Looking At Stock Markets And Stock Exchanges

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02 Nov 2017

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Chapter 3

Literature Review

Volatility is one of the main features of the financial market, playing a significant role in managing portfolio, pricing of options and market conventions (Poon and Granger, 2003). Stock returns volatility varies considerably across global and have received a great consideration from researchers over past years since it can be utilized as a means to calculate risk in financial markets. Instability of stock returns has been a topic of interest in financial literature since long. A broad range of research has been carried out on stock returns volatility in both advanced and developing markets since 1970s. Financial economists are also curious about the sources as well as the inconsistencies relating to market volatility.

3.1 Theoretical Review

3.1.1 Stock Markets and Stock Exchanges

A stock exchange or bourse is a corporation or mutual organization which provides the facilities for stock brokers to trade company stocks and other securities. Stock exchanges also provide facilities for the issue and redemption of securities, as well as other financial instruments and capital events including the payment of income and dividends.

In other words, Stock Exchanges are an organised marketplace, either corporation or mutual organisation, where members of the organisation gather to trade company stocks and other securities. The members may act either as agents for their customers, or as principals for their own accounts.

Stock exchanges also facilitates for the issue and redemption of securities and other financial instruments including the payment of income and dividends. The record keeping is central but trade is linked to such physical place because modern markets are computerised. The trade on an exchange is only by members and stock broker do have a seat on the exchange.

The securities traded on a stock exchange include shares issued by companies, unit trusts and other pooled investment products as well as bonds. To be able to trade a security on a certain stock exchange, it has to be listed there.

Usually there is a central location at least for recordkeeping, but trade is less and less linked to such a physical place, as modern markets are electronic networks, which gives them advantages of speed and cost of transactions. Trade on an exchange is by members only; a stock broker is said to have a seat on the exchange.

The Stock Exchange provides companies with the facility to raise capital for expansion through selling shares to the investing public. The Stock Exchange also play an important role in the economy by mobilising Savings for Investment, Redistribution of Wealth, Improving Corporate Governance, Creates Investment Opportunities for Small Investors, Raises Capital for Development Projects and finally it acts as a barometer of the Economy.

3.1.2 Factors Affecting the Stock Market

Many kinds of factors affect the stock market. Social unrest can cause the market to drop, while a company discovering a new source of renewable energy can cause stock market prices to soar. Several economic factors affect the stock market that every investor should be aware of before getting involved in market investing.

Inflation And Deflation: Inflation, which is the rate at which the price of goods and services increases, can have an adverse affect on the stock market. High inflation causes investors to think that companies may hold back on spending; this causes an across the board decrease in revenue and the higher cost of goods coupled with the drop in revenue causes the stock market to drop. Deflation is when the cost of goods drops. While deflation sounds like it should be welcomed by investors, it actually causes a drop in the stock market because investors perceive deflation as the result of a weak economy.

Interest Rates: Interest can have an impact on the stock market. Higher interest rates mean that money becomes more expensive to borrow. To compensate for the higher interest costs, companies may have to cut back spending or lay off workers. Higher interest rates also mean that a company’s money cannot borrow as much as it used to, and this has an adverse affect on company earnings. All of this adds up to a drop in the stock market.

Foreign Markets: Economic trends in foreign markets can have an effect on the stock market. When the economies in foreign countries are down, local companies cannot sell as many goods overseas as they used to. This causes a drop in revenue, and that can show up as a drop in the stock market. Foreign stock exchanges also have an effect on the local stock market. If foreign exchanges start to fail or experience sharp drops, then that kind of activity can cause local investors to anticipate a ripple effect, resulting in a drop in the stock exchange.

3.1.3 Stock Market Volatility

Volatility, in its simplest form, refers to the variation in the price of a stock. Volatility of a security market is determined by the variation in the price over a period of time, calculated as the standard deviation of the market returns. The greater the variance, the greater is the asset volatility. An awareness of volatility in stock markets is therefore essential for finding out the cost of capital and for assessing investment and leverage decisions as volatility is identical to risk. Considerable shifts in volatility of financial can have major negative effects on risk averse investors.

3.1.4 Sources of Volatility

The issue of stock market volatility has obtained much attention in the finance literature. Securities markets are often characterized by periodic bouts of volatility, whereby prices will increase and decrease sharply and randomly. This volatility is often incited by economic causes, which have an effect on the confidence that investor have on the listed companies, resulting in a movement of their funds into and out of the securities.

Inflation can be seen as a major source of stock volatility. Inflation is said to occur when there is a continuous rise in the general price levels which causes the value of a currency to fall. Whilst mild inflation is regarded as normal, it is feared that if the rate of inflation is rising too fast, this can lead to volatility in the securities market, since inflation has an unpredictable effect on an economy and have an effect on different firms in different ways. As their expenses are rising, companies are likely to charge a higher price for their goods.

Consumer expenditure is the lifeblood of an economy. There is development in the economy as consumer spending rises and firms suffer when there is a fall in consumer spending. That's why, investors focus mainly on consumer expenditure indices. Signs of a variation in consumer expenditure can affect the economy. When the market obtains different indications; for instance, enhanced consumer assurance along with a fall in expenses can cause volatility.

Interest rates are defined as the amount charged, by a lender for the use of money by the borrower. Time and again, this rate may be influenced by the monetary policy adopted by central bank. When there is a low rate of interest, people are likely save less money, since banks are offering low returns on their deposits. When there is an increase in interests, saving increases as well. The consequences of variations in the interest rate can be understood in different ways by different investors, which results in volatility.

The wellbeing of foreign economies, generally revealed in activities on their stock exchanges, can have various different impacts on local markets. In certain cases, investors will fear that crises in foreign countries may affect the local country and thus cause securities prices to drop. In other circumstances, investors will transfer funds from overseas firms into local firms, resulting in an increase in prices. The interaction of these two responses can generate volatility.

The bond and the securities markets are directly related. Many firms listed on the securities market have issued bonds on the bond market or, in the case of investment banks and other firms that manage huge financial portfolios, hold several of the bonds. Instability in the bond market, can have an effect on the price charged by firms to lend money and this can be the source volatility in the securities market.

Dividends are among the most frequent sources of stock market volatility. Basically, dividends are the income paid to investors by firms when the business is flourishing. If a company has a very unproductive year, it may not make any dividend payments. If investors come across information that makes it looks that dividends for a firm (or particularly an industry) will go down, then securities prices will rapidly drop. Unfortunately, volatility most often indicates an abrupt reduction in price rather than an unexpected increase.

