Modelling Abrupt Shift in Time Series Using Indicator Variable: Evidence From Nigerian Insurance Stock
Chapter One
Aim and Objectives of the study
The aim of this study is to model abrupt shift in time series using indicator variable: Evidence from the Nigerian Insurance stocks quoted on the floor of the Nigerian stock exchange using incorporated dummy variable on the volatility models. The aim of this study will be achieved using the following objectivesto:
- examine the stationarity of the returns and test for normality of theresiduals
- to model the volatility in the return using different volatility
- observe the significance of the indictor variable on the volatility of the
- compare the models in term of fitness and forecasting accuracy and recommend a suitable volatility model for volatility
CHAPTER TWO
LITERATURE REVIEW
ARCH and GARCH models, which stand for autoregressive conditional heteroscedasticity and generalized autoregressive conditional heteroscedasticity, have become widespread tools for dealing with heteroscedastic time series. The goal of such models is to provide a volatility measure – like a standard deviation — that can be used in financial decisions concerning risk analysis, portfolio selection and derivative pricing. Applications of the ARCH/GARCH approach are widespread in situations where volatility of returns is a central issue. Many banks and other financial institutions use the idea of “value at risk” as a way to measure the risks faced by their portfolios.
Engle (1982)first proposed the autoregressive conditional heteroscedasticity (ARCH) model for modeling the changing variance of a time series; Engle used an ARCH model to study inflation in the United Kingdom. Bollerslev (1986)showed that a GARCH model with a small number of terms may be more efficient than an ARCH model with many terms. Empirical studies in recent years have focused on volatility investigation on the pattern of financial assets such as ARCH effect, volatility clustering, and persistence and leverage effect. For example, (Tse and Tsui, 1997), (Pesaran and Robinson, 1993), (Yoon and Lee, 2008), (Longmore and Lee, 2004), (Taylor and Tsun1986) and many others used many extension of the GARCH model proposed by Nelson (1991) like the GARCH-in Mean, IGARCH, EGARCH, TARCH, PARCH.
The use of dummy variables requires the imposition of additional constraints on the parameters of regression equations to obtain estimates for the model. Among the possible constraints the most useful are (a) to set the constant term of the equation to zero, or (b) to omit one of the dummy variables from the equation. In econometrics time series analysis, dummy variables may be used to indicate the occurrence of wars or major strikes. Dummy variables are used frequently in time series analysis with regime switching, seasonal analysis and qualitative data applications. Dummy variables are involved in studies for economic forecasting, bio- medical studies, credit scoring, response modelling, etc
Alabi (2014) used dummy variable to compare the year 2012 internally generated revenue (IGR) and wage bills of the six geopolitical zones in Nigeria by categorizing the geopolitical zones as dummy variables in a regression model to find out if the average internally generated revenue and wage bills of the geopolitical zone are statistically different from each other. From his analysis, he concluded that the northeast and northwest zones are statistically different.
Ajabet al.,(2012) investigated stock market volatilities exploiting a number of asymmetric models (EGARCH, ICSS-EGARCH, GJR-GARCH, and ICSS-GJR-GARCH). The finding supports the widely accepted view that accounting for the regime shifts detected by the iteratedcumulative sums of squares (ICSS) algorithm in the variance equations overcomes the overestimation of volatility persistence.
Moustafa (2011) model and forecast time vary stock return volatility in the Egyptian stock market using four models. The empirical results show that EGARCH is the best model between the examined models according to the usual evaluating statistical metrics (RMSE, MAE, and MAPE) and found no significance difference between the errors of competing models.
Scott (2006)used GARCH models with dummies to study the impact of U.S monetary policy on inflation. From the analysis, he concluded that the impact of U.S monetary policy on inflation is negative but not significant on the parameter of the dummy variable the parameter. Stock return volatility represents the variability of stock price changes during a period of time. This phenomenon has attracted growing attention of academia, policy makers and other players in this sector. This is because return is a major measure of risk associated with asset instead of price because if you want an investment that gives 10% of your return you invest on it than in price i.e. it is much better to deal with return than price. Also, high volatility in stocks, bonds and foreign exchange markets usually raise from important public policy issues about stability of financial market and impact of stock volatility on the economy cannot be sub estimated.
