Question

A particular random variable follows a process given by Y[t] = 1 + 0.4*E[t-1] + E[t], where E[t] is a Gaussian White Noise innovation with mean 0 and variance of 1 (This process is not estimated, but rather we know the true data generating process as described here). Theoretically, the first order autocorrelation coefficient is approximately"

A.O
B.0.16
C. 0.345
D. 0.4

Answer 1

The theoretical first order autocorrelation coefficient is approximately 0.4 for the given time series, due to the weight of 0.4 given to the previous term's error.

Step-by-step explanation:

The student's question pertains to finding the theoretical first order autocorrelation coefficient for a time series process described by Y[t] = 1 + 0.4*E[t-1] + E[t], where E[t] is described as Gaussian White Noise with mean 0 and variance of 1. This process suggests that the current value Y[t] is dependent on its own previous value's error term (with a lag of one time period), which introduces autocorrelation in time series data. In this context, the autocorrelation coefficient measures the strength of the linear relationship between the current value and its previous values.

To calculate the theoretical autocorrelation, we look at lag-1 autocorrelation since the time series includes the term 0.4*E[t-1]. The coefficient 0.4 provides a clue since it is the weight given to the previous term's error. So we would expect the theoretical autocorrelation to be approximately 0.4, which is option D.