Stock market efficiency can also be seen as a reason of some volatility. Although the securities market is mostly electronic, not all information movement is instantaneous. Information requires time to arrive at investors and have an effect on the market itself. There are interruptions and misunderstandings. Consequently, the market loses firmness and responds too easily to information that is not evenly corresponded.

Investor response is a further source of volatility in the securities market. If the market seems as if it is collapsing, then many investors will promptly dispose of their shares or trade to compensate expected losses. This makes the market drop even more rapidly in a snowball reaction. Investor reactions to unexpected movements of the market often worsen the problem.

Business performances and shifts directly have an impact on the securities market. This indicates that aspects in businesses that swiftly vary also be at the origin of sudden market changes, and thus causing increased volatility. A company may all of a sudden amend a marketing promotion, or get itself manipulated by latest business legislation, or may have to to abruptly alter inventory. Any practice that a business may rapidly modify can also cause abrupt changes in the securities market.

3.1.5 Stock Market shocks

The term "shock" refers to an outlier which has been triggered by an event exogenous to the market. Therefore, a stock market shock can be referred to as a disruption of market equilibrium (that is, a market adjustment) which reflects substantial pieces of market news. Market shocks can have an impact on financial stability and have repercussions in the real economy.

News of local or world events can impact stock value. If a company announces the closing of a division or the layoff of workers, that may cause the company’s stock price to drop. On the other side, bad news about a company may cause the stock value of its competition to go up. Market shocks may also result from announcements made by the company, such as merger decisions, dividend payments or publication of financial statements.

3.1.6 Causes of Market Shocks

There are several circumstances whereby pieces of news relating to a particular company can cause a market shock which in turn impact on share prices. Some of them are described below:

Market Scandals: Traders tend to frown upon corruption in the stock market. Mutual fund scandals that have occurred in the past few years and corporate corruption such as Enron are two such examples. If people cannot trust the stock market, why would they invest their hard-earned money in it? In these situations it is harder for the market to go up because there is a lower demand for stocks.

Analyst Recommendations: Many traders rely on experts' opinions about companies and future stock prices. However, they are not always correct. Nobody can predict what will happen in the future. They can, however, make educated guesses based on past performances and future prospects for the companies and industries they follow. Analysts’ recommendations on "buy" or "sell" decisions affect prices of stocks in question as investors normally take heed of such recommendations. The public normally accepts the advice given by the analysts since the analysts are specialists in their respective fields. 

Credit Rating News: Many Credit rating agencies track the performance of companies and rate them on periodical basis. If a major credit rating agency downgrades its rating on a company and the news is released on TV channels or print media, than market reacts to it and share price fall. The reverse happens when credit rating agency upgrade their rating on a company.

3.1.7 Impact of Market shocks on share prices

Market Shock is an important factor that affects the share price. When there is positive news or shock about a particular stock or company, people try to invest all their money in that particular stock or market. This leads to increase in the interest of buying the stock. But there are many circumstances where news could also bring a negative effect where it could ruin the prospect of the particular stock. So it is very important to know the overall news of a stock or company where people can invest their money so that it grows within a very short period of time.

News from the specific company and other domestic and global events also play a large role in the direction of the share price and stock market. Some examples of these are interest rates of major economies, monetary policies and export policies, oil prices, inflation, and terrorist attacks and so on. Every analyst and trader has a different perception of what that stock price should be now and where it might be in the future, and trading decisions are made accordingly. 

3.1.8 Relationship between Market Shocks and Stock Market Volatility

Stock market volatility shocks are associated in a causal way to output and inflation volatility shocks. A non negligible portion of the short run stock volatility process is not explainable on the basis of the persistent volatility factors, and may be seen as a reaction to shocks to market volatility itself.

There are many economic reasons for which larger, in magnitude, return shocks can cause persistent shifts in the level of market volatility, which can change over time. These can be attributed to Financial leverage effects or feedback volatility (risk premium). If the shifts in volatility are not accounted for, they will overstate evidence of very high persistence in volatility. A smaller degree of persistency can dampen the feedback volatility effects faster, and thus positive (good) return shocks will result in significant drops of volatility.

3.1.9 Announcements causing Stock Market Volatility

Stocks price changes due to market forces, i.e. buying and selling of the available stocks in the market. The following are the some announcements that affect or even predict the buying or selling of stock that ultimately affects stock prices of companies.

The earning results and earning guidance: The main objective of a company is to make profit. Therefore, investors and traders always assess a company based on its Earning Per Share Revenue and its future earning potential. In Mauritius, companies generally report the earnings results every quarter-yearly. A company that achieves good earning results (EPS and Revenue) expects a boost in its share price and one that delivers poor earning result shall see a beating in its share price. Sometimes, besides reporting the EPS and Revenue for the past quarter, a company may also issue guidance (expected value) for the EPS and Revenue in coming quarter or coming years. This is also closely monitored by investors and is an important factor that will affect the company stock price.

Take-over or merger: In general, a company being taken-over is anticipated to get a stock price boost and the company taking over another company shall experience a drop in its share price. This is assuming that the company is being taken over at a premium, meaning it is being bought over at a higher price than its last traded stock price. Depends on the agreed term, a company can be bought over by cash or stock (of the acquirer) or a combination of the two. In some minority cases, the stock price of the acquirer may get a boost if it is perceived that the acquisition shall contribute to its earning or revenue in the near future.

New product introduction to markets or introduction of an existing product to new markets: The introduction of new product to market is seen as a revenue enhancer for a company. This also applies to an existing product that breaks into new markets. Sometimes, the prospect of a new product introduction suffices to improve the stock price of a company, this is often observed in surges in stock prices of pharmaceuticals companies after the announcement of successful clinical trials, or FDA approvals for new drugs.

New major contracts or major Government Orders: A company that is able to obtain new major contracts or major government order is expected to see a bull run in its stock price. Those companies that fail in the contract bidding normally experience the fate of sell-off in its stocks.

Share buy-back: The act of share buy-back by a company will reduce the number of share available in the open market. Due to the law of supply and demand, a reduction in share available for trading in this case will cause a drop in supply, this will normally help increase the share price. Also, the continuing buying back of share of a company will also acts as a support for the share price that helps to maintain or increase the share price.

