Autoregressive Conditional Heteroscedasticity Effects Research Articles

Metallic natural resources commodity prices volatility in the pandemic: Evidence for silver, platinum, and palladium

The current study investigates volatility in natural resource commodity prices in the case of the US. Particularly, this study focused on the rarely explained indicators of natural resources, including palladium, platinum, and silver price volatility, from February 28, 2012, to March 18, 2020. Since the Covid-19 pandemic creates havoc in the global economic system, that creates uncertainty in the natural resources market. Therefore, the period of the Covid-19 pandemic is also considered in the empirical investigation. This study uses the traditional autoregressive conditional heteroscedasticity (ARCH) approach, which reveals that the ARCH effect is valid in the mentioned variables in both the pre and post Covid-19 pandemic periods. Besides, this study also employed the threshold generalized autoregressive conditional heteroscedasticity (TGARCH) and exponential generalized autoregressive conditional heteroscedasticity (EGARCH) models to analyze shock asymmetry. The estimated outcomes asserted that platinum and silver prices are more sensitive to negative shocks such as the Covid-19 pandemic. However, positive shocks play a more influential role in palladium price volatility. Thus, the shock asymmetry is valid for all three metallic resources. Based on the empirical findings, this study suggests implementing price ceiling policies. Besides, metallic resources hedging and the imposition of strong regulations in the financial market could help reduce volatility in natural resources.

Empirical determinants of exchange-rate volatility: evidence from selected Asian economies

PurposeThis paper aims to explore the empirical determinants of exchange-rate volatility (ERV) in selected Asian economies, namely, Bangladesh, China, India, Indonesia, Malaysia and Pakistan. Specifically, it examines how the volatility of foreign reserves, government spending, industrial production, gold prices and terms of trade affect monthly ERV during the examined period.Design/methodology/approachThe authors carry out the empirical analysis by using monthly data for the period January 1997–March 2019. First, the volatility of the underlying variables is measured based on the conditional variances obtained by estimating the univariate (generalized) autoregressive conditional heteroskedasticity [(G)ARCH] model for each variable during the study period. Next, the autoregressive conditional heteroscedasticity (ARCH)-Lagrange multiplier test is applied to ensure that there are no remaining ARCH effects in the residuals. Finally, the multivariate autoregressive-moving average-GARCH (1, 1) models are estimated to examine whether and how the volatility of the underlying variables affects ERV.FindingsThe results reveal that the current period volatility of exchange rates is significantly affected by ERV in the previous period in all selected countries. The results also indicate that the volatilities of the underlying macroeconomic variables are quite differently related to ERV in examined Asian countries. Foreign-reserve volatility (VFXRES) has negative and significant impacts on ERV in Bangladesh, China and Malaysia. Government-spending volatility is negatively related to ERV in India, whereas it is positively related to ERV in all other examined countries. The results also suggest that although terms-of-trade volatility reduces ERV in both Bangladesh and Pakistan, it amplifies ERV in the remaining examined countries. However, gold-price volatility (VGOLDP) significantly, positively contributes to ERV in Bangladesh, Indonesia and Malaysia. On the contrary, the higher volatility in industrial production (VIPI) results in lower ERV in Indonesia and Pakistan, whereas it increases ERV in China, India and Malaysia.Practical implicationsThe findings have several important policy implications. First, the findings suggest that both Bangladesh and Malaysia should keep an adequate level of foreign reserves to stabilize their foreign exchange rates. Second, as government-spending volatility has a vital role in determining ERV, it is necessary to bring sustainability and continuity in government expenditures. Bangladesh and Pakistan can stabilize their foreign exchange rates by making exports more competitive, viable and accessible.Originality/valueThis paper significantly contributes to the existing literature by exploring how the behavior of unexpected variations in the factors determining exchange rates affects ERV in selected Asia countries. Most of the published studies have examined the determinants of exchange rates by considering the macroeconomic variables at their levels. Departing from the existing studies, this paper significantly relates the volatility (second moment) of exchange rate determinants to the behavior of ERV. Further, this paper provides firsthand empirical evidence on this issue for the selected Asian economies.

