Autoregressive Conditional Heteroskedasticity

One of the implications of the intertemporal capital asset pricing model (CAPM) is that the risk premium of the market portfolio is a linear function of its variance. Yet, estimation theory of classical GARCH-in-mean models with linear-in-variance risk premium requires strong assumptions and is incomplete. We show that exponential-type GARCH models such as EGARCH or Log-GARCH are more natural in dealing with linear-invariance risk premia. For the popular and more di¢ cult case of EGARCH-in-mean, we derive conditions for the existence of a unique stationary and ergodic solution and invertibility following a stochastic recurrence equation approach. We then show consistency and asymptotic normality of the quasi maximum likelihood estimator under weak moment assumptions. An empirical application estimates the dynamic risk premia of a variety of stock indices using both EGARCH-M and Log-GARCH-M models.

COMMON PERSISTENCE IN CONDITIONAL VARIANCES' BY TIM BOLLERSLEV AND ROBERT F. ENGLE Since the introduction of the autoregressive conditional heteroskedastic (ARCH) model in Engle (1982), numerous applications of this modeling strategy have already appeared. A common finding in many of these studies with high frequency financial or monetary data concerns the presence of an approximate unit root in the autoregressive polynomial in the univariate time series representation for the conditional second order moments of the process, as in the so-called integrated generalized ARCH (IGARCH) class of models proposed in Engle and Bollerslev (1986). In the IGARCH models shocks to the conditional variance are persistent, in the sense that they remain important for forecasts of all horizons. This idea is readily extended to a multivariate framework. Even though many time series may exhibit persistence in variance, it is likely that several different variables share the same common long-run component. In that situation, the variables are naturally defined to be co-persistent in variance, and the co-persistent linear combination is interpretable as a long-run relationship. Conditions for co-persistence to occur in the multivariate linear GARCH model are presented. These conditions parallel the conditions for linear co-integration in the mean, as developed by Engle and Granger (1987). The presence of co-persistence has important implications for asset pricing relationships and in optimal portfolio allocation decisions. An empirical example relating to the time series properties of nominal U.S. dollar exchange rates for the deutschemark and the British pound provides a simple illustration of the ideas.

This paper will discuss the current research in building models of conditional variances using the Autoregressive Conditional Heteroskedastic (ARCH) and Generalized ARCH (GARCH) formulations. The discussion will be motivated by a simple asset pricing theory which is ...

TItis paper models weekly excess returns of 10-year Treasury notes and long-tenn Treasury bonds flOm 1968 through 1993 using an exponential generalized autoregressive conditional heteroskedasticity in mean (EGARCH-M) approach. The results indicate the presence of conditional heteroskedasti-;;ity and a strong tendency for the ex-ante volatility of excess returns to increase more following negative excess return innovations compared to positive innovations of equal magnitude. In addition, increases in ex-ante volatility are associated in some subperiods with rising excess returns on longer-tenn instruments, although the slope of the yield curve and lagged excess returns generally remain~;ignificant predictors of excess returns.

Maize is one of the major staples and cash crops for many Tanzanians. Excessive volatility of maize prices destabilises farm income in maize-growing regions and is likely to jeopardise nutrition and investment in many poor rural communities. This study investigates whether market reform policies in Tanzania have increased the volatility of maize prices, and identifies regional characteristics that can be attributed to the spatial price volatility. To achieve the objectives, an autoregressive conditional heteroskedasticity in mean (ARCH-M) model is developed and estimated in this study. Results show that the reforms have increased farm-gate prices and overall price volatility. Maize prices are lower in surplus and less developed regions than those in deficit and developed regions. Results also show that the developed and maize-deficit regions, and regions bordering other countries have experienced less volatile prices than less developed, maize-surplus and non-bordering regions. Our findings indicate that investments in communication and transportation infrastructures from government and donor countries are likely to increase interregional and international trade, thereby reducing the spatial price volatility in Tanzanian maize prices in the long run.

