ECON 3350/7350: Applied Econometrics for Macroeconomics and Finance
Tutorial 2: Univariate Time Series – I
This tutorial aims to get you familiar with the fundamental features of univariate time series models.
1. Derive the expected value, variance, covariance, autocorrelation function (ACF), and partial autocorrelation function (PACF) for the time series yt having the fol- lowing data generating processes (DGP):
(a) AR(1):yt =a0 +a1yt−1 +εt,0≤|a1|<1. (b) MA(1): yt = β0 + β1εt−1 + εt.
(c) ARMA(1,1):yt =a0 +a1yt−1 +β1εt−1 +εt,0≤|a1|<1.
2. Compute the true ACF values for the following DGPs:
(1) DGP1: yt = 0.75yt−1 + εt
(2) DGP2: yt = −0.75yt−1 + εt
(3) DGP3: yt = 0.95yt−1 + εt
(4) DGP4: yt = 0.5yt−1 + 0.25yt−2 + εt (5) DGP5: yt = 0.25yt−1 − 0.5yt−2 + εt (6) DGP6: yt = 0.75εt−1 + εt
(7) DGP7: yt = 0.75εt−1 − 0.5εt−2 + εt (8) DGP8: yt = 0.75yt−1 + 0.5εt−1 + εt
3. Thedatafilearma.csvcontains(simulated)dataforeachoftheDGPsinQuestion 2. Import the data to Stata and use the variable t to declare time series. Compute, plot, and describe the behavior of the ACF and PACF of each DGP. Discuss the effects of parameter signs. Hint: Use the ac and pac commands, respectively.
1