Autoregressive Conditional Heteroskedasticity

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 ...

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 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...

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...

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 ...

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.

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.

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...

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.

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 ...