Emerging stock markets of Asia have become a matter of interest for international financial researchers and policy-makers during the last couple of decades. Series of reforms, increasing financial transparency and decreasing restrictions on transactions have made these markets better diversification opportunities for international investors. This paper examines independently as well the linkages of stock markets across the selected Asian countries. The volatility spillover is modelled through an asymmetric multivariate generalized autoregressive conditional heteroscedastic model. In large number of empirical studies of risk return analysis, it is observed that economic stability and good perspectives have been key assets for the development of emerging markets. Diversification of funds to reduce portfolio risk is also one of the point of attraction to domestic and foreign institutional investors. In this work, risk and uncertainty is studied for selected stock markets of emerging economies of Asia. Data of daily stock prices of selected markets is collected for recent decade and detail autoregressive conditional heteroskedasticity (ARCH) and its generalised models are used to estimate conditional and asymmetric volatilities. Keywords Volatility spillovers, emerging market, diversification, unexpected volatility, ARCH effect Asia-Pacific Journal of Management Research and Innovation 13(1&2) 13-33

The  study examines exchange rate volatility with GARCH models using monthly exchange rate data from January 1990 to November 2013. Simple rate of returns is employed to model the exchange rate volatility of Ghana Cedi-United States Dollar. The models included both symmetric and asymmetric models that capture the most common stylized facts about returns such as volatility persistence and leverage effect. The result identified EGARCH (2, 2) as the overall best fitted model. This model has the least AIC of -6.28 and SIC of -6.16.  Diagnostic test of the models residuals with the Ljung-Box test, the ARCH-LM test and the ACF plots revealed that the models are free from higher order autocorrelation and conditional heteroscedasticity separately. Our results also revealed persistence of volatility and the non-existence of leverage effects as shown by the asymmetric models. Keywords : Leptokurtic, volatility persistence, leverage effect.

This paper uses a multivariate GARCH modelling to describe the relationship between the systemic risk and the stock return in the banking industry in Thailand, Malaysia, Korea, Indonesia and Philippines. The banking industry comprises the large banks and the small-medium size banks. The advantage of this approach is the incorporation of time-variation in volatility consistent with empirical observations about the behaviour of stock return. Second the factor approach is adopted to incorporate intra-industry contagion within the banking sector. This so-called industry effect is designed to capture intra-industry information spillover between the large and the small-medium banks. Finally, the study provides evidence on these relations before and after the Asian financial crises of 1997, thereby implicitly testing for the impact of structural break.

Financial time series data cannot be adequately modelled by a normal distribution and empirical evidence on the non-normality assumption is very well documented in the financial literature; see [R.F. Engle, Autoregressive conditional heteroskedasticity with estimates of the variance of UK inflation, Econometrica 50 (1982) 987-1008] and [T. Bollerslev, Generalized autoregressive conditional heteroscedasticity, J. Econometrics 31 (1986) 307-327] for details. The kurtosis of various classes of RCA models has been the subject of a study by Appadoo et al. [

This paper offers an original survey of the Malaysian crisis and the effects of the consequent imposition of capital controls by authorities in September 1998 and of their subsequent relaxation in February and September 1999. We identify Malaysia’s unique strengths and weaknesses before the crisis, appreciate the differential timing and nature of the Malaysian crisis vis-à-vis the other neighbouring crisis countries, and distinguish carefully between the restrictive and incentive components of the imposed controls. Against this backdrop, we analyse both the “level” (first-order) effects and the “volatility” (second-order) effects of controls on key macroeconomic, banking and financial market variables. On the level effects, we found the Malaysian recovery (starting late 1998) to be at least as quick, strong and lasting as that of the other crisis countries, and discovered important channels of influence from controls to interest rates (which were lowered) and stock markets (which re...

Forecasting models based on the assumption that returns are normally distributed do not perform sufficiently on shallow markets. These models are more likely to fail in the estimation of the extreme points that can be reached especially at high volatility markets, and this situation is led to investors in predicting volatility. In the volatility forecasting of crypto money, which is seen as an alternative investment tool for the financial investors, single volatility models such as, ARCH, GARCH, T-GARCH, GARCH-M, E-GARCH, and I-GARCH and long memory models (AP-GARCH and C-GARCH) was utilized. In addition, the most suitable model was tried to be tested among the models used for volatility estimation. In this context, the price data of Bitcoin, Ethereum and Ripple cryptocurrency with the highest market value in the crypto money market have been utilized between 24/08/2016-07/05/2018. According to the results of the research, for Bitcoin and Ethereum, the volatility effect of the shocks is permanent and the effect of the positive shocks is more than that of the negative shocks, whereas for Ripple, the volatility effect of the shocks is transient and the passivity of the volatility is short.