Dividend: After the announcement of a dividend. The stock price may increase by an amount close to the dividend per share value. However, the stock price may drop on the ex-dividend date by the dividend per share amount. This is because anyone buying a stock on or after the ex-dividend date are not entitled to the corresponding dividend payment.

3.1 Empirical Review

Madhavan (1992) explains volatility in the form of price divergence. Low volatility is needed since it reduces the unnecessary risk taken by investors and because to this market traders can easily sell their assets without facing the risk of adverse massive price movements. On the other hand, Jayasuriya (2002) argue that volatility is harmful as it makes investors averse to holding stocks, increase risk premiums and the cost of capital, and decreases investment

There are a number of negative implications of the stock market volatility. One implication is that market volatility influences the economy by having an impact on spending patterns of the consumer (Campbell, 1996; Starr-McCluer, 1998;Ludvigson and Steindel 1999 and Poterba 2000). The impact of volatility on consumer expenditure is related to the wealth effect. Increased wealth causes increased spending while fall in stock market reduces spending. Business investment (Zuliu, 1995) and economic growth (Levine and Zervos, 1996 andArestis et al 2001) are also directly concerned by stock market volatility. In case of increased volatility, equity investments can be seen as more risky and the investments can be shifted to relatively less risky assets.

3.2.1 Determinants of Stock market volatility

A increasing concern has come forward in recent years investigating the determinants of volatility spread across stock markets.

3.2.1.1 Inflation

The link between stock market returns and inflation, if any has raised the interest of researchers and practitioners in the same way mainly since the twentieth century. The basis of the discussion is the Fisher (1930) equity stocks declaration. According to the generalized Fisher (1930) hypothesis, equity stocks signify claims against real assets of a business; and as such, may provide a hedge against inflation. If so, then investors could exchange their financial assets in return for real assets when anticipated inflation is asserted. In such a situation, share prices in nominal terms should completely mirror expected inflation and the linkage between these two variables should be positively correlated ex ante (Ioannides, et.al., 2005:910). This debate of equity market providing a hedge against inflation may also mean that investors are wholly paid off for the increase in the general price level through equivalent rises in nominal share market returns and therefore, the real returns stay unaffected.

Further extension of the hedge hypothesis posits that since equities are claims as current and future earnings, then it is expected that in the long run as well, the stock market should equally serves as a hedge against inflation. Fama (1981) however, put up a proxy hypothesis when he argued the relationship between high rates of inflation and future real economic growth rates as negative. Views that rationalize the negative co-movements between inflation rates and real stocks returns however differ.

The inflation illusion hypothesis of Modigliani and Cohn (1970) point’s out, that the real effect of inflation is caused by money illusion. According to Bekaert and Engstrom (2007:1), inflation illusion suggest that when expected inflation rises, bond yields duly increase, but because equity investors incorrectly discount real cash flows using nominal rates, the increase in nominal yields leads to equity under-pricing and vice versa.

3.2.1.2 Interest Rate

Available literature in finance, discusses the relationship between interest rates and stock returns in different ways. Relating short term interest rates with stock returns and market volatility, Shanken (1990) and Campbell (1987) found that nominal one-month T-bill yield has a significantly positive relation with market variance but negatively correlated with future stock returns. Whitelaw (1994) also reported a positive relationship between market volatility and the one-month T-bill yield. Bren’ et al. (1989) provided evidence that one-month interest rate is helpful in predicting the sign and the varianceof the excess return on stocks.

Rizwan and Khan (2007) also examined role of macroeconomic variables and global factors on the volatility of the stock returns in Pakistan. They analyzed Pakistan’s equity market as a consequence of interest rate, exchange rate, industrial production, and money supply being domestic macroeconomic variables and 6-month LIBOR and Morgan Stanley Capital International (MSCI) All Countries World Index as global variables. After applying EGARCH and VAR models they collectively explained varying importance of domestic macroeconomic variables in explaining the relationship between stock returns and volatility in Karachi Stock Exchange and did not discussed contribution of each variable separately.

3.2.1.3 GDP growth

Empirical studies have identified that the economic fluctuations within a country influence stock market returns and volatility. Using the US data Schwert (1989b, 1990b) and others identified stock market volatility increases during economic recession. However, the influence from stock market volatility to macroeconomic volatility is higher than that from macroeconomic volatility to stock market volatility. According to Ritter (2005), the relationship between stock returns and economic growth is significant for investors to manage their portfolios utilizing the release of macroeconomics news to identify stock market trends.

In addition, Brooks et al. (1999) argued that the good and bad news of GDP and current account balance have no impact on stock returns. Groenewold (2003) also could not find an influence on the share prices from real output after deregulation of the financial market. However, the findings of Groenewold (2003) indicated that the share prices influence real output the during post- deregulation period. In contrast, Chaudhuri and Smiles (2004) identified a significant effect on the stock returns from the growth rate of real GDP. They also found that negative effect from the two lags of real consumptions towards the stock price movement.

Besides the influence from domestic economic factors, Kim and In (2002) and Kim (2003) identified international macroeconomic influence towards the stock returns and volatility. Even though these two studies incorporate influence from other countries to their models, their approaches are confined to univariate GARCH models. Thus, they did not capture the varying volatility implications on covolatility across local and international stock markets and macroeconomic variables from corresponding countries. The current study therefore, focuses to fill this gap in the literature.

3.2.1.4 Stocks traded

During the last decades a number of interesting studies have sought to explain the empirical relationship between trading volume and stock returns. The early literature is well represented by Ragalski (1978), Figlewski and Cornell (1981) who studied the basic relationship between the variables. The linear and non-linearcausality between the stock prices and trading voume has also received a substantial amount of attention in the literature Campbell et.al (1993), Hiemstra and Jones (1994). This investigation has also been extended to bond and futures markets Clark (1973), Hanna (1978), Grammatikos and Saunders (1986) and the examination of cross-country spillovers between trading volume and stock returns Lee and Rui (2002).

Furthermore, Ragunathan and Pecker (1997) focus on the relationship between volume and price variability for the Australian futures market and explore positive relationship between volume and volatility by documenting asymmetric volatility response to unexpected shocks in trading volume by using the model developed by Bessembinder and Seguin (1993). Positive unexpected shocks to trading volume were found to induce an average increase in volatility at 76 per cent, while negative unexpected shocks to trading volume induce a smaller response in volatility. Daigler and Wiley (1999) examine the volume-volatility relation in futures markets for Chicago Board of Trade for four types of traders.

