"KUL" <m9828353@urc1.cc.kuleuven.ac.be wrote: QUESTION: What is Multiple Time Series Analysis ( MTSA) ? ANSWER: I'm glad you asked. Univariate time series simply uses the past values of one series to develop an autoprojective relationship which goes by many names... ARIMA , RATIONAL EXPECTATIONS to name two. It explicitly uses the previous values BUT since these previous values captured the impact of omitted causal series (X for eXogenous) thus IMPLICITELY captures the effect of these omitted X's. Please see http://www.autobox.com/t1c9.html for an enlightening discussion if the dual role that an ARIMA plays. See http://www.autobox.com/t1a13a.html for modern procedures for ARIMA MODEL identification. Note that Pulses, Seasonal Pulses, Level Shifts and Local Time Trends have to be taken into consideration along with potentially changing variance , parameters and even model form. More on this can be found at http://www.autobox.com/teach.html. Transfer Functions are a form or MTSA where the assumption is made that the X's cause the Y and not vice-versa . A single equation model with one or more inputs an be identified and estimated and checked diagnostically. Please read "Lies My Mother Never Told Me" which summarizes the roles of regression vis-a-vis Transfer Functions at http://www.autobox.com/t1c6.html. A regression is a particular case of a transfer function and assumes bunches of things. A Transfer Function can reduce to a simple multiple regression if the data so indicates and in-model step-down testing reduces unneeded structure. For a discussion of "REGRESSION AS A SUBSET OF TRANSFER FUNCTIONS" please see http://www.autobox.com/t1c8.html. A more general MTSA is when there are multiple dependent series and possibly multiple input series. This happens quite naturally when you are interested in estimating or predicting simultaneously products that are either substitutes or complements or have in general a cross dependence. This is called VECTOR ARIMA and a number of vendors unable to deploy VECTOR ARIMA promote a subset called VAR (NO IMA). For downloadables and explanatory material on VARIMA please see http://www.autobox.com/mts.html. Using VARIMA, variables can be either endogenous or exogenous. Endogenous variable prediction can then be based on a combination of lags of the series of interest and appropriate lags of other variables (endogenous or exogenous) in the model. I hope this helps. If you wish to pursue more please either see http://www.autobox.com/referenc.html or sign up for the seminar on AUTOBOX coming up in June in Washington D.C. at the International Institute of Forecasters annual meeting. http://ifsm2.ifsm.umbc.edu/ISF/ P.S. The same Gaussian assumptions as in ARIMA must be implemented in either Transfer Functions or Vector ARIMA.