The asymptotic distribution of maximum likelihood estimators is derived for a class of exponential generalized autoregressive conditional heteroskedasticity (EGARCH) models. The result carries over to models for duration and realised volatility that use an exponential link function. A key feature of the model formulation is that the dynamics are driven by the score.

The Malawi kwacha was floated in February 1994. Since then, the Reserve Bank of Malawi (RBM) has periodically intervened in the foreign exchange market. This report analyses the effectiveness of foreign exchange market interventions by RBM. We used a generalized autoregressive conditional heteroskedastic (GARCH; 1, 1) model to simultaneously estimate the effect of intervention on the mean and volatility of the kwacha. We also ran an equilibrium exchange rate model and use the equilibrium exchange rate criterion to compare results with those from the GARCH model. Using monthly exchange rates and official intervention data from January 1995 to June 2008, results from the GARCH model indicated that net sales of United States dollars by RBM depreciate, rather than appreciate, the kwacha. Empirically, this implies the RBM “leans against the wind”, i.e., the RBM intervenes to reduce, but not reverse, around-trend exchange rate depreciation. However, results from the GARCH model for the po...

We compare the computation of value at risk with daily and with high frequency data for the Deutsche mark-US dollar exchange rate. Among the main points considered in the Ž. paper are: a the comparison of measures of value at risk on the basis of multi-step Ž. volatility forecasts; b the computation of the degree of fractional differencing for high frequency data in the context of a Fractionally Integrated Generalized Autoregressive Ž. Ž. Conditional Heteroskedasticity FIGARCH model; and c the comparison between deterministic and stochastic models for the filtering of high frequency returns.

Volatility plays an important role in the field of financial econometrics as one of the risk indicators. Many various models address the problem of modeling the volatilities of financial asset returns. This study provides a new empirical performance comparison of the four different GARCH-type models, namely GARCH, GARCH-M, GJR-GARCH, and log-GARCH models based on simulated data and real data such as the DJIA, S&P 500, and S&P CNX Nifty indices on a daily period from January 2000 to December 2017. We also investigate the estimation results obtained using Solver’Excel and verify those results against the results obtained using a Markov chain Monte Carlo method. The simulation study showed that the GARCH model is outperformed by other models. Meanwhile, the empirical study provides evidence that the GJR-GARCH model provides the best fitting, followed by the GARCH-M, GARCH, and log-GARCH models. Furthermore, this study recommends the use of Excel’s Solver in practice when the parameter ...

Forecasting prices in electricity markets is critical for consumers and producers in planning their operations and managing their price risk. We utilize the generalized autoregressive conditionally heteroskedastic (GARCH) method to forecast the electricity prices in two regions of New York: New York City and Central New York State. We contrast the one-day forecasts of the GARCH against techniques such as dynamic regression, transfer function models, and exponential smoothing. We also examine the effect on our forecasting of omitting some of the extreme values in the electricity prices. We show that accounting for the extreme values and the heteroskedactic variance in the electricity price time-series can significantly improve the accuracy of the forecasting. Additionally, we document the higher volatility in New York City electricity prices. Differences in volatility between regions are important in the pricing of electricity options and for analyzing market performance.

Credit risk is the most important type of risk in terms of monetary value. Another key risk measure is market risk, which is concerned with stocks and bonds, and related financial derivatives, as well as exchange rates and interest rates. This paper is concerned with market risk management and monitoring under the Basel II Accord, and presents Ten Commandments for optimizing Value-at-Risk (VaR) and daily capital charges, based on choosing wisely from: (1) conditional, stochastic and realized volatility; (2) symmetry, asymmetry and leverage; (3) dynamic correlations and dynamic covariances; (4) single index and portfolio models; (5) parametric, semiparametric and nonparametric models; (6) estimation, simulation and calibration of parameters; (7) assumptions, regularity conditions and statistical properties; (8) accuracy in calculating moments and forecasts; (9) optimizing threshold violations and economic benefits; and (10) optimizing private and public benefits of risk management. For practical purposes, it is found that the Basel II Accord would seem to encourage excessive risk taking at the expense of providing accurate measures and forecasts of risk and VaR.