A risk model to compute the volatility and the need for collateral margins in energy futures contracts in Brazil

PurposeBrazil is characterized by the inexistence of a more robust system of guarantees and rules to minimize risks and protect agents in energy futures contracts. In this sense, this study aims to answer the question of how a centralized clearing agent can compute safety margin requirements to help reduce the systemic risk of the energy futures contracts market in Brazil.Design/methodology/approachThe intermediate steps and specific objectives are to analyze the volatility behavior, identify the autoregressive conditional heteroscedasticity effects and model the variance of the return series. Based on this, the authors calculate the value-at-risk and conditional value-at-risk metrics for the energy futures contracts. As a robustness test, the authors added a peak over threshold methodology from extreme values theory.FindingsIn general, monthly products require margins because of their higher variance. With the asymmetrical distribution of returns, the authors needed to consider different maintenance margins for the long and short positions. It was also shown that two guarantee margins were required to secure the contracts as follows: the initial margin and the maintenance margin. The three factors that defined the size of the maintenance margin the volatility, skewness and kurtosis of the return series.Originality/valueThe contribution of this study lies in promoting the understanding of the risk dimensions of the energy derivatives market in Brazil and it offers concrete recommendations for how to mitigate this risk through market mechanisms and structures. Similar arrangements can be applied to other emerging markets.

Forecasting Wind Speed in Peninsular Malaysia: An Application of ARIMA and ARIMA-GARCH Models

In the global energy context, renewable energy sources such as wind is considered as a credible candidate for meeting new energy demands and partly substituting fossil fuels. Modelling and forecasting wind speed are noteworthy to predict the potential location for wind power generation. An accurate forecasting of wind speed will improve the value of renewable energy by enhancing the reliability of this natural resource. In this paper, the wind speed data from year 1990 to 2014 in 18 meteorological stations throughout Peninsular Malaysia were modelled using the Autoregressive Integrated Moving Average (ARIMA) to forecast future wind speed series. The Ljung-Box test was used to determine the presence of serial autocorrelation, while the Engle’s Lagrange Multiplier (LM) test was used to investigate the presence of Autoregressive Conditional Heteroscedasticity (ARCH) effect in the residual of the ARIMA model. In this study, three stations showed good fit using the ARIMA modelling since no serial correlation and ARCH effect were present in the residuals of the ARIMA model, while the ARIMA-GARCH had proven to precisely capture the nonlinear characteristic of the wind speed daily series for the remaining stations. The forecasting accuracy measure used was based on the value of root mean square error (RMSE) and mean absolute percentage error (MAPE). Both ARIMA and ARIMA-GARCH model proposed provided good forecast accuracy measure of wind speed series in Peninsular Malaysia. These results will help in providing a quantitative measure of wind energy available in the potential location for renewable energy conversion.

RETRACTED: The impact of the presence of autoregressive conditional heteroscedasticity (ARCH) effects on spurious regressions

Spurious (nonsensical) regressions with independent random walks or even with stationary series are well known. However, how their spuriosity is affected by nonlinearity in series has been scantly addressed. In this study, we examine, using Monte Carlo analysis, the effect of autoregressive conditional Heteroskedasticity (ARCH) on nonsensical regressions and we find that ARCH can neutralize most of spuriosity. Specifically, our analysis of finite sample behavior of the t-ratio in a spurious regression framework where ARCH effects are included in a Data Generating Process (DGP) model and Monte Carlo experiments show that large ARCH effects somehow weaken the degree of spuriosity. This will have implications for unit root and cointegration analysis. Our simulations suggest that many of the regressions in the literature, based on individual predictor variables, may be spurious.

Volatility clustering, risk-return relationship and asymmetric adjustment in the Finnish housing market

PurposeThe purpose of this paper is to examine whether the house prices in Finland share financial characteristics with assets such as stocks. The studied regions are 15 main regions in Finland over the period of 1988:Q1-2018:Q4. These regions are divided geographically into 45 cities and sub-areas according to their postcode numbers. The studied type of dwellings is apartments (block of flats) divided into one-room, two rooms and more than three rooms apartment types.Design/methodology/approachBoth Ljung–Box and Lagrange multiplier tests are used to test for clustering effects (autoregressive conditional heteroscedasticity effects). For cities and sub-areas with significant clustering effects, the generalized autoregressive conditional heteroscedasticity (GARCH)-in-mean model is used to determine the potential impact that the conditional variance may have on returns. Moreover, the exponential GARCH model is used to examine the possibility of asymmetric effects of shocks on house price volatility. For each apartment type, individual models are estimated; enabling different house price dynamics, and variation of signs and magnitude of different effects across cities and sub-areas.FindingsResults reveal that clustering effects exist in over half of the cities and sub-areas in all studied types of apartments. Moreover, mixed results on the sign of the significant risk-return relationship are observed across cities and sub-areas in all three apartment types. Furthermore, the evidence of the asymmetric impact of shocks on housing volatility is noted in almost all the cities and sub-areas housing markets. These studied volatility properties are further found to differ across cities and sub-areas, and by apartment types.Research limitations/implicationsThe existence of these volatility patterns has essential implications, such as investment decision-making and portfolio management. The study outcomes will be used in a forecasting procedure of the volatility dynamics of the studied types of dwellings. The quality of the data limits the analysis and the results of the study.Originality/valueTo the best of the author’s knowledge, this is the first study that evaluates the volatility of the Finnish housing market in general, and by using data on both municipal and geographical level, particularly.