Another stand of the literature has focused more directly on the casuality between trading volume and stock returns. Several studies have tested by using (VAR) Granger Causality between the two series using different samples and estimated techniques. Campbell, Grossman and Wang (1993) examine the level of price changes is influencedby high volume will tend to be reversed, and the reversal will be less due to price changes on days with low volume. Blume et.al (1994) derives that investors can able to predict the market information with past price and trading volume. Wang (1994) shows that investors trade informational and non-informational reasons will also lead to different dynamic between trading volume and stock returns.

3.2.1.5 Exchange Rate Regimes

There exists a branch of literature that considers the impact of exchange rate volatility on the macro economy, which depends on the exchange rate regime which the economy follows, although there has been no clear agreement on the ideal regime for macroeconomic performance.

Those who are in favour of fixed exchange rate regimes, such as Mc Kinnon (1963), Mundell (1973), Frankel and Rose 2002) stipulate that the macroeconomy growth is enhanced through higher trade levels which would promote economic stability, foreign direct investment, economic growth and hence standard of living. However, more recently, Fischer (2001), argues that fixed exchange rates would support speculative capital inflows, moral risk and overinvestment. On the other side, those who are in favour of flexible exchange rates (Meade 1951, Friedman 1953 et al), argue that fluctuating exchange rate helps to correct disequilibrium both, local and external, despite real asymmetric shock. Under a situation of fixed exchange rate regime and international capital mobility, money supply is believed to be derived such that money demand shocks cause money supply to change and therefore LM shocks leave output or inflation unchanged. Under a fixed exchange rate, an external shock is detrimental to the domestic economy. A decline in foreign income might lead to a fall in domestic demand for exports and since exports are an important function of aggregate demand, the adverse shock to aggregate demand will lead to a fall in domestic income and employment via the multiplier effect.

Under a system where exchange rate is determined by market forces, the effect will be alleviated through a depreciation of the exchange rate. Hence a foreign shock will have different effects under different exchange rate regimes. Similarly, a rise in foreign interest rates may lead to a depreciation and an increase in income under fluctuating exchange rates while under a fixed exchange rate system, there is bound to be a monetary contraction and a decrease in income. Empirical studies regarding exchange rate volatility and macroeconomic performance is limited in small island economies. However, empirical studies comprise of Baxter and Stockman (1989), Flood and Rose (1995),Crosby (2000), Bayoumi and Eichengreen (1994) and Kwan and Lui (1999). Baxter and Stockman (1989) reveal a smaller amount of evidence on macroeconomic behaviour or trade flows under differing exchange rate regimes for a sample of 49 countries.

3.2.2 Stock Volatility and Market Shocks

There are several economic reasons for which return shocks, to some extent can cause persistent changes in the level of market volatility, which can vary over time. These can be attributed to financial leverage effects or feedback volatility (risk premium) effects (French et al (1987), Schwert(1990), Campbell and Hentschel (1992), Bekaert and Wu (2000), or more recently, Mele (2007) and Ozdagli (2012)). If the above shifts in volatility are not taken into consideration, they will overemphasize evidence of very high persistence in volatility (Psaradakis and Tzavalis (1999)). As more recently noted by Malik (2011), a smaller degree of persistency can dampen the feedback volatility effects faster, and thus positive (good) return shocks will result in significant falls of volatility.

The empirical literature stated above treats large stock market return shocks as exogenous. To examine their effects on volatility, it relies on the intervention- dummy variable analysis of Box and Tiao (1975), based on exogenous information from the sample to determine the time points that the breaks driven by large shocks occur. Of course, more sophisticated multi break testing procedures can be applied to find out from the data the timing of the breaks, like those employed for breaks in the mean of series (Bai and Perron (2003)). But, as in the intervention analysis, these methods do not treat the break process as an endogenous process, specified as a part of volatility model. By doing this, volatility models can allocate for richer dynamics which can facilitate the classification of different economic sources (or market events) of volatility shifts from the data and to study the dynamic effects of market return shocks on volatility functions. Separating the impact of these return shocks on volatility from those of ordinary return shocks can also have important repercussions for long-term portfolio management and hedging, as it will bring more attention on controlling important sources of risks caused by long-term shifts in volatility leaving aside its short-term ones. As shown by many studies based on intervention analysis, these type of shifts in volatility or stock prices co-movements tend to be mainly driven by large market shocks (Karolyi and Stulz (1996); Chen et al (2003)).

Moreover, economic shocks lead to lower prices because of restricted opportunities for portfolio diversification since all stocks are connected to the domestic economy. Investors are compensated for assuming this risk by means of higher expected returns, which is explained by a higher cost of capital. In the integrated market, investors hold an internationally diversified portfolio meaning that bad news shocks in one country can be offset by good news shocks from elsewhere. Investors do not require a premium to compensate for individual market volatility meaning that the cost of capital is lower in integrated markets (Bekaert and Harvey, 1998)..

3.2.4 Implications of Stock Market Volatility

According to Krainer (2002), the extent of volatility in the stock market cam help to forecast the path of an economy’s growth and the composition of volatility can entail that investors now require to hold more securities in their portfolios to attain diversification

There are, however a number of negative implications of the stock market volatility. One implication is that market volatility influences the economy by having an impact on spending patterns of the consumer (Campbell, 1996; Starr-McCluer, 1998;Ludvigson and Steindel 1999 and Poterba 2000). The impact of volatility on consumer expenditure is linked to the wealth effect. Increased wealth causes increased spending while fall in stock market reduces spending.

However, a drop in stock market will weaken consumer assurance and thus reduce consumer spending. Stock market volatility may also have an effect on business investment (Zuliu, 1995) and economic growth directly (Levine and Zervos, 1996 and Arestis et al 2001). An increase in stock market volatility can be taken as an increase in risk of investing in stocks and therefore a transfer of funds to less risky assets. This shift could lead to a rise in cost of finance to businesses and consequently new business might tolerate this effect as investors will turn to acquire shares in larger, renowned firms.