This paper attempts to compare the forecasting performance of the ARIMA model and hybrid ARMA-GARCH Models by using daily data of the Iran’s exchange rate against the U.S. Dollar (IRR/USD) for the period of 20 March 2014 to 20 June 2015. The period of 20 March 2014 to 19 April 2015 was used to build the model while remaining data were used to do out of sample forecasting and check the forecasting ability of the model. All the data were collected from central bank of Iran. First of all, the stationary of the exchange rate series is examined using unit root test which showed the series as non stationary. To make the exchange rate series stationary, the exchange rates are transformed to exchange rate returns. By using Box-Jenkins method, the appropriate ARIMA model was obtained and for capturing volatilities of returns series, some hybrid models such as: ARIMA-GARCH, ARIMA-IGARCH, ARIMA-GJR and ARIMA-EGARCH have been estimated. The results indicate that in terms of the lowest RMSE, MAE...

Abstract: This study seeks to apply the generalized autoregressive conditional heteroskedasticity (GARCH) model to assess the impact of inflation on stock market returns and volatility using monthly time series data from two West African countries, that is, Nigeria and Ghana. In addition, the impact of asymmetric shocks was investigated using the quadratic GARCH model developed by Sentana (1995), in both countries. Results for Nigeria show weak support for the hypothesis which states that bad news exert more adverse effect on stock market volatility than good news of the same magnitude; while a strong opposite case holds for Ghana. Furthermore, inflation rate and its three month average were found to have significant effect on stock market volatility in the two countries. Measures employed towards restraining inflation in the two countries, therefore, would certainly reduce stock market volatility, improve stock market returns and boost investor confidence.

We use the Dynamic Conditional Correlation model with Generalized Autoregressive Conditional Heteroskedasticity (DCC-GARCH) developed by Engle (Journal of Business & Economic Statistics 20(3):339-350, 2002) to examine dynamics in the correlation of returns between publicly traded REITs and non-REIT stocks. The results suggest that REIT-stock correlations form three distinct periods. During the first period, ending in August 1991 with the start of the modern REIT era, correlations were high and without trend, never dipping below 59%. During the second period, ending in September 2001 with the inclusion of REITs in broad stock market indexes, correlations declined precipitously to 30%, enabling substantially higher portfolio allocations to both high-return asset classes and therefore higher portfolio returns without increasing portfolio volatility. During the third period, since September 2001, correlations increased steadily but only reached 59% in late 2008. A simple portfolio optimization suggests that asset managers would be willing to pay 20 basis points per year, plus the difference in transaction costs, for the ability to use DCC-GARCH modeling of dynamic correlations in place of rolling 24-month asset correlations.

The literature has so far focused on the risk-return tradeoff in equity markets and ignored alternative risky assets. This paper examines the presence and significance of an intertemporal relation between expected return and risk in the foreign exchange market. The paper provides new evidence on the intertemporal capital asset pricing model by using high-frequency intraday data on currency and by presenting significant time-variation in the risk aversion parameter. Five-minute returns on the spot exchange rates of the U.S. dollar vis-à-vis six major currencies (the Euro, Japanese Yen, British Pound Sterling, Swiss Franc, Australian Dollar, and Canadian Dollar) are used to test the existence and significance of a daily risk-return tradeoff in the FX market based on the GARCH, realized, and range volatility estimators. The results indicate a positive, but statistically weak relation between risk and return on currency.

This paper presents an empirical analysis of real stock return volatility contagion from emerging markets and financial centers to the Turkish market since 1992. We first present descriptive statistics and contemporaneous correlation of the real stock returns and unconditional stock return volatility. Using simple rolling regressions and goodness of fit measures, we identify periods of persistent volatility in the Istanbul Stock Exchange (ISE) and volatility contagion towards the ISE. Finally, using Generalized Autoregressive Conditional Heteroskedasticity (GARCH) estimations, we obtain robust estimates of volatility contagion from stock markets to the ISE. There is clear evidence of volatility contagion from the financial centers especially in the aftermath of the Asian Crisis to the ISE.