APPLICATION OF SHORT-TERM FORECASTING MODELS FOR ENERGY ENTITY STOCK PRICE (STUDY ON INDIKA ENERGI TBK, JII)

Share price as one kind of financial data is the time series data that indicates the level of fluctuations and heterogeneous variances called heteroscedasticity. The method that can be used to overcome the effect of autoregressive conditional heteroscedasticity effect is the generalised form of ARCH (GARCH) model. This study aims to design the best model that can estimate the parameters, predict share price based on the best model and show its volatility. In addition, this paper discusses the prediction-based investment decision model. The findings indicate that the best model corresponding to the data is AR(4)-GARCH(1,1). The model is implemented to forecast the stock prices of Indika Energy Tbk, Indonesia, for 40 days and significantly presented good findings with an error percentage below the mean absolute.

RETRACTED: The impact of the presence of autoregressive conditional heteroscedasticity (ARCH) effects on spurious regressions

Abstract Spurious (nonsensical) regressions with independent random walks or even with stationary series are well known. However, how their spuriosity is affected by nonlinearity in series has been scantly addressed. In this study, I examine, using Monte Carlo analysis, the effect of autoregressive conditional Heteroskedasticity (ARCH) on nonsensical regressions and I find that ARCH can neutralize most of spuriosity. Specifically, my analysis of finite sample behavior of the t-ratio in a spurious regression framework where ARCH effects are included in a Data Generating Process (DGP) model and Monte Carlo experiments show that large ARCH effects somehow weaken the degree of spuriosity. This will have implications for unit root and cointegration analysis. My simulations suggest that many of the regressions in the literature, based on individual predictor variables, may be spurious.

Asymmetric impact of shocks on Islamic stock indices: a cross country analysis

PurposeSeveral studies focus on asymmetric impact of shocks on conventional stocks. However, only few studies explore Islamic stocks, but none has examined the asymmetric impact of shocks on Islamic stocks. This study aims to fill the gap by investigating the asymmetric impact of shocks on Islamic stocks. Specifically, it identifies the effect of good and bad news on Islamic stock market. The study also aims to examine the returns and volatility spillover effects across different Islamic markets.Design/methodology/approachTo carry out the empirical analysis, the authors have applied the exponential generalized autoregressive conditional heteroscedasticity (ARCH) model on daily Islamic stock indices of 18 countries. The study covers the period from July 2009 to July 2016. The authors have started their empirical analysis by examining the time series properties and testing the presence of ARCH effects. Further, the authors have applied several post-estimation tests to ensure the robustness of the results.FindingsThe results indicate that there is significant leverage effect in Islamic stocks traded in the sampled countries. That is, negative shocks or bad news have stronger effects on Islamic stock returns’ volatility as compared to positive shocks or good news. The authors also found that there are significant mean spillover effects for the examined countries. This finding implies that increased Islamic stock returns in country have significant and positive effects in Islamic stocks’ returns in another other. Similarly, the results regarding the volatility spillover effects suggest that there are significant volatility spillover effects across all examined countries. However, the authors found both positive and negative volatility spillover effects. It should also be noted that in some cases, the authors did not find any significant volatility spillover effect.Practical implicationsThe findings of this study have several important policy implications for both investors and policymakers. As the findings suggest that Islamic stock indices are integrated across countries both in terms of returns (mean) and risk (volatility), they are useful for investors to design well-diversified portfolios. The significant volatility spillovers suggest policymakers to design such policy that may help in reducing the adverse effects of increased volatility of Islamic stock of other/foreign countries on the Islamic stocks of the home countries. The significant evidence of the presence of leverage (asymmetric) effects suggest investors to use effective and active hedging instruments to hedge risk, particularly, in bad times.Originality/valueUnlike other studies on Islamic stocks, this study takes into account the asymmetric effects of positive and negative shocks. Further, the study examines the mean and variance spillover effects for a large panel of countries having Islamic stocks. Finally, several pre- and post-estimation tests are applied to ensure the robustness of the results.

