Remarks Concerning Graphical Models for Time Series and Point Processes

A statistical network is a collection of nodes representing random variables and a set of edges that connect the nodes. A probabilistic model for such is called a graphical modeL These models, graphs and networks are particularly useful for examining statistical dependencies based on conditioning as often occurs in economics and statistics. In this paper the nodal random variables will be time series or point processes. The cases of undirected and directed graphs are focussed on.

[1]  Book Review:Business Cycles in the United States of America, 1919-1932 J. Tinburgen , 1941 .

[2]  A. W. Phillips,et al.  Mechanical Models in Economic Dynamics , 1950 .

[3]  Amiel Feinstein,et al.  Information and information stability of random variables and processes , 1964 .

[4]  D. Brillinger,et al.  A PERMANENT INCOME HYPOTHESIS RELATING TO THE AGGREGATE DEMAND FOR MONEY (AN APPLICATION OF SPECTRAL AND MOVING SPECTRAL ANALYSIS) , 1970 .

[5]  Grace Wahba,et al.  Some Tests of Independence for Stationary Multivariate Time Series , 1971 .

[6]  Donald L. Snyder,et al.  Random point processes , 1975 .

[7]  M. Kanter Lower Bounds for Nonlinear Prediction Error in Moving Average Processes , 1979 .

[8]  T. Speed,et al.  Structural Analysis of Multivariate Data: A Review , 1982 .

[9]  David F. Hendry,et al.  The Econometric-analysis of Economic Time-series , 1983 .

[10]  Emanuel Parzen TIME SERIES MODEL IDENTIFICATION BY ESTIMATING INFORMATION , 1983 .

[11]  P. Brémaud Point processes and queues, martingale dynamics , 1983 .

[12]  John Geweke,et al.  Inference and causality in economic time series models , 1984 .

[13]  P. Robinson On the errors-in-variables problem for time series , 1986 .

[14]  D. Freedman As Others See Us: A Case Study in Path Analysis , 1987 .

[15]  J. Q. Smith Influence Diagrams for Statistical Modelling , 1989 .

[16]  N. Wermuth,et al.  On Substantive Research Hypotheses, Conditional Independence Graphs and Graphical Chain Models , 1990 .

[17]  Steffen L. Lauritzen,et al.  Independence properties of directed markov fields , 1990, Networks.

[18]  Andrew Harvey,et al.  Forecasting, Structural Time Series Models and the Kalman Filter. , 1991 .

[19]  David R. Brillinger,et al.  Nerve Cell Spike Train Data Analysis: A Progression of Technique , 1992 .

[20]  N. Wermuth,et al.  Linear Dependencies Represented by Chain Graphs , 1993 .

[21]  J. Pearl,et al.  Logical and Algorithmic Properties of Conditional Independence and Graphical Models , 1993 .

[22]  J. Pearl Causal diagrams for empirical research , 1995 .

[23]  D. Edwards Introduction to graphical modelling , 1995 .