How can I statistically test if the line in a graph is moving upwards, downwards or sideways? I have a dataset that produces a line as shown in the picture below. I would like to statistically test when the line is moving upwards, downwards or sideways (not moving significantly). What would be best practice in order to do so?
I'm thankful for any help!

 A: What do you exactly mean by upwards, downwards or sideways?
You could fit a linear regression model on the data. You will get a coefficient for the slope and a confidence interval. If the coefficient is not significant then you could say that there is no trend.
A: Linear regression against time ASSUMES a model form and uncorrelated residuals to actually test the significance of estimated parameters. Your series might be adequately described with a local time trend (NOT GLOBAL) and a few level shifts and possible pulses and a possible memory component (arima) but only your data knows for sure. Post your actual data and I will try and help further .
How to make this data stationary might help you better understand how data like this gets objectively studied.
A: If you want to know the direction point to point, I believe that you can evaluate easily the slope: $\frac{Y_{t+1}-Y_{t}}{x_{t+1}-x_t}$. If this result is positive, it is going upwards. On the other hand, if it is negative it is going downward. If it is zero, it is going sideway.
If your question is about to know the average direction, you should estimate a non parametric function to learn the average direction. Andrew Lo has done this in the past to play with finance. See the paper.