PEMODELAN RETURN HARGA SAHAM MENGGUNAKAN MODEL INTERVENSI–ARCH/GARCH (Studi Kasus : Return Harga Saham PT Bayan Resources Tbk)

The intervention method is a time series model which could be used to model data with extreme fluctuation whether up or down. Stock price return tend to have extreme fluctuation which is caused by internal or external factors. There are two kinds of intervention function; a step function and a pulse function. A step function is used for a long-term intervention, while a pulse function is used for a short-term intervention. Modelling a time series data needs to satisfy the homoscedasticity assumptions (variance of residual is homogeneous). In reality, stock price return has a high volatility, in other words it has a non-constant variance of residuals (heteroscedasticity). ARCH (Autoregressive Conditional Heteroscedasticity) or GARCH (Generalized Autoregressive Conditional Heteroscedasticity) can be used to model data with heteroscedasticity. The data used is stock price return from August 2008 until September 2018. From the stock price return data plot is found an extreme fluctuation in September 2017 (T=110) that is suspected as a pulse function. The best model uses the intervention pulse function is ARMA([1,4],0) (b=0, s=1, r=1). The intervention model has a non-constant variance or there is an ARCH effect. The best variance model obtained is ARMA([1,4],0)(b=0, s=1, r=1)–GARCH(1,1) with the AIC value is -205,75088. Keywords: Stock Return, Intervention, Heteroscedasticity, ARCH/GARCH

Monitoring simple linear profiles in the presence of generalized autoregressive conditional heteroscedasticity

AbstractIn this paper, monitoring of simple linear profiles is investigated in the presence of nonequality of variances or heteroscedasticity, ie, generalized autoregressive conditional heteroscedasticity. In this condition, using of the common methods regardless of the heteroscedasticity leads to the fault interpretations. We consider a simple linear profile and assume that there is a generalized autoregressive conditional heteroscedasticity (GARCH) (1,1) model within the profiles. Here, we particularly focus on Phase II monitoring of simple linear regression. We studied the generalized autoregressive conditional heteroscedasticity effect, briefly GARCH effect, on the average run length criterion. As the remedial measures, the weighted least squares method to estimate the regression parameters and the heteroscedasticity‐consistent approaches to estimate the covariance matrix of regression parameters, are used to extract the GARCH effect. Two control chart methods namely T2 and exponentially weighted moving average 3 are discussed to monitor the simple linear profiles. Their performances are evaluated by using the average run length criterion. Finally, a real case from an industry field is studied.

Applying time series models to estimate time lags between sap flux and micro-meteorological factors

ABSTRACTSap flux (Ft) measurements are extensively used to scale-up canopy transpiration and conductance, but time lag between sap flux and canopy transpiration is a problem. As canopy transpiration is nearly synchronous with micrometeorological drivers, better understanding of the lag relationships between Ft and micrometeorological drivers and soil water conditions would benefit the up-scaling of canopy transpiration from sap flux. Time series modeling at different spatial and temporal scales can identify and incorporate time lag effects, as well as multiple variables affecting transpiration and the interactions between them. SARIMAX and GARCH hybrid models were used to capture seasonality and autoregressive conditional heteroscedasticity effects. Two univariate hybrid models were designed to measure vapor pressure deficit () and photosynthetic active radiation (), and one multivariate hybrid model was used in each season. Sap flow lagged behind canopy transpiration by 0–10 min in the dry season and 10–20 min in the wet season. had a stronger influence on transpiration than . Only the interaction between and in the wet season was observed. This study extends the application of time series modeling to the prediction of sap flow dynamics.

