1. Stock Price Modelling
2.1 The Forecastability of Stock Return through ARMA Model
In this part, we picked the stock price of Commonwealth Bank of Australia (CBA) from January 1, 2003 to May 30, 2013 to test for Jane’s hypothesis that the stock return is not predictable and the theory will be test through an ARMA model.
First, obtain the stock price data from Yahoo finance and import in to Eviews, obtain the log return of the adjusted stock price through command: series r=dlog(adj_price)
Plot the graph for r (Appendix 17), and the graph indicate a constant mean but may have volatility clustering, which means the variance may be time varying.
Obtain the correlogram for r (Appendix 18), but it is hard to identify the ARMA model through correlogram.
Then do the unit root test for log return rt through ADF test. The test results concluded in Appendix 19. The test results suggest the log return rt to be stationary, which is I(0). That suggest the series may take an ARIMA(p,0,q) model.
Reconsider the correlogram of log return (Appendix 18), although there are no bars plot outside the dot line in the first several lags, the 8th, 12th and 28th lag has been plotted outside the dot line. Thus, we may consider a ARMA model with r(-8), r(-12) and r(-28) in the AR part and ma(8), ma(12) and ma(28) in the MA part. Input in Eviews: r c r(-8) r(-12) r(-28) ma(8) ma(12) ma(28)
Conduct the model estimation and obtain the result in Appendix 20. The estimation result indicate that all the coefficients are significant except for the ma(28) term, whose p-value is quite close to 0.05. However, the R2 is 0.017148, which indicate the model is a very poor fit.
Obtain the correlogram for the residual of this model (Appendix 21), and the correlogram show no spike lies outside the spot line any more.
Then do the forecast for the last week, last month and last 3 months in 2013 (Appendix 22). Get the forecast series and compared with the real return, it seems the...