Lecture 16 Formulating and Estimating Time Series Models of Conditional Heteroskedasticity References: Hamilton, Chapter 21 Enders, Chapter 3
Estimation and inference in regressions typically rely on the assumption that the error term is conditionally hom
Lecture 28 Cointegration:III
Suppose that yt is an n-dimensional cointegrated process with VAR representation: (L)yt = t , t ~ wn() where (L) = In 1L - - pLp and, since yt is I(1), it must be that det(1) = 0 Facts 1. yt cannot have a VAR(p) if yt ~ CI 2.
Lecture 30 Inference in the VECM
Recall the VEC representation of a ndimensional cointegrated system with cointegrating rank h yt = D + C1yt-1 +.+ Cp-1yt-p+1 + C0yt-1 + t where t ~ w.n. () C0 = -BA', A is an nxh matrix, h < n, which spans the CI space of
Lecture 31 Structural VARs: I
Let's assume that yt (or yt) is an n-dimensional I(0) process with a VAR(p) representation, i.e., yt = A0 + A1yt-1 + . + Apyt-p + t where t ~ w.n. (). Note that the n elements of t can be contemporaneously correlated (but not
Lecture 26 Cointegration:I Introduction Let yt = [y1t y2t] where y1t any y2t are I(1) process. (yt is a 2-dimensional I(1) proc.) In general, 1y1t + 2y2t will be I(1) for all [1 2] R2 (s.t. 1 and/or 2 is nonzero). However, there may be a nonzero R2 s.t. 1
Lecture 19 - Decomposing a Time Series into its Trend and Cyclical Components
It is often assumed that many macroeconomic time series are subject to two sorts of forces: those that influence the long-run behavior of the series and those that influence the
The simple random walk does not have a tendency to increase or decrease over time since its changes are serially uncorrelated and have zero mean. Starting from an initial value y0, yt = y0 + (1 + . + t) E(yt) = E(y0) E(ytyt-1,yt-2,.) = yt-1 (a rw is a mar
The Life-Cycle and Real Business Cycle Models1
These notes present two theories. The rst, the Life-Cycle Model (LCM) represents the
professions best eorts to explain consumption. The second, the Real Business Cycle Model
(RBC), appends the LCM to result i
Lecture 29 Cointegration IV Johansen's MLE of the CI Space
Assume that yt is an n-dimensional I(1) process with VEC form: yt = C1yt-1 +.+ Cp-1yt-p+1 + C0yt-1 + t where t ~ w.n. () C0 = -BA', A is an nxh matrix, h < n, which spans the CI space of y (i.e.,
Lecture 32 Structural VARs: II Consider the following VAR of y1t, the growth rate of real GDP, and y2t, the inflation rate: yt = A0 + A1yt-1 + t where t ~ w.n.(). We assume that t = Cvt where vt = [v1t v2t] is a serially and contemporaneously uncorrelated