Since in this paper we are focused on 2002 to 2006 we see that the seasonal and the cyclic component are present. We take a time plot of the returns data of home furnishers to investigate if the data exhibit trend in this case. From the above trend, we can see that there is a linear trend in the returns of the home furnishers. To eliminate the trend to make the returns data stationary, we take the differencing of lag 1 and observe the progress of the remains. The time plot of the returns also shows that the return data exhibit trend. Thus from the above analysis of the returns and return squared, the returns can be predicted and have a very high predictive power while the return squared has very low predictive power. Broadly speaking, a time series is said to be stationary if there is no systematic change in the mean (no trend). If there is a systematic change invariance and is strictly periodic variations (seasonal and cyclic component) are removed. Most of the probability theory of time series analysis is concerned with stationary time series and for this reason, time series analysis requires one to change a non-stationary time series to a stationary time series analysis so as to use it. In this study, we plot the variables and test their stationary using a particular variation of the unit root test- the Augmented Dickey-Fuller test. We then difference the time series of returns to make the series stationary. After differencing the return data we can observe that the data is stationary. This can be clearly seen in the time series plot of the differenced data at a lag. The plot of differenced data of returns below shows that the data is stationary after differencing it once.
Forecasting the Stock