[2019] STAT 153 Introduction to Time Series - Midterm Exam - Q5 Autocorrelation
5. For each statement, indicate whether it is true or false and give a short explanation.
You only get points when both, True/False and the explanation, are correct.
(a) For the sample autocorrelations of n = 1,000 i.i.d. white noise random variables at lags h = 1, . . . , 100, you expect on average 5 of them to be larger than 1.96 in absolute value.
[ ]True [ ]False Explanation:
(b) The sample autocorrelations of an AR(1) process with i.i.d. white noise are (for large sample size) approximately i.i.d..
[ ]True [ ]False Explanation:
(c) Applying a linear (time invariant) filter to a stationary process results again in a stationary process.
[ ]True [ ]False Explanation:
(d) When you want to fit a seasonal parametric function of the form st = a0 + ?kf=1 (af cos(2πft/d)+bf sin(2πft/d)) with parameters a0,a1,...,ak,b1,...,bk it can be helpful to chose k > d/2.
[ ]True [ ]False Explanation:
(e) A time series {Xt} where Xt follows a Gaussian distribution for each t is a Gaussian process. [ ]True [ ]False
Explanation:
(f) Whether a time series is invertible or not is fully determined by its finite dimensional distributions.
[ ]True [ ]False Explanation:
(g) Whether a time series is strongly stationary or not is fully determined by its mean and covariance function.
[ ]True [ ]False Explanation:
(h) Whether a Gaussian process is strongly stationary or not is fully determined by its mean and covariance function.
[ True [ ]False Explanation: (8 Points)
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