Robustness of Some Portmanteau Correlation Tests in Financial Time Series

SYNOPTIC ABSTRACTThe Box–Pierce and Ljung–Box tests are portmanteau tests generally used to test the independence in time series data. These tests can also be applied to the squares of the observations to detect independence. Because most financial time series data show heavy-tailed behavior, these tests may incorrectly reject the null hypothesis of no correlation when there is volatility clustering in the data. A modified version of the Box–Pierce test is introduced to capture this heavy-tailed behavior and showed that the modified test performs better when there is an autoregressive conditional heteroscedasticity (ARCH) effect. In this article, we introduce a correction factor for the Ljung–Box test. In addition, we conduct a series of simulations to study the robustness of the Box–Pierce and Ljung–Box tests and their modified versions in situations where the data exhibit ARCH, generalized ARCH (GARCH), and stochastic volatility (SV) effects. Our simulation studies indicate that the modified versions of the Box–Pierce and Ljung–Box tests are more robust when the data exhibit ARCH, GARCH, and SV effects.

Examining the relationship between stock return volatility and trading volume: new evidence from an emerging economy

Using daily stock return data for individual stocks from an emerging economy, this article examines the relationship between return volatility and trading volume under the theoretical postulate of the mixture of distributions hypothesis. The results suggest that the contemporaneous trading volume as a proxy for latent information arrival to the market did not contribute to the removal of significant ARCH or Generalized Autoregressive Conditional Heteroscedasticity effects that are found in stocks at the first stage of the investigation. The same holds for the lagged volume except for one case. This, perhaps, suggests that the trading volume (contemporaneous or lagged) is not adequately conveying information to induce traders’ views of the desirability of trade and, therefore, points to the need for searching for other micro and macro variables to be used as potential proxy for information arrival to the stock market of the emerging economy.

Testing Second-Order Dynamics for Autoregressive Processes in Presence of Time-Varying Variance

This article considers the volatility modeling for autoregressive univariate time series. A benchmark approach is the stationary autoregressive conditional heteroscedasticity (ARCH) model of Engle. Motivated by real data evidence, processes with nonconstant unconditional variance and ARCH effects have been recently introduced. We take into account this type of nonstationarity in variance and propose simple testing procedures for ARCH effects. Adaptive McLeod and Li’s portmanteau and ARCH-LM tests for checking the presence of such second-order dynamics are provided. The standard versions of these tests, commonly used by practitioners, suppose constant unconditional variance. The failure of these standard tests with time-varying unconditional variance is highlighted. The theoretical results are illustrated by means of simulated and real data. Supplementary materials for this article are available online.

Conditional Heteroscedasticity in Streamflow Process: Paradox or Reality?

The various physical mechanisms governing the dynamics of streamflow processes act on a seemingly wide range of temporal and spatial scales; almost all the mechanisms involved present some degree of nonlinearity. Against the backdrop of these issues, in this paper, attempt was made to critically look at the subject of Autoregressive Conditional Heteroscedasticity (ARCH) or volatility of streamflow processes, a form of nonlinear phenomena. Towards this end, streamflow data (both daily and monthly) of the River Benue, Nigeria were used for the study. Results obtained from the analyses indicate that the existence of conditional heteroscedasticity in streamflow processes is no paradox. Too, ARCH effect is caused by seasonal variation in the variance for monthly flows and could partly explain same in the daily streamflow. It was also evident that the traditional seasonal Autoregressive Moving Average (ARMA) models are inadequate in describing ARCH effect in daily streamflow process though, robust for monthly streamflow; and can be removed if proper deseasonalisation pre-processing was done. Considering the findings, the potential for a hybrid Autoregressive Moving Average (ARMA) and Generalised Autoregressive Conditional Heteroscedasticity (GARCH)type models should be further explored and probably embraced for modelling daily streamflow regime in view of the relevance of statistical modelling in hydrology.

Conventional and advanced time series estimation: application to the Australian and New Zealand Intensive Care Society (ANZICS) adult patient database, 1993–2006

