Section 1: Ford
Figure 1: Time series plot for raw Ford data.
Figure 1 shows a time series plot of the raw Ford stock prices against time. From this plot, a gradual but continuous upward trend can be observed. This trend was disrupted in 2005 when the stock prices experienced a huge rise moving from below 5 to above 25. This rise in stock price by Ford was not sustained as can be seen from the plot; the prices which reached a peak of above 25 fell to a about 10 by the end of 2005 and fell further in 2006 to a level below 5 fluctuations in the stock price existed and in 2007 the prices began to level out.
Raw data is likely to be affected by non-stationarity and this can result in bias in the analysis. For the purpose of this analysis, it is required that the returns be continuously compounded. To achieve this I have taken the log and first difference of the raw data: this also achieves stationarity in the time series data. Figure 2 shows the plot of these new values where Ford is the raw data, l_Ford is the log of the raw data and d_l_Ford is the first difference of the log data.
Figure 2 Using Box and Jenkins approach to estimate the best forecasting model requires 3 steps; identification, estimation and model checking. The aim is to choose a parsimonious model for forecasting. The table 1 below shows the values of the Akaike Criterion, Schwarz Criterion and Hannan-Quinn.
IDENTIFICATION
In this paper the Information Criteria will be used instead of the ACF and PACF. The information criteria include a function of the RSS and some penalty for