Before assessing your main question, we need to clarify some points:
1) inference is not the same thing of computing or showing the correlation;
2) since you are working with time series, you need to check if the series are both stationary or cointegrated; if it is not the case, you're correlation may be spurious and your conclusion, fallacious;
3) quantitative measures are in the vast majority of cases preferred to graphical methods; in the case of correlation, you should compute an appropriate coefficient rather than giving your conclusion using only a plot. After you have computed the coefficient, you should test if it is statistically significant.