CHAPTER THREE
METHODOLOGY
Data for the study
Data for this study were from daily closing prices of Insurance stocks traded on the floor of the Nigerian Stock Exchange (NSE). These time series data cover almost fourteen years starting from 2nd January 2000 to 26th May, 2014. These Insurance are AIICO, GUINEAINS, GUINNESS, LASACO, LAWUNION, NEM, NIGERINS, PRESTIGE, UNIC AND WAPIC.
These makes the total number of Insurancecompainesto be considered ten. These data are available on Cash Craft website (www.cashcraft.com).
Computation of return series from price
æ Pt
Let Rt
= ln ç ÷
P
(3.1
where Pt and
Pt-1 are the present and previous closing prices and Rt
the continuously compounded return serieswhich is the natural logarithm of the simple gross return.
Steps-involve in building volatility models
Building a volatility model for an asset return series consists of principal steps namely:
- Compute return series from priceseries
- Test for the stationarity of the returnseries
- Specify the mean equation by building an econometric model such as AR (Autoregressive Model), MA (Moving Average), or ARMA (Autoregressive MovingAverage).
- Use the residuals of the mean equation to test for ARCH
- Specify volatility model if ARCH effects are statistically significant and performa joint estimation of the mean and volatility
- Check the fitted model carefully and refine it if
CHAPTER FOUR
RESULTS
Introduction
This chapter presents a detailed analyses of the data collected. To really come out with a good model of daily return volatility of some of the Nigerian Insurance stocks, both the symmetric and asymmetric models were fitted to the return series. Various heteroscedastic models considered include ARCH (1), ARCH (2), ARCH (3), GARCH (1, 1), GARCH (2, 1),
GARCH (1, 2), GARCH (2, 2), EGARCH (1, 1), EGARCH (1, 2), EGARCH (2, 1), EGARCH
(2, 2) and TARCH (1, 1) with each model incorporated with dummy variable as their independent variable to monitor the trend of the model in each of the stocks.
Furthermore, this Chapter also explains the properties of the return series, time plot for the return series, test for unit root, specification of the appropriate mean equation for return series, test for ARCH effect using Lagrange Multiplier, estimation of the parameters of the volatility models with incorporated dummy variable, selection of best of the twelve competing models and forecast performance evaluation of these models using Root Mean Square Error, Mean Absolute Error and Mean Absolute Percentage Error.
CHAPTER FIVE
SUMMARY, CONCLUSION AND RECOMMENDATION
This study examined the volatility pattern of some of the Nigerian Insurance stocks. Twelve different heteroscedastic models were considered by also incorporating an indicator variable using data set gathered which is the daily closing price between 2nd January, 2000 to 26th May, 2014.
Summary
Symmetric and Asymmetric distribution of the return in Nigerian Insurance stock
The symmetric nature of the return as observed in this study for majority Insurance stocks, is an indication that government regime shift has a significant impact on the return pattern of some of the Nigerian Insurance stock while the asymmetric nature of the return as observedin this study for majority Insurance stocks, is an indication that government regimeshift has a significant impact on the return pattern of Nigerian Insurance stocks. This phenomenon is referred as the leverage effect. This finding supported some of their studies in Nigeria (Dellah& Ade 2010). This result is not consistent with other studies conducted in other emerging capital market in other countries of the world (Sulimon, 2012; Moustafa, 2011; Hein, 2008) based on the symmetric nature of the return on some of the stocks.