In this paper, we extend the concept of the news impact curve of volatility developed by Engle and Ng (1993) to the higher moments and co-moments of the multivariate generalized autoregressive conditional heteroskedasticity (GARCH) model with non-normal innovations. For this purpose, we present a new methodology to describe the joint distribution of GARCH processes in a non-normal setting. Then, we provide expressions for the response of the moments of the subsequent distribution to a shock. This tool enhances the understanding of the temporal evolution of the joint distribution. We use our methodology to provide stylized facts for the four largest international stock markets. In particular, we document the persistence of large (positive or negative) daily returns. In a multivariate setting , we find that foreign holdings provide a good hedge against changes in domestic volatility after good shocks but a bad hedge after crashes. Finally, using generalized impulse responses, we show that the effect of shocks on the higher moments of the distribution is short-lasting.

Support vector machines (SVMs) are a new nonparametric tool for regression estimation. We will use this tool to estimate the parameters of a GARCH model for predicting the conditional volatility of stock market returns. GARCH models are usually estimated using maximum likelihood (ML) procedures, assuming that the data are normally distributed. In this paper, we will show that GARCH models can be estimated using SVMs and that such estimates have a higher predicting ability than those obtained via common ML methods.

In this study we are in the quest for most appropri ate GARCH-family model for modeling the differenced log Consumer Price Index (CPI) CPI i.e. percentage change in CPI for Pakistan. Using variou s specifications for mean equation, study estimated GARCH (1,1) and GJR-GARCH (1,1). The study also estimates EGARCH (1,1) for monthly data of CPI. The estimation results reveal that ARMA (1,1)- GARCH (1,1) comes out to be most appropriate specification for modeling inflation volatility. Th e study finds no evidence of asymmetry in the response of inflation volatility t o negative and positive shocks.

The importance of managerial decisions related to interest-sensitive cash flows has received considerable attention in the insurance literature. Consistent with the interest-sensitive nature of insurer assets and liabilities, empirical research has shown that insurer insolvency is significantly related to interest rate volatility. We investigate the interest rate sensitivity of monthly stock returns of life insurers based on a generalized autoregressive conditionally heteroskedastic in the mean (GARCH-M) model. We examine three different portfolios (equally weighted, risk-based, and size-based) with binary variables to explicitly account for varying interest rate strategies adopted by the Federal Reserve System. Results based on data for the period 1975 through 2000 indicate that life insurer equity values are sensitive to long-term interest rates and that interest sensitivity varies across subperiods and across riskbased and size-based portfolios. The results complement insolvency research that links insurer financial performance to changes in interest rates.

In this era of shaky global economic and financial conditions for about a decade now since the global financial crisis 2008, how the volatilities of Islamic equities worldwide are behaving, especially in terms of their regime changing behavior, if any, is the main issue of concern in this paper. To this end, a relatively novel technique, namely, Markov regime switching GARCH (MSGARCH) is applied to some selected broad based Islamic equity indices from both advanced and emerging world and of their combinations. The results tend to indicate that in general there is no persistence in any particular regime to prevail, rather a high regime switching behavior between volatile and less volatile regimes are present in Islamic equities around the world. This perhaps reflects the prolonged uncertainties prevailing in the world economies and therefore implies higher risk for the investors in predicting their investment outcome.

Extreme returns in stock returns need to be captured for a successful risk management function to estimate unexpected loss in portfolio. Traditional value-at-risk models based on parametric models are not able to capture the extremes in emerging markets where high volatility and nonlinear behaviors in returns are observed. The Extreme Value Theory (EVT) with conditional quantile proposed by McNeil and Frey (2000) is based on the central limit theorem applied to the extremes rater than mean of the return distribution. It limits the distribution of extreme returns always has the same form without relying on the distribution of the parent variable. This paper uses 8 filtered EVT models created with conditional quantile to estimate value-at-risk for the Istanbul Stock Exchange (ISE). The performances of the filtered expected shortfall models are compared to those of GARCH, GARCH with student-t distribution, GARCH with skewed student-t distribution and FIGARCH by using alternative back-t...

