PARCH Model Research Articles

FORECASTING MODELS FOR SECTOR-WISE STOCK PRICE INDICES: COLOMBO STOCK EXCHANGE

The stock markets of a country play a vital role in its economy. Stock market indices are vital fragments of information for investors. It is very important to develop models that reflect the pattern of the stock price movements for different sectors since it becomes very significant to investors and policymakers. Therefore, the aim of this research study was to develop models to forecast different sector indices in Colombo Stock Exchange and to compare sector-wise models. The investigation was performed using secondary data for a sample of ten listed sectors in the Colombo Stock Exchange (CSE) for the thirty-four years from 2nd January 1985 to 31st March 2019. Secondary data were collected by using the data library maintained by Colombo Stock Exchange. Financial time series data analysis techniques were used to analyze the collected data. It was applied the ARCH family models in this research study, which included the Autoregressive conditional heteroscedasticity model (ARCH), Generalized Autoregressive conditional heteroscedasticity model (GARCH), Threshold Autoregressive conditional heteroscedasticity model (TARCH), Exponential generalized autoregressive conditional heteroscedastic model (EGARCH), Integrated Generalized Autoregressive conditional heteroscedasticity model (IGARCH) and Power Autoregressive conditional heteroscedasticity model (PARCH) since the sector indices are financial time series data. Findings revealed that the appropriate model to forecast the sector indices of Oil Palms sector, Services sector and Stores & Supplies sector as PARCH (2,1) model, Beverage, Food & Tobacco sector as PARCH (1,1) model, Chemicals & Pharmaceuticals sector as PARCH (2,2) model, Banking Finance & Insurance sector and Investment Trusts sector as IGARCH (2,2) model, Footwear & Textiles sector as EGARCH (1,1) model, the Manufacturing sector as EGARCH (1,3) model and Hotels & Travels sector as TARCH (1,1) model. The findings of this research study are useful to policymakers and investors for their decision-making.

THE IMPACT OF SHOCKS ON THE VOLATILITY OF THE DUBAI GENERAL MARKET INDEX (DFMGI), USING ASYMMETRIC GARCH MODELS

This research paper aims to study the effects of good and bad news on the volatility of the Dubai General Market Index (DFMGI) return series for 5,5 years during the period spanning from January 1, 2018, to June 30, 2023, using the asymmetric GARCH models: EGARCH(1,1), TGARCH(1,1) and PARCH(1,1). The study concluded that positive and negative shocks asymmetric impact fluctuations in price returns in the Dubai financial market. This means that negative shocks significantly impact volatility more than positive shocks. The study also concluded that the best asymmetric GARCH model among the three used is the PARCH(1,1) model.

Pay Senedi Endeksleri ile Endeks Vadeli İşlemler Arasındaki Volatilite İlişkisi: Türkiye ve Dünya Örnekleri Arasında Karşılaştırmalı Analiz

Bu çalışmanın konusunu, pay senedi endeksleri ile bu endekslerin dayanak varlık olduğu vadeli işlemler arasındaki volatilite ilişkisinin analizi oluşturmaktadır. Bu çalışma, spot endeksler ile endeks vadeli işlemler arasındaki volatilite ilişkisinin yönünü tespit etmeyi amaçlamaktadır. Bu çalışmanın temel amacı, Türkiye örneğinde yüksek işlem hacmi göz önünde bulundurularak BIST 30 endeksi ve BIST 30 endeks vadeli işlemleri arasındaki volatilite ilişkisinin ekonometrik yöntemlerle incelenmesi, elde edilen verilerin Dünya’daki önemli endekslerle karşılaştırılması ve analiz sonuçlarının değerlendirilmesidir. Bu amaçla, BIST 30 endeksi ve BIST 30 endeks vadeli işlemleri arasında herhangi bir volatilite ilişkisi olup olmadığı hususu ekonometrik yöntemlerle analiz edilerek, Dünya örnekleri ile kıyaslamalar yapılmıştır. Dünyanın gelişmiş borsalarında işlem gören DAX 30 ve S&P 500 spot piyasa endeksleri ile DAX 30 ve S&P 500 endeks vadeli işlemleri arasındaki volatilite ilişkisine bakılarak Türkiye örneği ile karşılaştırmalar yapılmıştır. Getiri ve işlem hacimlerine ilişkin oynaklık tahminleri için Otoregresif Koşullu Değişen Varyans (ARCH) Modelleri kullanıldığından, spot endeksler ile endeks vadeli işlemler arasındaki volatilite ilişkisi GARCH, TARCH, EGARCH ve PARCH modelleri ile analiz edilmiştir. Uygulama aşamasında elde edilen bulgular, 2006-2021 yıllarını kapsayan dönemde her iki piyasa arasında çift yönlü volatilite ilişkisi olduğunu ortaya çıkarmıştır. Ancak bu çift yönlü ilişki, koşullu varyans denklemindeki açıklayıcı değişkenlerinin katsayılarının çok küçük olması nedeniyle istatistiksel olarak çok önem arz etmemektedir.

