Please carefully read the below instructions so that you will be able to earn a bonus payment. If you do not seriously play the experiment you will earn 0 bonus payment.
Thank you very much for your participation. This study will take you about 50 minutes to complete. You will receive a base payment of $0.30. If you seriously try to make accurate predictions, you will also earn a bonus payment. The bonus amount will then typically lie between $6$ and $12. The precise amount will depend on the accuracy of your predictions. If you do not make an effort to make accurate predictions, you will earn no bonus payment.
In this study, we would like to understand how people make predictions about future realizations of random processes. We will first show you 60 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 60 rounds, where in each round one new observation of each random process is shown.
In each of the 60 rounds, we will ask you to predict the value of the red process in the current round and its value in the next round. You can make your predictions by clicking in the green bars on the right in the graph on the next screen. 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, you will not yet know the current value of the red process. However, the values of the other two processes in the current round will already be shown to you. 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 of the other two processes 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 couple of values of the process are also likely to be high; and when the latest value of a process is low, the process is likely to give more low values for a couple of rounds. Furthermore, because the three processes are closely related, 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.
In each of the 60 rounds 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 in that round, and one prediction made already one round earlier). In every round, your score will be based on one of these two predictions. This prediction will be randomly selected, and you can see which of your two predictions was selected in the table at the bottom of your screen (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|/20], where Δ is the difference between your prediction and the realized value. We estimate that the best performer will receive an average score of 20 per round.
At the end of the experiment, we will calculate your total score in the 60 rounds of predictions. Your score will only be turned in to a bonus payment if the average performance of both your predictions about the current round and your predicions about the next round are above a certain threshold. This threshold is chosen as to exclude completely random predictions that are made without any understanding of the three processes. If you take your time to try to fully understand the experiment and carefully consider each of your predictions, you will achieve this threshold and get a bonus payment. The bonus payment will then ba a payment in U.S. dollars equal to your total score divided by 100.
After you have carefully read and understood the above instructions, click 'next' to start the experiment. You will be able to look again at these instructions by scrolling down during te experiment.
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