This paper introduces new methods of estimating Value-at-Risk (VaR) using Range-Based GARCH (General Autoregressive Conditional Heteroskedasticity) models. These models, which could be either based on the Parkinson Range or Garman-Klasss Range, are applied to 10 stock market indices of selected countries in the Asia-Pacific Region. The results are compared using the traditional methods such as the econometric method based on the ARMA-GARCH models and RiskMetricsTM. The performance of the different models is assessed using the out-of-sample VaR forecasts. Series of likelihood ratio (LR) tests namely: LR of unconditional coverage (LRuc), LR of independence (LRind), and LR of conditional coverage (LRcc) are performed for comparison. The result of the assessment shows that the model based on the Parkinson Range GARCH (1,1) with Student’s t distribution is the best performing model on the 10 stock market indices. It has a failure rate, defined as the percentage of actual return that is s...

Conventional streamflow models operate under the assumption of constant variance or season-dependent variances (e.g. ARMA (AutoRegressive Moving Average) models for deseasonalized streamflow series and PARMA (Periodic AutoRegressive Moving Average) models for seasonal streamflow series). However, with McLeod-Li test and Engle's Lagrange Multiplier test, clear evidences are found for the existence of autoregressive conditional heteroskedasticity (i.e. the ARCH (AutoRegressive Conditional Heteroskedasticity) effect), a nonlinear phenomenon of the variance behaviour, in the residual series from linear models fitted to daily and monthly streamflow processes of the upper Yellow River, China. It is shown that the major cause of the ARCH effect is the seasonal variation in variance of the residual series. However, while the seasonal variation in variance can fully explain the ARCH effect for monthly streamflow, it is only a partial explanation for daily flow. It is also shown that while the periodic autoregressive moving average model is adequate in modelling monthly flows, no model is adequate in modelling daily streamflow processes because none of the conventional time series models takes the seasonal variation in variance, as well as the ARCH effect in the residuals, into account. Therefore, an ARMA-GARCH (Generalized AutoRegressive Conditional Heteroskedasticity) error model is proposed to capture the ARCH effect present in daily streamflow series, as well as to preserve seasonal variation in variance in the residuals. The ARMA-GARCH error model combines an ARMA model for modelling the mean behaviour and a GARCH model for modelling the variance behaviour of the residuals from the ARMA model.

This paper explores the Support Vector Machine and Least Square Support Vector Machine models in stock forecasting. Three prevailing forecasting techniques-General Autoregressive Conditional Heteroskedasticity (GARCH), Support Vector Regression (SVR) and Least Square Support Vector Machine (LSSVM) are combined with the wavelet kernel to form three novel algorithms Wavelet-based GARCH (WL_GARCH), Wavelet-based SVR (WL_SVR) and Wavelet-based Least Square Support Vector Machine (WL_LSSVM) to solve the non-linear and non-parametric financial time series problem. This paper presents a platform for comparison of the wavelet-based algorithm using Hang Sang Index, Dow Jones and Shanghai Composite Index which has significant influence to each other. It has been discovered that wavelet-based model is not as good as the LS-SVM model. The best result is from LS-SVM without wavelet-based kernel.

In operational forecasting of the surface O 3 by statistical modelling, it is customary to assume the O 3 time series to be generated through a homoskedastic process. In the present work, we've taken heteroskedasticity of the O 3 time series explicitly into account and have shown how it resulted in O 3 forecasts with improved forecast confidence intervals. Moreover, it also enabled us to make more accurate probability forecasts of ozone episodes in the urban areas. The study has been conducted on daily maximum O 3 time series for four urban sites of two major European cities, Brussels and London. The sites are: Brussels (Molenbeek) (B1), Brussels (PARL.EUROPE) (B2), London (Brent) (L1) and London (Bloomsbury) (L2). Fast Fourier Transform (FFT) has been used to model the periodicities (annual periodicity is especially distinct) exhibited by the time series. The residuals of "actual data subtracted with their corresponding FFT component" exhibited stationarity and have been modelled using ARIMA (Autoregressive Integrated Moving Average) process. The MAPEs (Mean absolute percentage errors) using FFTeARIMA for one day ahead 100 out of sample forecasts, were obtained as follows: 20%, 17.8%, 19.7% and 23.6% at the sites B1, B2, L1 and L2. The residuals obtained through FFTeARIMA have been modelled using GARCH (Generalized Autoregressive Conditional Heteroskedastic) process. The conditional standard deviations obtained using GARCH have been used to estimate the improved forecast confidence intervals and to make probability forecasts of ozone episodes. At the sites B1, B2, L1 and L2, 91.3%, 90%, 70.6% and 53.8% of the times probability forecasts of ozone episodes (for one day ahead 30 out of sample) have correctly been made using GARCH as against 82.6%, 80%, 58.8% and 38.4% without GARCH. The incorporation of GARCH also significantly reduced the no. of false alarms raised by the models.

