Connection Between Px and S
The purpose of our research is to prove that a local PX index is influenced by development of S&P500 index. We assume that this connection will exist for at least values from previous week, it will be positive and thus we will try to construct model that would predict PX index movements one week ahead.
We have used weekly data on PX and S&P500 indices returns since 2.1.2006 to 2.1.2012, thus we have 314 observations in total. The data was downloaded form Prague Stock Exchange and Yahoo Finance website.
By specifying PX return as a variable dependent on its value from previous period and S&P 500 return from previous period and using Robust regression with Newey-West standard errors, we have arrived to the following model:
pxret= -0.1078807 + 0.236115*spret1
where pxret is PX return in t and spret1 is a value of S&P500 return in t-1.
This means that PX index is positively influenced by developments of S&P500 index from previous week and with zero return in previous week tends to go down.
The table bellow shows statistics of the model.
We use robust method because original OLS model was influenced by heteroskedasticity and serial correlation of residuals. The original and final model significantly differs because the OLS model contained also lagged value of PX return, which was in robust regression rejected as insignificant thus we found that, unlike S&P index, PX return was not proved that it influence its future development.
The latter plot shows the data with a regression line. The presence of outlier point is visible but because the observation is valid we decided to leave it in our data set.
We were concerned with stationarity of our index data because a plot of PX returns shown below