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.
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.
The three processes are also closely related to each other. As a result, information about the light blue process and the purple process are relevant for your predictions of future realizations of the red process. 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). Note the following:
At the time that you make your two predictions about the future of the red process, you will know the current values and past values of the red process, the purple process and the light blue process. Because the three processes are persistent and closely related to each other, a high current value of the purple process or the light blue process also makes it likely that the red process will be high (when they are positively related) or low (when they are negatively related) in the next few rounds.
The reason why you may want to use information about the light blue process and/or the purple process to predict the value of the red process in the next two rounds is that the observations of the three processes differ in how informative they are for future values of the processes. This difference in informativeness arises because the three random processes have different degrees of 'noise'. 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. Note, in particular, that observations of the light blue process and the purple process are both more informative about future values of the red process than observations of the red process itself.
# {% endif %} {% if tcurrent == 0 %}There are two reasons why you may want to use information about the light blue process and/or the purple process to predict the value of the red process in the next two rounds. First of all, 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. Because the three processes are persistent and closely related to each other, a high current value of the purple process or the light blue process also makes it likely that the red process will be high (when they are positively related) or low (when they are negatively related) in the next few rounds.
The second reason is that the observations of the three processes differ in how informative they are for future values of the processes. This difference in informativeness arises because the three random processes have different degrees of 'noise'. 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. Note, in particular, that observations of the light blue process and the purple process are both more informative about future values of the red process than observations of the red process itself.
{% endif %}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. Each time, you 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 will 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 around 40 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 Pounds equal to your total score divided by 400, plus the £4.50 base payment.