Ch05: Characterizing a Relationship between Time Series

Chapter Summary:

Before the analysis of relationship between different variables, it is necessary to characterize the series in term of its cycle and trend. After analyzing the trend and cycle of the series, it is possible to identify the relationship between different variables (econometrically).

The simplest technique to analysis the relationship between different variables is correlation and regression (OLS). However, the underlying assumption for this simple procedure is that time series are stationary, which are taken under analysis. When the given series are stationary then correlation and regression analysis give the same results, if they are not same, then it implies that there is non-stationary factor. In case of non-stationary factor OLS give spurious relationship (relationship which have no specific meaning).

It is often mention that economic and financial time series are non-stationary. The mainly reason for the non-stationary is that time trend, and the dependence of the current value of the series on the previous value (autoregressive process). When analyst face non-stationary, then to explore the relationship between different variables, we use co-integration technique. OLS and co-integration technique will give us long relationship, however, for the short run relationship, we move one step ahead in co-integration technique, which is known as error correction mechanism. Error correction give would show how much the deviation from the long run relationship is possible in the short run.

For the statistical significance we use different type of statistics, i.e. R² , adjusted R² , t-statistic, F statistics, AIC, SBC, etc.