Description

Analysis of data sets
1. (36 points)
(a) Compute 3 distinct 250 point simulations from a MA(1) model (Example 2.2.5) with θ = .8 and with noise {Zt} ∼ WN(0,1), where Zt is distributed as N(0,1).
(b) For each simulation, plot the time series data with properly labeled axis (so you will have 3 plots).
(c) For each simulation, plot the sample acf (correlogram) (so you will have 3 plots).
(d) Compute ρ(1) for this MA(1) model (see equation (2.2.3)).
(e) Do the correlograms present evidence consistent with the model? Two points to check: (a) Estimate ρ(1) from the plot and compare to ρ(1) and (b) For h > 1, b count how many values of ρ(h) are significantly large and compare to the fact that b ρ(h) = 0 for |h|> 1.
(f) What conclusion do you draw from the variations in your results – why did I have you check results for 3 simulations?
2. (36 points)
(a) This experiment involves a AR(1) model (Example 2.2.6) with ϕ = .99 and with noise {Zt} ∼ WN(0,1), where Zt is distributed as N(0,1).
(b) Compute a simulation with 46 values, plot the time series data with properly labeled axis and plot the sample acf (correlogram).
(c) Compute a simulation with 62 values, plot the time series data with properly labeled axis and plot the sample acf (correlogram).
(d) Compute a simulation with 500 values, plot the time series data with properly labeled axis and plot the sample acf (correlogram).
(e) Compute the formula for ρ(h) for this model (see equation (2.2.7)).
(f) Discuss whether or not the plots of correlogram (from a, b, and c) are consistent with the expected plots of ρ(h). Hint: Consider carefully how the values of ρ(h) decrease as h increases.
(g) Provide a potential reason for the results you found. Hint: Consider the discussion starting on the bottom of page 69 in the notes regarding limitations in the computation of ρ.
b
1