In this study, we would like to understand how people make predictions about future realizations of random processes. We will first show you 70 past realizations of 3 random processes in a graph: the red process, the purple process and the light blue process. Then, you will go through 70 rounds, where in each round one new observation of each random process is shown.
In each of the 70 rounds, we will ask you to predict the value of the red process in the next two future rounds. You can make your predictions by clicking in the green bars on the right in the graph. If you want to make further adjustments to your predictions before submitting, you can do so by dragging your predictions (red diamonds) to their desired positions.
At the time that you make these two predictions about the future of the red process, you will only know the past values of the red process and not yet its current value. However, you will already see the current values of the purple process and of the light blue process, in addition to their past values. The three processes are closely related to each other. Therefore, it is possible to calculate the most likely value that the red process will take in a particular round, based on the values that you expect the light blue process and/or the purple process to take in that round. You can study the relation between the three processes by looking at their past realizations in the graph (hover with your mouse over different time points to see the values of the three processes in numbers).
Moreover, all three processes are persistent. This means that when the latest value of a process is high, the next few values of the process are also likely to be relatively high; and when the latest value of a process is low, the process is likely to give relatively low values for a few more rounds. Furthermore, because the three processes are closely related to each other, a high most recent value of one process also makes it likely that the other two processes will be high or low in the next few rounds. Note here that, when two processes are positively related to each other, a high current value of one process implies that it is likely that both processes will be high in the next round. However, when two processes are negatively related, a high current value of one process implies that that process is likely to be high in the next round, but that the other process is likely to be low in the next round.
Due to differences in 'noise', the three processes differ in how informative an observed value is about the future values of that process and about the future values of other processes. The red process (the one that you need to predict) is the most 'noisy' and less informative about its future value than the other two processes. The purple process is already less noisy, and the light blue process is the least noisy of all. Therefore, observed values of the light blue process are the most informative about the future values of all three processes.
For each round (excluding round number 1 which you did not make any predictions about), you will receive a score based on your predictions about the red process in that round. You each time will have made two predictions about the same round (one prediction made one round before, and one prediction made already two rounds before). In every round, your score will be based on one of these two predictions. Which of the two predictions determines your score of that round will be randomly selected. In order to earn well, you should, therefore, carefully think about both your predictions in each round. In the table at the bottom of your screen, you will see which of your two predictions was selected in any of the past rounds (it will be printed in bold face). The more accurate the selected prediction is, the higher your score will be. If your prediction is out of a certain neighborhood around the actual value, you may receive a score of zero for that round.
The specific formula for the score of each prediction is 100 × max[0, 1-|Δ|/25], where Δ is the difference between your prediction and the realized value. We estimate that the best performer will receive an average score of around 35 per round.
At the end of the experiment, we will calculate your total score in the 70 rounds of predictions. Your payment will then be a payment in Euros equal to your total score divided by 250, plus the 2.50 Euro show up fee.