3.2.5 Previous Studies on Stock Market Volatility

Stock prices volatility is an extremely important concept in finance for numerous reasons. Researchers in quest of the causes of volatility has investigated the stock prices volatility from different angels. In this regards, from late twentieth century and particularly after introducing ARCH model by Engle (1982), as said by Bollerslev (1999) and Granger and Poon (2000) several hundred research that mainly accomplished in developed country and to some extent in developing countries has been done by researchers in this area using different methodology. A glimpse of these studies is as follows:

Engle (1982) published a paper that measured the time-varying volatility. His model, ARCH, is based on the idea that a natural way to update a variance forecast is to average it with the most recent squired "surprise"(i.e. the squired deviation of the rate of return from its mean).While conventional time series and econometric models operate under an assumption of constant variance, the ARCH process allows the conditional variance to change over time as a function of past errors leaving the unconditional variance constant. In the empirical application of the ARCH model a relatively long lag in the conditional variance equation is often called for, and to avoid problems with negative variance parameters a fixed lag structure is typically imposed.

Bollerslev (1986) to overcome the ARCH limitations introduced his model, GARCH, that generalized the ARCH model to allow for both a longer memory and a more flexible lag structure. As noted above, in the empirical application of the ARCH model, a relatively long lag in the conditional variance equation is often called for, and to avoid problems with negative variance parameters a fixed lag structure is typically imposed. In the ARCH process the conditional variance is specified as a linear function of past sample variance only, whereas the GARCH process allows lagged conditional variances to enter in the model as well.

Engle and Ng (1993) measure the impact of bad and good news on volatility and report an asymmetry in stock market volatility towards good news as compared to bad news. More specifically, market volatility is assumed to be associated with the arrival of news. A sudden drop in price is associated with bad news on the other hand, a sudden increase in price is said to be due to good news. Engle and Ng find that bad news create more volatility than good news of equal importance. This asymmetric characteristic of market volatility has come to be known as the "leverage effect". The studies of Black (1976), Christie (1982), FSS (1987), Schwert (1990) and Pagan and Schwert (1989) also explain this volatility asymmetry with the" leverage effect". However, their models do not capture this asymmetry. Engle and Ng (1993) provide new diagnostic tests and models, which incorporate the asymmetry between the type of news and volatility, they advise researchers to use such enhanced models when studying volatility.

Chapter 4

Data and Methodology

4.1 Data Descriptive

4.1.1 Data

The purpose of this dissertation is to model volatility of Mauritian stock market to find if it stock market volatility has a relationship with market shocks. In order to propose suitable specifications, it is reasonable to investigate the nature of the data set. The characteristics of the data and their descriptive statistics partly indicate appropriate models which should be performed. For instance, if the return series exhibit asymmetries, we should employ asymmetric models. Therefore, in this sub-section, the data and its descriptive statistics is showed and explained.

The data source is the yearly average stock prices of the Stock Exchange of Mauritius Total Return Index, the SEMTRI, obtained from the databank of the Stock Exchange of Mauritius (SEM) website.

The main purpose of the SEMTRI is to offer local and overseas market participants an essential means for measuring the performance of the domestic market. In addition to detecting the price changes of listed securities, which is already included in SEMDEX, the, SEMTRI, integrates a further feature to offer investors, in general, and especially long-term investors like pensions funds with a good evaluation of total return which merges both capital gains or losses on registered securities and gross dividends acquired on these stocks. Gross dividends are presumed to be re-invested in the securities forming part of the capital index, SEMDEX.

The returns on SEMTRI will be the dependent variable (Y) and there will also be five independent variables (Xs), namely Inflation rate, Interest rate spread (lending rate minus deposit rate, %), GDP growth, Stocks traded, turnover ratio (%) and Official exchange rate (LCU per US$, period average).The data source for the independent variables is the World Bank Website.

The variables sample starts in 1990 and ends in 2011, constituting a total of 22 observations.

4.1.2 Definition of variables

Return on SEMTRI: Return on SEMTRI is defined as the change in the value of the index. It is calculated using the formula (P1 - P0), where P1 is the actual index while P0 is the index for the previous period

Inflation, consumer prices (annual %): Inflation as measured by the consumer price index reflects the annual percentage change in the cost to the average consumer of acquiring a basket of goods and services that may be fixed or changed at specified intervals, such as yearly. The Laspeyres formula is generally used.

Interest rate spread (lending rate minus deposit rate, %): Interest rate spread is the interest rate charged by banks on loans to private sector customers minus the interest rate paid by commercial or similar banks for demand, time, or savings deposits. The terms and conditions attached to these rates differ by country, however, limiting their comparability.

GDP Growth: Annual percentage growth rate of GDP at market prices based on constant local currency. Aggregates are based on constant 2000 U.S. dollars. GDP is the sum of gross value added by all resident producers in the economy plus any product taxes and minus any subsidies not included in the value of the products. It is calculated without making deductions for depreciation of fabricated assets or for depletion and degradation of natural resources.

Stocks traded, turnover ratio (%): Turnover ratio is the total value of shares traded during the period divided by the average market capitalization for the period. Average market capitalization is calculated as the average of the end-of-period values for the current period and the previous period.

Official exchange rate (LCU per US$, period average): Official exchange rate refers to the exchange rate determined by national authorities or to the rate determined in the legally sanctioned exchange market. It is calculated as an annual average based on monthly averages (local currency units relative to the U.S. dollar).

4.1.3 Descriptive Statistics

An initial investigation of data exhibits some indications about Mauritian stock market, in terms of its mean, median, standard deviation, minimum value, maximum value, skewness and kurtosis, as shown in the table

SEMTRI Return

Inflation Rate

Interest Rate

GDP Growth

Stock Traded

Exchange Rate

 Observations

 22

 22

 22

 22

 22

 22

 Mean

 0.179034

 1.813263

 1.922475

 1.454531

 1.671848

 3.168706

 Median

 0.170840

 1.878114

 2.296261

 1.472694

 1.773550

 3.290891

 Maximum

 0.526394

 2.601807

 2.624065

 2.200177

 2.234865

 3.464479

 Minimum

-0.161034

 0.936019

-0.644357

 0.216230

 0.544727

 2.698906

 Std. Dev.

 0.189748

 0.401346

 0.896636

 0.449645

 0.466777

 0.268699

 Skewness

 0.152649

-0.326855

-1.956573

-0.943939

-1.214344

-0.544586

 Kurtosis

 2.234045

 2.960565

 5.498550

 3.908710

 3.909072

 1.690388

 Jarque-Bera

 0.623237

 0.393150

 19.75917

 4.024020

 6.164524

 2.659597

 Probability

 0.732261

 0.821540

 0.000051

 0.133720

 0.045855

 0.264531

 Sum

 3.938746

 39.89178

 42.29445

 31.99968

 36.78066

 69.71153

 Sum Sq. Dev.

