and Scheinkman (BDS) test indicates that most of the Dow Jones indices are not iid series, except for the filtered residuals from the GARCH of the Dow Jones Utility Average. The b) rescaled range analysis shows that after scrambling the data, all Hurst exponents are above 0.5, and a trend-reinforcing property, which helps in the conclusion of having a chaotic process. Lastly, the c) correlation dimension analysis complements the initial findings and concludes the presence of a high dimensional noisy chaotic structure in the four Dow Jones indices.
Journal of Futures Markets, 1993
R (1985); Hall et al. (1988)l has found that the distribution of futures prices is not normal but leptokurtic. Specifically, the empirical distributions of daily price changes have more observations around the means and in the extreme tails than does a normal distribution. Leptokurtosis also appears in stock returns l and exchange rate changes l. Further, nonlinear dependence has been found in futures price changes ; l. Yet, empirical research on market anomalies has either ignored the non-normality and dependence or resorted to nonparametric tests which generally are less powerful than parametric tests.
Indian Journal of Research in Capital Markets, 8(3), pp.8-21, 2021
The macroeconomic variables crude oil price, gold price, exchange rate, inflation and stock returns are highly volatile and are highly correlated to each other. The volatility in one market spills over to other markets. This paper examines the dynamic causality between crude oil price, exchange rate and BSE Sensex and their volatilities in India. The daily data on macro variables for 14 years between January 2006 to March 2019 is used in the GARCH estimation of causal effects of volatility spillovers. The GARCH estimates show that the volatility and volatility spillover of one market cause volatility and volatility spillovers in other markets in India. The crude oil price and exchange rate volatility and volatility spillovers cause volatility in the BSE Sensex. The volatility in BSE Sensex is highly overdone by internal shocks of the stock market itself.

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