Volatility of cryptocurrencies

Many models have been developed to model, estimate and forecast financial time series volatility, amongst which are the most popular autoregressive conditional heteroscedasticity (ARCH) model introduced by Engle (1982) and generalized autoregressive conditional heteroscedasticity (GARCH) model introduced by Bollerslev (1986). The aim of this paper is to determine which type of ARCH/GARCH models can fit the best following cryptocurrencies: Ethereum, Neo, Ripple, Litecoin, Dash, Zcash and Dogecoin. It is found that the EGARCH model is the best fitted model for Ethereum, Zcash and Neo, PARCH model is the best fitted model for Ripple, while for Litecoin, Dash and Dogecoin it depends on the selected distribution and information criterion.

Day of the Week Effect in Cryptocurrencies' Returns and Volatility

Calendar anomalies as the seasonal tendencies in stock returns are the signal of irregular behaviour of stock markets. These anomalies have been comprehensively studied in many matured as well as emerging stock markets. But there is lack of exploration of calendar anomalies in the cryptocurrency market. So, the present treatise is an attempt to fill this lacuna by studying day of the week effect on cryptocurrencies' returns and volatility. This study is based on the prices of eight cryptocurrencies (viz. Bitcoin, EOS, Ethereum, Bitcoin Cash, Litecoin, Tether, XRP and Stellar) for a period starting from July 2017 and up to March 2020. The series of daily and day-wise returns were initially studied for stationarity using Ng-Perron tests and augmented Dickey–Fuller test. The results from these tests confirmed that the cryptocurrencies' return series are stationary. The day of the week effect on cryptocurrencies returns was studied by introducing the dummies for each day of the week in the ordinary least square regression equation. The residuals from the ordinary least square regression equation were tested for ARCH effect using Engle's ARCH test. The results from the test confirmed the presence of ARCH effect in all series. The GARCH (1,1) model and PARCH model were further applied to account for ARCH effect and these models confirmed the presence of the day of the week effect in all the cryptocurrencies' returns and volatility except for day of week effect in Bitcoin and Tether returns. So, the significant day of the week effect was present in all cryptocurrencies' returns and volatility but the significant day of the week effect was absent in Bitcoin's returns and Tether's returns. These findings of significant day effect may help the existing and potential investors in taking investment decision in contemporary scenario of no ban in cryptocurrency market in India.

Testing the linkages of Arab stock markets: a multivariate GARCH approach

The authors undertook to examine 720 monthly observations of activity in 15 Arab stock markets over four years (from 2014 to 2017) to identify the dynamic linkages among those markets. To achieve this, several forms of the Generalized Auto-Regressive Conditional Heteroskedasticity (GARCH) model were utilized. Both panel and individual stationarity, in addition to cointegration tests, were employed to highlight the interaction between these markets. The results suggest that Arab stock markets have weak linkages with the exception of those of the Gulf Cooperation Council (GCC). The authors also find out that the TARCH, EGARCH, PARCH, and Component GARCH (1,1) models are suitable in terms of passing the econometric analysis tests. Nevertheless, they conclude that the EGARCH model is the most appropriate for capturing the cross-market dynamic linkages, thereby outperforming the other GARCH specifications under study. The empirical findings bear special implications for economic literature regarding linkages of stock markets in the Arab world.

