Implications of Aggregation with Common Factors

By Clive W. J. Granger. 1987

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Citations in the corpus

Temporal aggregation of univariate and multivariate time series models: a survey (2008, unknown): “Consequently η∗t = vech(εtε ′ t) + vech(εt−1ε ′ t−1) + v ∗ t = ηt + ηt−1 + v ∗ t (28) where v t represents the non-contemporaneous cross-products, while η t and ηt−1 are contemporaneous squared terms: v t = 2D + n (vech(εtε ′ t−1)), where D + n = (D ′ nDn) Dn and Dn is the duplication matrix.”
Non-Linear Models: Where Do We Go Next - Time Varying Parameter Models? (2008, methodology): “It is not clear that this encompassing is necessary, an example being given by the Min-Max model discussed by Granger and Hyung (2006). In these models the traditional + and - signs are replaced by max and min in a linear model. Thus the traditional AR(1)xt = axt−1 + et is replaced by xt = amax(xt−1”
Aggregation of Space-Time Processes (2001, background): “The case where the correlation between variables is due to the presence of a common factor is analyzed by Granger (1980, 1987) , who illustrates the implications of aggregating variables that depend on both common and idiosyncratic factors.”
Determining the Number of Factors in Approximate Factor Models (2000, background): “t =1 ,...T . Granger (1987) defined a sequence of random variables to be a dominant”
Heterogeneity and aggregation (2005, unknown): “This matches the micro log-wage regression (88) with xit replaced by E (xitjI = 1), zit replaced by E (zit) and the spread parameter changed from to p 0 zz + 2 .”
Common Factors in Conditional Distributions for Bivariate Time Series (2006, background): “Such common factors can become dominant under cross-sectional aggregation (see Granger (1987)).”
Theory and Practice of GVAR Modeling (2016, unknown): “…country specific variables, xit, from the system (27) is given by xit = Θiixit−1 + ∑ j=1,j 6=i Θij (xj,t−1 − Γjft) + Γift −Θ′iΓift−1 + uit, (32) 10See for instance Granger (1987), Forni and Lippi (1997), Pesaran (2003), Zaffaroni (2004) and Pesaran (2006). where Θij are appropriate partitioned…”
Crop Supply Dynamics and the Illusion of Partial Adjustment (2014, unknown): “However, aggregation will also increase the explanatory power of common factors (Granger 1987), and thus increase the signal-to-noise ratio and the bias from heterogeneous coefficients.”