Model used for forecasting
The result of study showes that symmetric volatility models are more superior to asymmetric models in dealing with regime switching. The Autoregressive Conditional Heteroscedasticity model (ARCH) proves to be the most suitable among the twelve competing volatility models considered. The result is considered to be in agreement with some of Dallah and Ade (2010) and Moustafa (2011) whose study observed that EGARCH (1, 1) model performed more than other volatility models, because in this study ARCH model is competing with EGARCH models. But in this study we find out that some of the stock actually exhibit asymmetric models, that is, EGARCH (1, 1) for AIICO and NEM, LAWUNION is EGARCH (2,
1), GUINNESS is GARCH (1, 2) while ARCH (1) for NIGERINS, UNIC and WAPIC while
ARCH (2) for PRESTIGE. To make a clear classification one can say that symmetric models are most suitable but one cannot ignore the changes in the trend of the series than to work with the appropriate suitable models for each of the stocks.
Summary of the Indicator variable on the volatility model
When the regime changes are incorporated into the model, it is found that the highly persistent volatility of the Insurance stock return rate is reduced for most of the stock, from the results presented in Table 4.6 and Table 4.7 in chapter four (4) above it gives a clear view in the parameter coefficient of the abrupt shift or pattern of the Insurance stocks on each of the volatility models using the indicator variable. It was observed that some of the stock did not actually exhibit downward shift in each of the volatility model carried out in this study while some exhibit a downward shift which indicate that their trend tend to drop from the series.
For AIICO Insurance, all heteroscedastic model fitted had all their parameter significant (p< 0.05) except that some of the model in the abrupt shift showed a positive values with significant level of 0.01.
The abrupt shift in modelling the time series using time plot of the closing price of some of the Insurance stocks is showed in appendix B.
Moreover, NEM, PRESTIGE and UNIC all the parameter estimated were significant except the leverage effect of the TARCH (1, 1) model (p>0.05). For PRESTIGE Insurance, the indicator variable is positive throughout the models indicating that the shift was positive. Results are presented in Table 4.6 and Table 4.7 with others Insurance stocks
Summary of finding
The preliminary analysis of the data obtained showes that the distribution of the returns in some of the Nigerian Insurance stocks were all stationary and that there was presence of ARCH effect (Heteroscedasticity) on eight of the Insurance. The results of the finding also revealed that the Nigerian Insurance stocks exhibit level of leverage which means that positive (good news) and negative (bad news) have a significant effect on the daily return pattern of the Nigerian Insurance stocks. Volatility persistence and clustering was also observed in the eight Insurance stocks. Finally, the results of the finding also revealed that the symmetric models outperformed their asymmetric counterpart in terms of forecasting ability.
Conclusion
This study had examined the daily return volatility of Nigerian Insurance sector stocks. The best model was computed using the AIC and SIC, the bolded models are considered the best fits model to be used in each of the stocks. The forecasting performance of several variants of conditional heteroscedasticity volatility models were evaluated using model evaluation performance measures like the Root Mean Square Error. The post estimation evaluation carried out revealed various conditional heteroscedasticity models to be most suitable for modelling the return pattern of the each Insurance. The EGARCH (1, 1) was suitable for AIICO and NEM, LAWUNION is EGARCH (2, 1), GUINNESS is GARCH (1, 2) while ARCH (1) for
NIGERINS, UNIC and WAPIC while ARCH (2) suitable for PRESTIGE. But looking at the Insurance and by evaluation one can say ARCH (1) was most suitable followed by EGARCH (1, 1). This finding is very crucial and informative to investors and intending investors who might want to invest in Insurance stocks.
Recommendation
Although the results of this study has proven to be consistent with some similar studies conducted in other emerging capital markets like Nigerian, the result should be treated with caution as this study covers some volatility models. We therefore recommend that appropriate models should be used in each of the Insurancestocks considered for this study in term of model selection, goodness of fit and forecasting.
Suggestion for further study
This study suggest further work on other useful volatility models like Multivariate GARCH models, stochastic volatility model, comparison of this research with dynamic conditional correlation models and hypotheses distribution with a more updated data even as the Nigerian Insurance stocks is developing. This will better inform investors, intending investors and investment analyst as volatility is the major index used to evaluate stock performance instead of price.
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