Foreign exchange volatility modelling of southeast asian major economies

This paper investigates the exchange rate volatility model in Southeast Asian countries. The countries selected were Indonesia, Malaysia, Thailand, The Philippines, Vietnam and Singapore. This paper aims to model the volatility of the regional currencies exchange rate against the international currency, i.e. US Dollar. The period covered in this study extended from 1 January 2013 until 31 July 2019. These were the daily exchange rate of 7 currencies of Southeast Asian countries. The currency involved were Indonesian Rupiah (IDR), Malaysian Ringgit (MYR), Thai Baht (THB), The Philippine Peso (PHP), Vietnam Dong (VND), and Singaporean Dollar (SGD). All currencies were measured in the exchange rate against the US Dollar (USD). The result indicated that PARCH model is the best method to explain the movement of MYR, VND, and SGD. GARCH can model THB and PHP. Only IDR that has volatility explainable by TARCH.

The effects of recent terrorist attacks on risk and return in commodity markets

The event study methodology of Brown and Warner (1985) is adopted and augmented to evaluate the effect of the recent terrorist attacks on risk and returns in commodity markets. The methodology is supplemented with various techniques, such as the non-parametric ranking test and kernel regression, to find out if 20 terrorist attacks (including in Paris, Nice, Brussels, Stockholm, Manchester, Jakarta, London and Melbourne) generated abnormal returns. Asset pricing models are fitted with interaction variables while GARCH, TARCH, EGARCH and PARCH models are used to determine changes in systematic risk. Our results show abnormal returns and delayed reactions of up to 120 days in the commodity markets—evidence which defies the efficient market hypothesis. In addition, we identify sector and commodity effects in risk analysis.

Volatilidad estocástica del tipo de cambio, impacto y desequilibrios en la economía mexicana

In this paper an empirical analysis of the exchange rate of the dollar during the period 2000-2016 is made, the objective is to select a statistical model that accurately characterizes the impacts of the price variation in the Mexican economy. The time series methodology is applied to study the volatility of the currency and the results of the ARCH model (Engle, 1982) and GARCH (Bollerslev, 1986) are compared. It is concluded that the GARCH model represents more accurately the changes in exchange rate volatility and the results validate the hypothesis of high volatility caused by factors beyond the performance of the Mexican economy. A comparative analysis between the GARCH, EGARCH and PARCH models is identified as a future line of research to extend the work.

Modeling Philippine Stock Exchange Composite Index Using Time Series Analysis

This study was conducted to develop a time series model of the Philippine Stock Exchange Composite Index and its volatility using the finite mixture of ARIMA model with conditional variance equations such as ARCH, GARCH, EG ARCH, TARCH and PARCH models. Also, the study aimed to find out the reason behind the behaviorof PSEi, that is, which of the economic variables - Consumer Price Index, crude oil price, foreign exchange rate, gold price, interest rate, money supply, price-earnings ratio, Producers’ Price Index and terms of trade - can be used in projecting future values of PSEi and this was examined using Granger Causality Test. The findings showed that the best time series model for Philippine Stock Exchange Composite index is ARIMA(1,1,5) - ARCH(1). Also, Consumer Price Index, crude oil price and foreign exchange rate are factors concluded to Granger cause Philippine Stock Exchange Composite Index.

Modeling Volatility: Evidence from the Bucharest Stock Exchange

Financial series tend to be characterized by volatility and this characteristic affects both financial series of developed markets and emerging markets. Because of the emerging markets have provided major investment opportunities in last decades their volatility has been widely investigated in the literature. The most popular volatility models are the Autoregressive Conditional Heteroscedastic (ARCH) or Generalized Autoregressive Conditional Heteroscedastic (GARCH) models. This paper aims to investigate the volatility of Bucharest Stock Exchange, BET index as an emerging capital market and compare forecasting power for volatility of this index during 2000- 2014. To do this, this paper use GARCH, TARCH, EGARCH and PARCH models against Generalized Error distribution. We estimate these models then we compare the forecasting power of these GARCH type models in sample period. The results show that the EGARCH is the best model by means of forecasting performance.

