Statistical Analysis of Stock Indices Research Paper

Statistical Analysis of Stock Indices - Research Paper Example On the other hand, according to Pelaez (1999, 232) 'there are many ways to forecast economic series, including extrapolation, econometric models, time-series models, and leading indicator models'. For the issue under analysis in this report, the test for unit root is considered as the most appropriate tool for evaluating the given data series from the Stock indices. The methodology applied has been considered as most appropriate after a thorough consideration of the specific subject involved. A technical overview on the nuances of the unit root test is presented followed by the analysis of the Stock indices given in SPSS v14.0. This method will enable the presentation of both the theories and the practical application using reliable software to ease the process and eliminate errors. Guido (2001, 164) says that 'the composite intrinsic value measure does not appear to be an adequate measure of a stock's or portfolio's value' in his experiment to compare the US and the Australian markets. Several possible reasons are offered for this difference, including the differing market structures, the use of a different index or the use of alternate statistical tests'. In the light of the above arguments, it is clear that for the data set under analysis it is essential to use a strong statistical tool to identify the relationship between the given stock indices. Dickey-Fuller statistic tests for the unit root in the time series data. Pt is regressed against Pt-1 to test for unit root in a time series random walk model, which is given as: Pt = r Pt-1 + ut (1) If r is significantly equal to 1, then the stochastic variable Pt is said to be having unit root. A series with unit root is said to be un-stationary and does not follow random walk. There are three most popular Dickey-Fuller tests used for testing unit root in a series. The above equation can be rewritten as: D Pt = d Pt-1 + ut (2) Here d = (r - 1) and here it is tested if d is equal to zero. Pt is a random walk if d is equal to zero. It is possible that the time series could behave as a random walk with a drift. This means that the value of Pt may not center to zero and thus a constant should be added to the random walk equation. A linear trend value could also be added along with the constant to the equation, which results in a null hypothesis reflecting stationary deviations from a trend. To test the validity of market efficiency, random walk hypothesis has been tested. Unit root test has been conducted on Pt, natural log values of indices price data by running the regression equations of the following type: D Pt = d Pt-1 + ut (3) D Pt = a + d Pt-1 + ut (4) D Pt = a + dPt-1 + b t + ut (5) where, a is constant term and b is the coefficient of trend term. The null hypothesis for each is: H0: d = 0 (viii) The null hypothesis that Pt is a random walk can be rejected if calculated t is greater than the tabulated t. From the aforementioned it is clear that the test for unit root is a reliable analytical tool to test the consistency of the data series. In case of the stock market indices we are analysing, the test for unit root is a reliable tool to test the extent to which the index is speculating. The output from the autoregressive analysis for unit root test reveals that the behaviour of the stock indices it is clear that "OMXCOPENHAGEN" and "MADRIDSEGENERAL" have