Presence Of Conditional Heteroscedasticity Research Articles

Dimension reduction in time series under the presence of conditional heteroscedasticity

Consider a time series, where the conditional mean is assumed to be an unknown function of linear combinations of past p observations and the conditional variance is assumed to be an unknown function of linear combinations of past q squared residuals. The linear combinations are assumed to contain all the necessary information about the time series that is available through the conditional mean and conditional variance, respectively. Nadaraya-Watson kernel smoother is used to estimate the unknown mean and variance function and an iterative approach is proposed to estimate the parameter matrices associated with the linear combinations. The estimators are shown to be consistent. To overcome computational challenges and provide numerical stability, a novel angular representation of parameter matrices is introduced. The numerical performance of the proposed method on forecasting the conditional mean is assessed by simulations studies. A real data of Brazilian Real (BRL)/U.S. Dollar Exchange Rate is analyzed. For the BRL/USD series, the estimated linear combinations yield a better time series model than an AR-ARCH model in terms of out-of-sample forecasts.

STATISTICAL INFERENCE FOR AUTOCOVARIANCE OF FUNCTIONAL TIME SERIES UNDER CONDITIONAL HETEROSCEDASTICITY

This paper investigates statistical inference methods for autocovariance estimation in functional time series under the presence of conditional heteroscedasticity. Functional time series data, which are characterized by observations evolving over continuous time or space, often exhibit complex dependencies and time-varying volatility patterns. In the presence of conditional heteroscedasticity, traditional autocovariance estimators may be biased or inefficient, necessitating the development of robust inference techniques. We propose a novel approach based on robust covariance estimation and bootstrap resampling to account for heteroscedasticity and provide reliable estimates of autocovariance. The efficacy of the proposed methodology is demonstrated through simulations and applications to real-world functional time series data, highlighting its ability to capture dynamic dependencies and volatility patterns under varying conditions.

MODELLING EXCHANGE RATE VOLATILITY OF SOMALI SHILLING AGAINST US DOLLAR BY UTILIZING GARCH MODELS

The main aim of this investigation was to model the volatility of Somali shilling against US dollar by using monthly data covering from 1950 to 2010. Further to that, this finding has adopted both symmetric and asymmetric generalized autoregressive conditional heteroscedastic (GARCH) family models in order to capture volatility clustering and leverage effect as the most stylized facts of exchange rate returns. Result from ARCH indicates presence of conditional heteroscedasticity in the residual series of exchange rate. Symmetric GARCH(1,1) model shows presence of volatility clustering and persistent coefficients of greater than one indicating that volatility is an explosive process. Results from asymmetric TCHARCH(1,1) and EGARCH(1,1) indicates presence of leverage effect in the series of exchange rate where positive news have large effect on volatility than bad news of same magnitude. This study has an important implication to investors, business and risk managers. Nevertheless, this study suggests monetary authority to print new currency and de-dollarize the economy in order to be able influence exchange rate volatility. The outcome from this finding also suggests that GARCH family models sufficiently capture the volatility of Somali shilling against US dollar. Keywords: exchange rate, Somali shilling, US dollar, conditional heteroscedasticity, volatility clustering and leverage effect JEL Classifications: F31, O24 DOI: https://doi.org/10.32479/ijefi.9788

Nonparametric Regression Estimation for Multivariate Null Recurrent Processes

This paper discusses nonparametric kernel regression with the regressor being a \(d\)-dimensional \(\beta\)-null recurrent process in presence of conditional heteroscedasticity. We show that the mean function estimator is consistent with convergence rate \(\sqrt{n(T)h^{d}}\), where \(n(T)\) is the number of regenerations for a \(\beta\)-null recurrent process and the limiting distribution (with proper normalization) is normal. Furthermore, we show that the two-step estimator for the volatility function is consistent. The finite sample performance of the estimate is quite reasonable when the leave-one-out cross validation method is used for bandwidth selection. We apply the proposed method to study the relationship of Federal funds rate with 3-month and 5-year T-bill rates and discover the existence of nonlinearity of the relationship. Furthermore, the in-sample and out-of-sample performance of the nonparametric model is far better than the linear model.

Testing for weak-form efficiency of crude palm oil spot and future markets: new evidence from a GARCH unit root test with multiple structural breaks

There is a sizeable literature that tests for weak-form efficiency in commodity and energy spot and future prices. While many studies now allow for multiple structural breaks to address the criticism that conventional unit root tests have low power to reject the unit root null in the presence of structural change, the extant literature overlooks the fact that conventional unit root tests are biased in the presence of conditional heteroscedasticity. We apply a recently developed generalized autoregressive conditional heteroscedasticity (GARCH) unit root test with multiple structural breaks to crude palm oil spot and future prices and find much more evidence against weak-form efficiency than that found using tests that fail to allow for conditional heteroscedasticity. Our results point to the importance of allowing for heteroscedasticity when testing for efficiency in commodity and energy spot and future prices.