The study looked into the stochastic properties of CPI-inflation rate for Nigeria from 1995Q1 to 2016Q4. The study employed an autoregressive fractionally integrated moving average and a general autoregressive conditional heteroskedasticity (ARFIMA-GARCH) methodology as well as ADF/KPSS to investigate the long-memory properties of CPI-Inflation for Nigeria. The study found that CPI-inflation in Nigeria is shock dissipating at a geometric rate (fast mean reverting ability). The ARFIMA-GARCH process showed that CPI inflation in Nigeria is a heteroskedastic fractionally integrated process with quick mean reverting ability. The study therefore concludes that shocks to CPI-inflation in Nigeria such as sudden hikes in prices of energy products will not cause a permanent change in general price level but will eventually return to its mean state, and therefore having an implication for the Inflation-Unemployment tradeoff of the Philips curve.

European electricity markets have been subject to a broad deregulation process in the last few decades. We analyse hedging policies implemented through different hedge ratios estimation. More specifically we compare naïve, ordinary least squares, and GARCH conditional variance and correlations models to test if GARCH models lead to higher variance reduction in a context of high time varying volatility as the case of electricity markets. Our results show that the choice of the hedge ratio estimation model is central on determining the effectiveness of futures hedging to reduce the portfolio volatility.

It is essential for financial institutions and academicians to understand volatility spillover and financial market returns. However, previous studies examined the effects of direct spillover only and ignored those of the newly emerging stock markets. Therefore, this study attempts to estimate the time-varying volatility of Pakistani and leading foreign stock markets. It also tries to explore the direct and indirect volatility spillover effect between Pakistani and eight leading foreign stock markets. Daily data were used from nine international equity markets (KSE 100, NIKKEI 225, HIS, S&P 500, NASDAQ 100, DOW JONES, GADXI, FTSE 350 and DFMGI) for the period between 2005 and 2016. The univariate GARCH and GJR models were employed for analysing volatility, and the multivariate GARCH Diagonal BEKK model was used to explore direct and indirect volatility spillover effects. In order to analyse the volatility spillover effect during and after the global financial crisis period, the data...

Permasalahan umum yang sering dijumpai dalam banyak studi keuangan yaitu volatilitas tak konstan untuk \emph{return} aset. Suatu pendekatan untuk memodelkan runtun waktu keuangan dengan heteroskedastisitas pada \emph{return} aset yaitu model GARCH. Studi ini bertujuan untuk menunjukkan bagaimana MS Excel dapat digunakan untuk mengestimasi model GARCH(1,1). MS Excel menawarkan suatu kemudahan penghitungan dan mungkin merupakan piranti yang paling banyak digunakan untuk menganalisis data keuangan. Untuk tujuan penyelidikan, studi ini mengadopsi data simulasi dan data riil kurs beli USD terhadap IDR periode 2010--2017. Parameter-parameter dalam model GARCH(1,1) diestimasi menggunakan metode likelihood maksimum dengan bantuan Solver yang tersedia di MS Excel. Hasil empiris pada data simulasi menunjukkan bahwa MS Excel menyediakan keakuratan yang baik untuk menaksir model GARCH(1,1). Aplikasi untuk data riil menghasilkan nilai-nilai optimal untuk model GARCH(1,1) yang serupa dengan yang ...

CENTER FOR ECONOMIC RESEARCH Board f larry Barkema Helmut Bester Eric van Damme, chairman Frank van der Duyn Schouten leffrey James Management Eric van Damme (graduate education) Arie Kapteyn (scientific director) Marie-Louise Kemperman (administration) Scientific Council