 0.756088

 3.382657

 16.88307

 4.245789

 4.575501

 1.516183

Skewness refers to an indicator used in distribution analysis as a sign of asymmetry and deviation from a normal distribution. The SEMTRI return has a positive skewness statistics, which indicates that it is a right skewed distribution. This means that most values are concentrated on left of the mean, with extreme values to the right. On the other hand, Inflation rate, Interest rate, GDP growth, Stocks traded and Exchange Rate have got a negative skewness coefficient. This signify that the distribution for those variables are skewed to the left, that is most values are concentrated on the right of the mean, with extreme values to the left.

Kurtosis is an indicator used in distribution analysis as a sign of flattening or "peakedness" of a distribution. The kurtosis statistics for SEMTRI return, Inflation rate and exchange rate are less than 3. This indicates the presence of a Platykurtic distribution, flatter than a normal distribution with a wider peak. The probability for extreme values is less than for a normal distribution, and the values are wider spread around the mean. The other variables Interest rate, GDP growth and stock traded has got a coefficient of more than 3, showing the existence of a Leptokurtic distribution, sharper than a normal distribution, with values concentrated around the mean and thicker tails. This means high probability for extreme values.

The fact that past stock data, that is the SEMTRI returns results in a platykurtic distribution, analysts will expect more volatility in future returns. This means that there is a higher probability than usual for extreme price movements to occur. However, given that the returns are positively skewed means that the distribution is dominated by positive surprises.

The Jarque–Bera test is a goodness-of-fit test of whether sample data have the skewness and kurtosis matching a normal distribution. The p-value for all the variables are greater than 0.05. Thus we do not reject the null of normality at the 5% level. This means that the series follow normal distributions

Probability is the probability that Jarque-Bera statistic exceeds (in absolute value) the observed value under the null hypothesis of a normal distribution.

4.2 Methodology

In the previous section, we have showed the evidence of significant variations from normality and obvious leptokurtosis in our data series. We need to specify the models suitable to capture these characteristics. The Generalized Autoregressive Conditional Heteroscedatic (GARCH) models have been proven to be particularly appropriate for modeling the time-varying volatility. These models are able to capture the three most common features in time series which are fat tails, skewness and volatility clustering. The time-varying in volatility and the mean non-stationarity causes the fat tails and skewness in distribution of stock returns, respectively.

4. 2.1 Stationary Test

Before performing any further tests on the data set, it is important to test for stationarity. The reason is that a stationary time series has three important properties. First, it has a finite mean which implies that a stationary series fluctuates around a constant long-run mean. Second, a stationary time series has a finite variance, i.e. variance is time invariant. Third, a stationary time series data set has finite auto-covariance. This reflects that theoretical auto-correlation coefficient decay fast as lag length increases.

4. 2.1.1 Augmented Dickey Fuller (ADF)

An augmented Dickey–Fuller test (ADF) is a test for a unit root in a time series sample. It is an augmented version of the Dickey–Fuller test for a larger and more complicated set of time series models. The augmented Dickey–Fuller (ADF) statistic, used in the test, is a negative number. The more negative it is, the stronger the rejection of the hypothesis that there is a unit root at some level of confidence.

The unit root test is then carried out under the null hypothesis \gamma = 0against the alternative hypothesis of \gamma < 0. Once a value for the test statistic

DF_\tau = \frac{\hat{\gamma}}{SE(\hat{\gamma})}

is computed it can be compared to the relevant critical value for the Dickey–Fuller Test.

If the test statistic is less (this test is non symmetrical so we do not consider an absolute value) than (a larger negative) the critical value, then the null hypothesis of \gamma = 0is rejected and no unit root is present.

4.2.1.2 Cointegration

Two non-stationary time series are cointegrated if they tend to move together through time In the opaque terminology used in the time series literature, each series is said to be "integrated of order 1" or I(1). If the two non-stationary series move together through time then we say they are "cointegrated." Economic theory would suggest that they should be tied together via arbitrage, but that is no guarantee, so we perform a formal statistical test.

4.2.1.3 Test for Correlation – Durbin Watson

The Durbin–Watson statistic is a test statistic used to detect the presence of autocorrelation (a relationship between values separated from each other by a given time lag) in the residuals (prediction errors) from a regression analysis. It is a test for first-order serial correlation in the residuals of a time series regression.

The "Durbin-Watson test for autocorrelation'' is a statistic that indicates the higher chance of that the deviation (error) values for the regression to have a first-order autoregression component.

If et is the residual associated with the observation at time t, then the test statistic is

d = {\sum_{t=2}^T (e_t - e_{t-1})^2 \over {\sum_{t=1}^T e_t^2}},

where T is the number of observations and r is the sample autocorrelation of the residuals

4.2.2 Testing for AutoRegressive Conditional Heteroskedasticity (ARCH) Effects

AutoRegressive Conditional Heteroskedasticity (ARCH) models are used to characterize and model observed time series. They are used whenever there is reason to believe that, at any point in a series, the terms will have a characteristic size, or variance. In particular ARCH models assume the variance of the current error term or innovation to be a function of the actual sizes of the previous time periods' error terms: often the variance is related to the squares of the previous innovations.

Such models are often called ARCH models (Engle, 1982), although a variety of other acronyms are applied to particular structures of model which have a similar basis. ARCH models are employed commonly in modeling financial time series that exhibit time-varying volatility clustering, i.e. periods of swings followed by periods of relative calm.

To recognize the presence of conditional heteroskedasticity is the same as to indentify whether an ARCH process appears in the innovation term sequence. The squared residual series εt2 are conducted to test the conditional heteroskedaticity which is known as ARCH effect (Tsay, 2005).

According to Tsay (2005), there are two available methods to test for the ARCH effects. The first test is the Ljung-Box Statistic Q(m) proposed by McLeod and Li (1983). The null hypothesis is that the first m lags of ACF of the squared residuals series are equal to zero. The Q-statistics are significant at all lags, indicating significant serial correlation in the residuals.

