Final answer:
The question deals with a moving-average process of order 2 used in time series analysis, which involves smoothing out noise in the data to detect trends.
Step-by-step explanation:
The student is asking about a moving-average process of order 2 in time series analysis, denoted as {xt}. The process is defined by xt = zt + θzt−2, where {zt} represents the white noise or error term at time t, and θ is a parameter. The term zt−2 refers to the error term two periods prior. This is a concept in stochastic processes and time series analysis, often covered in statistics or econometrics courses at the college level.
To understand the concept better, here's an example: Assuming θ equals 0.5 and you have known values for zt and zt−2, you could calculate xt by simply taking the current value of zt and adding half of the value from zt two periods ago. This process helps smooth out noise and can be useful to detect trends in time-series data.