Economics 674 Fall 2006 Project 3 (Due: Friday, December 1) Let t denote the inflation rate in period t. In the following problems, use the same inflation rate data you used in Projects 1 and 2 and the sample period 1960:I-2006:I. Report all pertinent res
Lecture 18 Testing for ARCH Effects in a Time Series Engle's LM Test: Consider a stationary time series, xt. Assume that if xt is conditionally heteroskedastic, then it has an ARCH(m) form, i.e., xt = ht1/2vt , vt ~ i.i.d. N(0,1) ht = + 1xt-12 + . + mxt-m
Lecture 17 Regression Models with ARCH(m) Errors: Estimation and Inference Assume yt = xt + t where xt is a a kx1 vector of weakly exogenous regressors (which allows for lagged dependent variables and includes the AR(p) model as a special case) t is an AR
Lecture 22 Spurious and Cointegrating Regressions The time series regression theory and application developed in Econ 672 and 674 have assumed that the time series we are working with are stationary (or trend stationary). If we are working with difference
Economics 674 Fall 2006 Project 1 Clarida, Gertler, and Gali (2000, QJE) formulate a model of the federal funds rate in period t, rt, which can be written in the form (*) rt = 0 + 1 E t + k t + 2 E xt + q t + (L)rt-1 + t
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where t is the inflation r
Lecture 24 Unit Root Tests, II The initial DF unit root tests assumed that under the unit root null hypothesis, the first differences in the series are serially uncorrelated. Since first differences of most macroeconomic time series are serially correlate
Lecture 21 The Hodrick-Prescott Filter Hodrick and Prescott, JMCB, 1997
In contrast to the trend-cycle decompositions we have talked about so far, the Hodrick-Prescott filter is a model-free based approach to decomposing a time tseries into its trend and
Lecture 27 Cointegration:II Testing for Cointegration There are two basic approaches that are commonly to test for cointegration. Residual Based Tests H0: no CI vs. HA: CI Use single-equation regression residuals Engle-Granger; Phillips-Ouliaris Likelihoo
Lecture 25 Unit Root Tests III The Ng-Perron Unit Root Test (Improved Finite Sample Performance)
The ADF and PP unit root tests are known (from MC simulations) to suffer potentially severe finite sample power and size problems. 1. Power The ADF and PP tes
Lecture 23 The Dickey-Fuller Test We have seen that the dynamic behavior of I(1) processes is quite different from the behavior of I(0) processes the way we go about defining and estimating the trend and cyclical components of a time series may depend on
Economics 674 Fall 2006 Project 2 Fit the following version of the Clarida, Gertler, Gali model by GMM rt = 0 + 1t+1 + 2xt+1 + 3rt-1 + 4rt-2 + t where rt is the federal funds rate in period t, t is the inflation rate in period t, xt is the "output gap," (