The second test is the Lagrange Multiplier test. The first step of the test is to estimate the mean equation:

Rt = c + εt

by OLS to obtain the estimated residual series ἓt and then run them on lagged squared terms and a constant as follows:

ἓ2 = ϒ0 + ϒ1 ἓ2t-1 + … ϒq ἓ2t-q + c

The null hypothesis is that ϒ0 = ϒ1 = … = ϒq = 0 The test statistic is defined as R2*T (the coefficient of multiple correlation multiplied by the number of observations) and follow a χ2 distribution with q degree of freedom. This procedure was suggested by Engle (1982). If the value of test statistic is greater than the critical value from the χ2 distribution (F> χ2m (α)) or the p value of F is less than α, then reject the null hypothesis. The rejection of null hypothesis indicates the evidence of the ARCH(q) effects.

We need to form an equation, showing the relationship between the dependent variable, SEMTRI Return with the independent variables, namely Inflation rate, Interest rate spread (lending rate minus deposit rate, %), GDP growth, Stocks traded, turnover ratio (%) and Official exchange rate (LCU per US$, period average), as shown below:

Y = -0.792597 + 0.197181X1+ 0.012210X2 + 0.087241X3 + 0.041674X4 + 0.114670X5 + μ

Where,

Y - SEMTRI Return

X1 - Inflation rate

X2 - Interest Rate

X3 - GDP Growth

X4 - Stock Traded

X5 - Exchange Rate

μ - error term.

4.2.2.1 ARCH LM Test

This is a Lagrange multipler (LM) test for autoregressive conditional heteroskedasticity (ARCH) in the residuals (Engle 1982). This particular specification of heteroskedasticity was motivated by the observation that in many financial time series, the magnitude of residuals appeared to be related to the magnitude of recent residuals. ARCH in itself does not invalidate standard LS inference. However, ignoring ARCH effects may result in loss of efficiency.

The ARCH LM test statistic is computed from an auxiliary test regression. To test the null hypothesis that there is no ARCH up to order q in the residuals, we run the regression,

еt2 = β0 + β1 е2t-1 + β2 е2t-2 +…+ βq е2t-q + υt

where e is the residual. This is a regression of the squared residuals on a constant and lagged squared residuals up to order q.

4.2.2.2 Ljung-Box test

The Ljung–Box test is a sort of statistical test which tests whether any of a group of autocorrelations of a time series are different from zero. Instead of testing randomness at each distinct lag, it tests the "overall" randomness based on a number of lags, and is therefore a portmanteau test.

The Ljung–Box test test can be defined as follows.

H0: The data are independently distributed (i.e. the correlations in the population from which the sample is taken are 0, so that any observed correlations in the data result from randomness of the sampling process).

Ha: The data are not independently distributed.

The test statistic is:

Q = n\left(n+2\right)\sum_{k=1}^h\frac{\hat{\rho}^2_k}{n-k}

where n is the sample size, \hat{\rho}_kis the sample autocorrelation at lag k, and h is the number of lags being tested. For significance level α, the critical region for rejection of the hypothesis of randomness is

Q > \chi_{1-\alpha,h}^2

where \chi_{1-\alpha,h}^2is the α-quantile of the chi-squared distribution with h degrees of freedom.

4.2.3 Generalized Autoregressive Conditional Heteroskedasticity (GARCH) Model

If an autoregressive moving average model (ARMA model) is assumed for the error variance, the model is a generalized autoregressive conditional heteroskedasticity (GARCH, Bollerslev(1986)) model.

In that case, the GARCH(p, q) model (where p is the order of the GARCH terms ~\sigma^2 and q is the order of the ARCH terms ~\epsilon^2 ) is given by

\sigma_t^2=\alpha_0 + \alpha_1 \epsilon_{t-1}^2 + \cdots + \alpha_q \epsilon_{t-q}^2 + \beta_1 \sigma_{t-1}^2 + \cdots + \beta_p\sigma_{t-p}^2 = \alpha_0 + \sum_{i=1}^q \alpha_i \epsilon_{t-i}^2 + \sum_{i=1}^p \beta_i \sigma_{t-i}^2

4.2.3.1 GARCH(p, q) model specification

The lag length p of a GARCH(p, q) process is established in three steps:

Estimate the best fitting AR(q) model

y_t = a_0 + a_1 y_{t-1} + \cdots + a_q y_{t-q} + \epsilon_t = a_0 + \sum_{i=1}^q a_i y_{t-i} + \epsilon_t .

Compute and plot the autocorrelations of \epsilon^2 by

\rho = {{\sum^T_{t=i+1} (\hat \epsilon^2_t - \hat \sigma^2_t) (\hat \epsilon^2_{t-1} - \hat \sigma^2_{t-1})} \over {\sum^T_{t=1} (\hat \epsilon^2_t - \hat \sigma^2_t)^2}}

The asymptotic, that is for large samples, standard deviation of \rho (i) is 1/\sqrt{T} . Individual values that are larger than this indicate GARCH errors. To estimate the total number of lags, the Ljung-Box test is used until the value of these are less than, say, 10% significant. The Ljung-Box Q-statistic follows \chi^2 distribution with n degrees of freedom if the squared residuals \epsilon^2_t are uncorrelated. It is recommended to consider up to T/4 values of n. The null hypothesis states that there are no ARCH or GARCH errors. Rejecting the null thus means that there are existing such errors in the conditional variance.

4.2.3.2 GARCH(1,1) model

The most popular approach to estimating current volatility is GARCH(1,1) A GARCH(1,1) model lags on only one squared return and only one variance. That's the meaning of (1,1). But we need to weight the terms, and we need to give weight to the constant too. The constant is the long-run average variance; it exerts a gravitational pull on the time series. The more weight we assign to the long-run variance, the less "persistent" the time series and the more the time series is pulled toward the mean or exhibits a tendency to "regress to the mean."

GARCH(1,1) has three terms. Each is a weighting factor multiplied by, respectively, the long-run variance, a single lagged return squared, and a single lagged variance:

Garch_400w

Once more, the GARCH(1,1) model incorporates long-run variance (VL), the most recent squared return(u2), and the the most recent variance (sigma2). It weighs each of these and the weights must sum to one (gamma + alpha + beta = 1).

Chapter 5: Results and Analysis

5.1 Testing for stationarity

5.1.1 ADF Test

The Augmented Dickey Fuller was carried out using the software eviews suing the option "Unit Root Test."