Forecasting Volatility of Stock Indices with ARCH Model

The main motive of this study is to investigate the use of ARCH model for forecasting volatility of the DSE20 and DSE general indices by using the daily data. GARCH, EGARCH, PARCH, and TARCH models are used as benchmark models for the study purpose. This study covers from December 1, 2001 to August 14, 2008 and from August 18, 2008 to September 10, 2011 as in-sample and out-of-sample set sets respectively. The study finds the past volatility of both the DSE20 and DSE general indices returns series are significantly, influenced current volatility. Based on in-sample statistical performance, both the ARCH and PARCH models are considered as the best performing model jointly for DSE20 index returns, whereas for DSE general index returns series, ARCH model outperforms other models. According to the out – of- sample statistical performance, all models except GARCH and TARCH models are regarded as the best model jointly for DSE20 index returns series, while for DSE general index returns series, no model is nominated as the best model individually. Based on the in-sample trading performance, all models except GARCH are considered as the best model jointly for DSE20 index returns series, while ARCH model is selected as the best model for DSE general index returns series. A per outputs of out-of-sample trading performance, the EGARCH model is the best performing model for DSE20 index returns series, whereas the GARCH and ARCH models are considered as the best performing model jointly for DSE general index returns series.

Does Information Help Intra‐Day Volatility Forecasts?

ABSTRACTWhile much research related to forecasting return volatility does so in a univariate setting, this paper includes proxies for information flows to forecast intra‐day volatility for the IBEX 35 futures market. The belief is that volume or the number of transactions conveys important information about the market that may be useful in forecasting. Our results suggest that augmenting a variety of GARCH‐type models with these proxies lead to improved forecasts across a range of intra‐day frequencies. Furthermore, our results present an interesting picture whereby the PARCH model generally performs well at the highest frequencies and shorter forecasting horizons, whereas the component model performs well at lower frequencies and longer forecast horizons. Both models attempt to capture long memory; the PARCH model allows for exponential decay in the autocorrelation function, while the component model captures trend volatility, which dominates over a longer horizon. These characteristics are likely to explain the success of each model. Copyright © 2013 John Wiley & Sons, Ltd.

Asymptotic inference for periodic ARCH processes

In this paper, we consider the conditional least squares (CLS) estimators for periodic ARCH models (P-ARCH). The CLS estimators applied to the square-transformed P-ARCH model have an explicit form which does not depend on the distribution of the innovation. Since the CLS are not asymptotically efficient in general, we give a necessary and sufficient condition ensuring the asymptotic efficiency of the CLS based on the local asymptotic normality (LAN) approach.

Measuring risk for large hedgers and large speculators in major US futures markets

Using the Commodity Futures Trading Commission's Commitments of Traders data, considering both the generalized autoregressive conditional heteroskedasticity (GARCH) and the power ARCH volatility-based models, it has been found that the lagged volatility and the news about volatility from the previous month are significant in explaining large hedger and speculator volatilities. A greater reliance on the ARCH term by speculators suggests their greater reliance on past information for making their current decisions. Furthermore, the hedger volatility in treasury bonds and coffee and the speculator volatility in gold and Standard & Poor's 500 futures have experienced increasing volatility persistence to shocks during the 1990s. In all remaining markets, hedger and speculator volatilities have shown a tendency to decay over time in response to shocks, supporting the belief that both players are informed and react well to news volatility. The PARCH model explains the volatility of both players more accurately by exhibiting a greater number of negative components of volatility than theGARCH model. Both models, under the normal and t-distributions, support the fact that most futures returns in the 29 US markets were leptokurtic. The PARCH model, under a normal distribution, was ranked first in explaining actual returns and forecasting the one-month futures return for both players. The PARCH model, under the t-distribution, was ranked last due to its high sensitivity for the standard deviation of returns. Idiosyncratic volatility was found to be a poor proxy of volatility in forecasting the onemonth futures return.