Automatic Specification Testing for Vector Autoregressions and Multivariate Nonlinear Time Series Models

This article introduces an automatic test for the correct specification of a vector autoregression (VAR) model. The proposed test statistic is a Portmanteau statistic with an automatic selection of the order of the residual serial correlation tested. The test presents several attractive characteristics: simplicity, robustness, and high power in finite samples. The test is simple to implement since the researcher does not need to specify the order of the autocorrelation tested and the proposed critical values are simple to approximate, without resorting to bootstrap procedures. In addition, the test is robust to the presence of conditional heteroscedasticity of unknown form and accounts for estimation uncertainty without requiring the computation of large-dimensional inverses of near-to-singularity covariance matrices. The basic methodology is extended to general nonlinear multivariate time series models. Simulations show that the proposed test presents higher power than the existing ones for models commonly employed in empirical macroeconomics and empirical finance. Finally, the test is applied to the classical bivariate VAR model for GNP (gross national product) and unemployment of Blanchard and Quah (1989) and Evans (1989). Online supplementary material includes proofs and additional details.

Measuring the Impact of Financial Crisis on International Markets: An Application of the Financial Stress Index

The scope of paper is to examine whether the recent financial crisis has had any impact on international capital markets and more precisely on the 4 primary international stock markets of England, France, Japan, the United States and Greece. The research is based on the use of the Financial Stress Index (FSI) from July 2005 until December 2008 and August 2009. Research results showed that the recent financial crisis has had a negative impact on all examined markets, with the Tokyo stock exchange being the one mostly affected. It was, also, found increased variability of performances following the start of the financial crisis, a fact that is indicative of the presence of conditional heteroscedasticity. As far as the Greek market is concerned, the recent financial crisis has not affected in general the credit expansion towards enterprises and households; however, it has affected the credit expansion to enterprises and households on a case-to-case basis.

Long Memory in Stock Trading Volume: Evidence from Indian Stock Market

In this paper, we have examined the long memory property of Indian stock market by analyzing the trading volume series. Given the absence of trading volume index data, we have constructed trading volume series for the Indian stock market. We used maximum likelihood method to analyze the constructed trading volume index. The estimation of ARFIMA model, obtained a significant parameter for the order of fractional integration, and this could be consistent with the long autocorrelations observed in the trading volume series. The finding that stock-trading volume is a long memory process is robust, given different estimating methods, different sub samples, temporal aggregation and tests on individual stocks. Because of the conditional heteroscedasticity in the series, we have also carried out ARFIMA-GARCH procedures to check whether long persistence was robust in the presence of conditional heteroscedasticity.

Testing for Nonlinear Autoregression

This article considers consistent testing the null hypothesis that the conditional mean of an economic time series is linear in past values. Two specific tests are discussed, the Cramér–von Mises and the Kolmogorov–Smirnov tests. The particular feature of the proposed tests is that the bootstrap is used to estimate the nonstandard asymptotic distributions of the test statistics considered. The tests are justified theoretically by asymptotics, and their finite-sample behaviors are studied by means of Monte Carlo experiments. The tests are applied to five U.S. monthly series, and evidence of nonlinearity is found for the first difference of the logarithm of the personal income and for the first difference of the unemployment rate. No evidence of nonlinearity is found for the first difference of the logarithm of the U.S. dollar/Japanese Yen exchange rate, for the first difference of the 3-month T-bill interest rate and for the first difference of the logarithm of the M2 money stock. Contrary to typically used tests, the proposed testing procedures are robust to the presence of conditional heteroscedasticity. This may explain the results for the exchange rate and the interest rate.

Reconsidering the gains in efficiency from ML estimation versus OLS in ARCH models

This paper provides an improved approximation to the asymptotic relative efficiency of the MLE against OLS when estimating the mean equation in the presence of conditional heteroscedasticity. Results are given which show that the existing approximation may considerably understate the efficiency gains of ML when the conditional heteroscedasticity is substantial.

Modelling the volatility in East European emerging stock markets: evidence on Hungary and Poland

In this paper, stock market volatility in the East European emerging markets of Hungary and Poland is investigated using daily indexes. The results suggest the presence of non-linearity in the indexes through the BDSL statistic, while the presence of conditional heteroscedasticity is detected through LM tests. Conditional volatility is then modelled as a GARCH process; however, as measured by a GARCH-M model, this does not seems to be priced in the Hungarian and Polish stock markets. Moreover, the evidence rejects the Martingale hypothesis that future changes of stock prices in the two markets are orthogonal to past information. The well-known day-of-the-week effect, reflected in significantly positive Friday and negative Monday returns, does not seem to be present in these markets. While a marked decline in conditional volatility in the Polish market after June 1995 may be explained by appreciating Zloty exchange rates against the German Mark and increasing integration with developed markets, a similar (...

On the validity of the weak–form efficient markets hypothesis applied to the London stock exchange: comment

The empirical work and interpretation of the results of Al–Loughani and Chappell (1997) is commented upon. On the basis of the reported results, and contrary to the authors' conclusion, it is argued that although the random walk hypothesis is rejected, the weak–form market efficiency hypothesis (WFME), for the London stock exchange cannot be rejected. Some further comments on WFME in the presence of conditional heteroscedasticity are made.