Time series analysis has seen limited application in the biomedical Literature. The utility of conventional and advanced time series estimators was explored for intensive care unit (ICU) outcome series. Monthly mean time series, 1993-2006, for hospital mortality, severity-of-illness score (APACHE III), ventilation fraction and patient type (medical and surgical), were generated from the Australia and New Zealand Intensive Care Society adult patient database. Analyses encompassed geographical seasonal mortality patterns, series structural time changes, mortality series volatility using autoregressive moving average and Generalized Autoregressive Conditional Heteroscedasticity models in which predicted variances are updated adaptively, and bivariate and multivariate (vector error correction models) cointegrating relationships between series. The mortality series exhibited marked seasonality, declining mortality trend and substantial autocorrelation beyond 24 lags. Mortality increased in winter months (July-August); the medical series featured annual cycling, whereas the surgical demonstrated long and short (3-4 months) cycling. Series structural breaks were apparent in January 1995 and December 2002. The covariance stationary first-differenced mortality series was consistent with a seasonal autoregressive moving average process; the observed conditional-variance volatility (1993-1995) and residual Autoregressive Conditional Heteroscedasticity effects entailed a Generalized Autoregressive Conditional Heteroscedasticity model, preferred by information criterion and mean model forecast performance. Bivariate cointegration, indicating long-term equilibrium relationships, was established between mortality and severity-of-illness scores at the database level and for categories of ICUs. Multivariate cointegration was demonstrated for {log APACHE III score, log ICU length of stay, ICU mortality and ventilation fraction}. A system approach to understanding series time-dependence may be established using conventional and advanced econometric time series estimators.

Time-varying predictability in crude-oil markets: the case of GCC countries

This paper uses a time-varying parameter model with generalized autoregressive conditional heteroscedasticity effects to examine the dynamic behavior of crude-oil prices for the period February 7, 1997–January 8, 2010. Using data from four countries of the Gulf Cooperation Council, we find evidence of short-term predictability in oil-price changes over time, except for several short sub-periods. However, the hypothesis of convergence towards weak-form informational efficiency is rejected for all markets. In addition, we explore the possibility of structural breaks in the time-paths of the estimated predictability indices and detect only one breakpoint, for the oil markets in Qatar and the United Arab Emirates. Our empirical results therefore call for new empirical research to further gauge the predictability characteristics and the determinants of oil-price changes.

Price volatility of south-east fishery's quota species: an empirical analysis

This study investigates the autoregressive conditional heteroscedasticity (ARCH) and generalized-ARCH (GARCH) effects in the price series of Australian South-East Fishery's quota species. It is found that in all cases significant ARCH and/or GARCH effects are present. To search for the origins of these effects a weakly exogenous variable (trading volume) is introduced to the conditional variance equation of the ARCH and GARCH models, provided that such effects are observed in the first stage of investigation. It is found that in 14 cases the estimated coefficients of the trading volume are negative. In all cases, the 'trading volume' variable does not contribute to the removal of the ARCH and/or GARCH effects. Finally, the policy implications of the findings are discussed.

On robust testing for conditional heteroscedasticity in time series models

We consider robust and powerful tests for autoregressive conditional heteroscedasticity (ARCH) in the residuals from a nonlinear dynamic regression model. We advocate a new robustified autocorrelation function of the squared residuals, which relies essentially on the squared of winsorized robust residuals. This new tool allows us to introduce two new portmanteau-type test statistics which are robust to outliers. Each robust test statistic can be interpreted using a spectral approach. The first portmanteau test is based on a comparison between the estimated spectral density of the squared winsorized residuals and the spectral density under the null hypothesis of no ARCH effect via a quadratic norm. This test statistic consists in a weighted sum of squared robust autocorrelations of the squared residuals and it provides a robust version of the test statistic proposed by Hong and Shehadeh (J. Business Econom. Statist. 17 (1999) 91). Furthermore, it gives a generalized version of the robust Lagrange multiplier test of van Dijk et al. (J. Appl. Econom. 14 (1999) 539). However, since testing for ARCH represents a one-sided problem, we propose a robust testing procedure which takes into account the one-sided nature of the alternative hypothesis. The resulting test statistic is a weighted sum of robust autocorrelations of the squared residuals and it gives a robust version of Hong's (J. Time Ser. Anal. 18 (1997) 253) one-sided test for ARCH effects. One-sided tests for ARCH at individual lags are considered, as complementary tools. Both proposed portmanteau tests have a convenient asymptotic normal distribution under the null hypothesis of no ARCH effect, when the unknown parameters are estimated by a robust and consistent method. The new robust tests rely on the choice of a kernel. Typically, more weight can be given to lower orders of lags and less weight to higher orders of lags, giving more powerful procedures for many time series. Asymptotic arguments suggest that the first test statistic should be more powerful than the second asymptotically, but to exploit the one-sided nature of the alternative hypothesis can be particularly powerful with small samples. That issue is addressed in our Monte Carlo experiments. Using the highly robust S-estimators of regression to estimate robustly the regression parameters, the proposed robust test statistics are studied and compared empirically to many nonrobust and robust tests for ARCH effects, under various scenarios for the occurrence of outliers.