멱변환 이분산성 시계열 모형을 이용한 인터넷 트래픽 예측 기법 연구

본 연구에서는 재무시계얼 자료의 변동성을 분석하는데 유용하게 쓰이는 멱변환 시계열 모형을 인터넷 트래픽 자료 특성 분석에 적용하여 효용성을 보이고자 한다. 트래픽의 특성인 장기기억(long memory)특성을 설명하기 위하여 멱변환 GARCH(PGARCH) 모형을 소개하고 기존의 GARCH 모형보다 더 유용함을 시뮬레이션과 실제 인터넷 트래픽 자료에 적합시켜 입증하였다. In this paper, we show the performance of the power transformation GARCH(PGARCH) model to analyze the internet traffic data. The long memory property which is the typical characteristic of internet traffic data can be explained by the PGARCH model rather than the linear GARCH model. Small simulation and the analysis of the real internet traffic show the out-performance of the PARCH MODEL over the linear GARCH one.

Misspecification Testing for the Conditional Distribution Model in GARCH-Type Processes

In this article, we study goodness of fit tests for some distributions of the innovations which are usually adopted to explain the behavior of financial time series. Inference is developed in the context of GARCH-type models. Functional bootstrap tests are employed, assuming that the conditional means and variances of the model are correctly specified. The performances of the functional tests are assessed with a Monte Carlo experiment, based on some of the most common distributions adopted in the financial framework. The results of an application to the series of squared residuals from a PARCH(1,1) model fitted to a series of foreign exchange rates returns are also shown.

Optimal sampling frequency for volatility forecast models for the Indian stock markets

AbstractThis paper evaluates the performance of conditional variance models using high‐frequency data of the National Stock Index (S&P CNX NIFTY) and attempts to determine the optimal sampling frequency for the best daily volatility forecast. A linear combination of the realized volatilities calculated at two different frequencies is used as benchmark to evaluate the volatility forecasting ability of the conditional variance models (GARCH (1, 1)) at different sampling frequencies. From the analysis, it is found that sampling at 30 minutes gives the best forecast for daily volatility. The forecasting ability of these models is deteriorated, however, by the non‐normal property of mean adjusted returns, which is an assumption in conditional variance models. Nevertheless, the optimum frequency remained the same even in the case of different models (EGARCH and PARCH) and different error distribution (generalized error distribution, GED) where the error is reduced to a certain extent by incorporating the asymmetric effect on volatility. Our analysis also suggests that GARCH models with GED innovations or EGRACH and PARCH models would give better estimates of volatility with lower forecast error estimates. Copyright © 2008 John Wiley & Sons, Ltd.

Standard deviation or variance: the better proxy for large hedgers and large speculators risk in U.S. futures markets

Using CFTC’s COT data, both GARCH and PARCH volatility based models found the lagged volatility and news about volatility from the previous month to be significant in explaining large hedgers’ and speculators’ volatility. The greater reliance on the ARCH term for speculators’ suggested their greater reliance on past information to extrapolate for their current decisions. Furthermore, hedgers’ volatility in Treasury bonds and coffee, and speculators’ volatility in gold and S&P500 futures have experienced increasing volatility persistence to shocks over the 1990s. In all remaining markets, hedgers’ and speculators’ volatility has shown a tendency to decay over time in response to shocks, supporting that both players are informed and react well to news volatility. The PARCH model explains volatility of both players better by exhibiting more negative components of volatility than the GARCH model. Both models, under normal and t distribution, supported that most futures returns in the 29 US markets were leptokurtic. Key words: CFTC, Cot, Garch, Parch, volatility. JEL classification: G13, G14, G15, G18

Standard Deviation or Variance: The Better Proxy of Risk for Large Hedgers and Speculators in the U.S. Futures Markets

Using CFTC's COT data, both GARCH and PARCH volatility based models found the lagged volatility and news about volatility from previous month to be significant in explaining large hedgers' and speculators' volatility. The greater reliance on the ARCH term for speculators' suggested their greater reliance on past information to extrapolate for their current decisions. Further, hedgers' volatility in treasury bonds and coffee and speculators' volatility in gold and S&P500 futures have experienced increasing volatility persistence to shocks over the 1990s. In all remaining markets, hedgers' and speculators' volatility has shown a tendency to decay over time in response to shocks, supporting that both players are informed and react well to news volatility. The PARCH model explains volatility of both players better by exhibiting more negative components of volatility than the GARCH model. Both models, under normal and t distribution supported that most futures returns in the 29 U.S. markets were leptokurtic.