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Coefficient of Determination - R Squared - Time-Series Prediction
In statistics, the coefficient of determination represents the strength of the relationship or the portion of common variation in two time-series or variables. It is a statistical measure of how well the regression line approximates the real values.
The coefficient of determination or RČ is mainly used to analyze how well a variable can predict another one. The returned value gives us the percentage of change of variable X that can be explained by changes in variable Y.
The coefficient of determination is calculated by taking the square of the Pearson correlation (simple linear correlation). A value of 1 or 100% indicates that moves in one time-series can be entirely explained by the second time-series, while a value of 0 or 0% means that that the first time-series cannot be explained by moves in the second time-series. RČ values range from 0 to 1.
Example:
The correlation between the weekly change of the S&P 500 Index (Ticker Symbol: ^GSPC) and the previous week change for the last 50 trading weeks is equal to 0.13.
The coefficient of determination is equal to 0.0169 or 1.69%, which means that weekly changes can explain only 1.69% of next week changes.
Formula Example:
a = r2(perf(close, 1), perf(close[1], 1), 50);
plot(a, "", colorGreen);
Calculate RČ of the current and previous rate of change using the last 50 trading bars.
Plot the coefficient of determination of each trading bar on a chart.
Trading financial instruments, including foreign exchange on margin, carries a high level of risk and is not suitable for all investors. The high degree of leverage can work against you as well as for you. Before deciding to invest in financial instruments or foreign exchange you should carefully consider your investment objectives, level of experience, and risk appetite. The possibility exists that you could sustain a loss of some or all of your initial investment and therefore you should not invest money that you cannot afford to lose. You should be aware of all the risks associated with trading and seek advice from an independent financial advisor if you have any doubts.
