Business Forecasting Using eViews - Essay Example

Introduction The use of eViews is an essential tool in the forecasting and analysis of econometric data. The presentation of data is in the form of graphs and models. These graphs and models relay a lot of information on the business under analysis. The business under analysis in this report is Roll Royce and the behaviour of its share prices. The figure shown below is the index time graph. The graph uses a large amount of data and this leads to a noisy graph, but the trend of the stocks is still visible. The company had a major crisis in the last quarter of 2002 until mid-2003. Some of their equipment failed in the market and they faced a multi-million pound lawsuit. This led to a huge deficit in their pension fund. This was the cause of the major fall of their share prices in that period. From the analysis, the prices were performing better from that point onward and rose in an almost steady gradient. This was until the first quarter of 2005 when the share price fell slightly, then another steady rise to mid-2006. Subsequently, there was a drop of the index by about 50. The graph then rises and a number of more falls follow before the end of the sample period. Due to the noise of the graph, trend identification is difficult (Brooks 2002). A histogram illustrates a slightly clearer representation of the data, this helps with the noise problem. Returns Due to the non-linearity and volatility of financial data, it is difficult to predict the level of the series at each period (Mills 1999). The figure below is stationary, which makes it more predictable. It also depicts the first differences in the series. It shows the first differences of the Rolls Royce shares during the period 01/01/2000 and ending 31/12/2007. The differences in this period are stationary relative to their mean; their variance is relatively stable as well. There is a slight increase in the middle of the graph between mid-2002 and mid-2003. The first difference of the logarithms is the returns to share in the financial market. This is the representation of the value. Returns = dlog (RR). A constant model should represent a data series with stationary a mean (Brooks 2002). This is the appropriate model for this series. The stationery mean’s representation is: dYt = c+et The change or the first difference of Y is c. If accurate prediction of the consequent references were possible from the series, then the next period would be an increment to the current level to achieve the next level. Reiterations for all higher levels takes place. The constant model expansion yields Yt = c+Yt-1+et This is the representation of an actual randomwalk model with a drift. This model captures, or gets the data generation of a financial series. Volatility Financial data are very volatile due to the many factors that affect its behaviour (Franses 1998). This makes it very unpredictable. Sometimes the first differences of the series have different variances, as the volatility diagram below depicts. The variance is almost stationary throughout the sample period, although there is a slight change in the differences around 2002 to 2003. After that, they are stationary and stable until the end of the period. Given the stationary appearance of the first difference, a constant model is the appropriate model for use in this series. The model forecasts the changes of the Rolls Royce share prices. Randomwalk Application of the constant model for the logged series of the first difference is an equivalent of the estimation of a random walk model for the original series. The data below originates from fitting a geometric randomwalk on DLOG (RR) on the period between 1/03/2000 and 12/31/2007. In this geometric randomwalk with growth, the constant term is 0.000498. This is a representative of the percentage average returns of 0.049% for the sample period between 1/03/2000 and 12/31/2007. This is also an increase in the daily value of the share price by 0.049%. In most financial forecasting series, the geometric randomwalk model is in use, by default. Its usefulness has limits to forecasting the mean of the returns. This is because it only takes into account the first moment of the series during analysis. Features of the returns The trading that takes place between buyers and sellers in the market makes up the financial time series at the financial market. Due to the many exogenous factors that influence the patterns and behaviour of the market, price series are not the preferential variables to work with (Mills 1999). For better analysis, the variables that are in use are the series of returns and the first difference of log price series. In the series of returns, volatility tends to happen in clusters. This is volatility clustering. This occurs due to the tendency of larger changes occurring whether positive or negative, which are always followed by clusters of changes of the complement sign. This observation takes place in 2003, then again between 2005 and 2006. The former consists of low signs, which precede high clusters. Volatility clusters in a financial series lead to increased leptokurtosis. This is the composition of distributions which exhibit fat tails and excessively high peaks. This is when the kurtosis is greater than 3. In the figure below for the financial series, the Kurtosis is 15.20733. Tgarch In our analysis, we start with a general GARCH model. The mean equation of the series includes a constant variable, while in the variance equation it includes an ARCH and a GARCH term. The ARCH term is from the mean equation of the logged squared residuals. The GARCH term is a derivative of the conditional variance equation from the logged dependent variable. Maximum likelihood is the technique that is most common in the estimation of the ARCH or GARCH models (Franses 1998). By using this technique on the series data, we yield the following results The coefficients of ARCH and GARCH are consistent and positive with the variance equation. They use the sign to indicate the direction of the variance. This helps determine whether the sum of the ARCH and GARCH coefficients (α+β) are close to one, and to which degree. When the sum of the two coefficients is less than one, the square of the expected variance value then converges to the unconditional variance. The scenario of ‘non stationary’ in variance occurs when the sum of α+β is greater than 1. In this case, the unconditional variance of the error term is not in the results. Garch Forecasting using the ARCH and GARCH models operates under the assumption that non-negativity is important (Franses 1998). The stationary GARCH model, α+β Read More