Variables

t-Statistic

Test critical values

1% level

5% level

10% level

SEMTRI return

-4.255480

-3.808546

-3.020686

-2.650413

Inflation rate

-3.895225

-3.808546

-3.020686

-2.650413

Interest rate

-5.941229

-3.831511

-3.029970

-2.655194

GDP growth

-5.083458

-3.788030

-3.012363

-2.646119

Stocks traded

-3.069136

-3.788030

-3.012363

-2.646119

Official exchange rate

-3.625850

-3.808546

-3.020686

-2.650413

In the case of SEMTRI returns, the test statistic (-4.255480) is less than the critical value at 1%, 5% and 10% levels of significance (which is -3.808546, -3.020686 and -2.650413respectively). Thus the null hypothesis of Ï’= 0 is rejected and no unit root is present. Thus, the series is trend stationary.

For Inflation rate, the test statistic (-3.895225) is less than the critical value at 1%, 5% and 10% levels of significance (which is -3.808546, -3.020686 and -2.650413 respectively). Thus the null hypothesis of Ï’= 0 is rejected and no unit root is present. Thus, the series is trend stationary.

The test statistic (-2.518984) for Interest rate is less than the critical value at 1%, 5% and 10% levels of significance (which is -3.831511, -3.029970 and -2.655194respectively). Thus the null hypothesis of Ï’= 0 is rejected and no unit root is present. Thus, the series is trend stationary.

GDP growth has a test statistic (-5.083458) which is less than the critical value at 1%, 5% and 10% level of significance (that is -3.788030, -3.012363 and -2.646119 respectively). Thus the null hypothesis of Ï’= 0 is rejected and no unit root is present. Thus, the series is trend stationary.

As for Official exchange rate, the test statistic (-3.625850) is less than the critical value at 5% and 10% level of significance (that is -3.020686 and -2.650413respectively). Thus the null hypothesis of Ï’= 0 is rejected and no unit root is present. Thus, the series is trend stationary.

5.1.2 Cointegration Test

The Johansen Cointegration test has been used to test for the presence of cointegrated variables in the time series. The results are as follows:

Unrestricted Cointegration Rank Test (Trace)

Hypothesized

Trace

0.05

No. of CE(s)

Eigenvalue

Statistic

Critical Value

Prob.**

None *

 0.983492

 219.6982

 95.75366

 0.0000

At most 1 *

 0.978929

 137.6197

 69.81889

 0.0000

At most 2 *

 0.729996

 60.42303

 47.85613

 0.0022

At most 3 *

 0.718135

 34.23664

 29.79707

 0.0144

At most 4

 0.348797

 8.910109

 15.49471

 0.3738

At most 5

 0.016435

 0.331434

 3.841466

 0.5648

The portion of the output indicates whether there is cointegration and the number of cointegrated vectors. The trace test indicates four cointegrating equations at the 5% level of significance, given that the p-value at 4 CE (that is 0.3738) is greater than 0.05.

The trace statistic figure tests the null hypothesis of r cointegrated relations against the alternative of k cointegrating relations, where k is the number of endogenous variables. We can see from the second column that the first four eigenvalues are much higher compared to the last two eigenvalues. This suggests that there exist four cointegrated relations. The null hypothesis r = 0 and r≤3 can clearly be rejected. The first four trace statistics values are also greater than their respective critical values.

Unrestricted Cointegration Rank Test (Maximum Eigenvalue)

Hypothesized

Max-Eigen

0.05

No. of CE(s)

Eigenvalue

Statistic

Critical Value

Prob.**

None *

 0.983492

 82.07851

 40.07757

 0.0000

At most 1 *

 0.978929

 77.19669

 33.87687

 0.0000

At most 2

 0.729996

 26.18638

 27.58434

 0.0746

At most 3 *

 0.718135

 25.32654

 21.13162

 0.0121

At most 4

 0.348797

 8.578674

 14.26460

 0.3229

At most 5

 0.016435

 0.331434

 3.841466

 0.5648

According to the maximum Eigenvalue test, it can be noted that there are two cointegrating equations at the 5% level of significance, given that the p-value at 2 CE (that is 0.0746) is greater than 0.05.

This can further be confirmed by the fact that the first two Max-Eigen Statistic are greater than their respective critical values at 5% level of significance. At two CEs, the Max-Eigen Statistic (that is 26.18638) is less than the critical value of 27.58434.

5.1.3 Testing for Correlation – Durbin Watson

The Durbin-Watson test is used to test for serial correlation in a time series. EViews produces the statistic whenever it does a regression.

In our case, the Durbin Watson Statistic is 1.457668, which is less than 2 and therefore there is evidence of positive serial correlation. This means that there exists a relationship between the variables in which the variables move in tandem.

5.2 Testing for ARCH Effect

The two tests for conditional heteroskedasticiy which will be performed in the dissertation are Lagrange Multiplier test and the Ljung-Box test as proposed by Tsay (2005).

The tests can be thought of as a test for autocorrelation in the squared residuals where the null hypothesis is that all q lags of the squared residual have the coefficient values equal to zero. The rejection of null hypothesis indicates the coefficients are significantly different from zero.

5.1.1 ARCH LM Test

The Lagrange Multiplier test is conducted at 5 lags of squared residuals as proposed by Brooks (2002). EViews reports two test statistics from this test regression. The F-statistic is an omitted variable test for the joint significance of all lagged squared residuals. The Obs*R-squared statistic is Engle’s LM test statistic, computed as the number of observations times the R2 from the test regression. The exact finite sample distribution of the F-statistic under H0 is not known but the LM test statistic is asymptotically distributed χ2 (q) under quite general conditions. The ARCH LM test is available for equations estimated by least squares, two-stage least squares, and nonlinear least squares.

The F-statistic and the LM-statistic are not significant as referred to the Appendix for the full t-statistics of the test for 5 lags in the squared residuals. The null hypothesis of homoskedasticity of LM test is therefore not rejected at 5% level of significance, indicating the absence of ARCH effect in the time series.

5.1.2 Ljung-Box test

The second one, Ljung-Box test, widely used by a number of authors such as Choudry (1996) and Haroutounian and Price (2001) is performed with 12 lags. The Ljung-Box Q-Statistic, with its corresponding probability value, is a test statistic for the null hypothesis of no autocorrelation for a specified order of autocorrelation lags. The fact that all the probability values are relatively large, this means that the Q-Statistics are insignificant. The Ljung-Box test further confirms the absence of ARCH effect in the time series.

5.3 GARCH (1,1) Model

Using default options in Eviews, the following equation was estimated

Y = -0.802411 + 0.208768X1+ 0.022900X2 + 0.09035



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