OVERVIEW Eco 5375 Economic and Business Forecasting Tom Fomby 301A Lee Fall 2009 ECONOMETRICS Hypothesis Testing y f x e Is x a significant explanator of y Typically use all of the data to test the hypothesis Forecasting Forecasting future values of y as a function of past values of y and current and past values of x no matter the explanation of the way x helps forecast the future values of y Use of out of sample forecasting experiments to gauge forecasting accuracy FORECASTING Univariate time series model the target variable y is modeled as a function of its past values y 1 y 2 etc and current and past errors in the past attempts of explaining y Multivariate time series model the target variable y is modeled as a function of its past values but also the current and past values of some other variables x1 x2 etc THREE MAJOR CONCEPTS Time Series Decomposition Identifying Useful Leading Indicators Combination forecasting Enhanced accuracy TIME SERIES DECOMPOSITION Y T C S I T trend C cycle S seasonal I irregular Trend Cycle Seasonal Irregular ADDING THE PARTS TOGETHER Y T ADDING THE PARTS TOGETHER Y T C ADDING THE PARTS TOGETHER Y T C S ADDING THE PARTS TOGETHER Y T C S I TRUE DATA GENERATING PROCESS Cosine Wave a amplitude 50 phase 0 period 20 Monthly Data obs 100 y t o 1t a cos t 2 Dt 2 3 Dt 3 12 Dt 12 t o 50 1 4 a 50 0 3146 0 2 75 3 125 12 150 t Niid 0 100 w 2 20 0 3146 FITTED MODEL See SAS program Decomposition sas X Time Y Trend plus Cycle plus Seasonal plus Irregular Predicted Value 700 650 600 550 500 450 400 350 300 250 200 150 100 50 0 50 100 0 10 20 30 40 50 60 70 80 90 100 FOR ACCURATE FORECASTING YOU NEED TO GET THE COMPONENTS RIGHT NEED TO DETERMINE THE COMPONENTS THAT ARE PRESENT AND THOSE THAT ARE NOT THREE POPULAR DECOMPOSITION METHODS in chronological order Deterministic Trend and Seasonal Dummy Variable Model with Autocorrelated Errors 1930 Ragnar Frisch Box Jenkins Model 1970 George E P Box and Gwilym M Jenkins Unobservable Components Model 1989 Andrew C Harvey First and third methods are most descriptive i e produce nice pictures of decomposition while the second method is not descriptive but is often the most accurate forecasting method Thus there is a trade off between descriptiveness and forecasting accuracy What is the purpose of your data analysis MULTIVARIATE TIME SERIES VECTOR AUTOREGRESSIONS VARs Christopher Sims 1980 A Model to help detect Good leading indicators x1 x2 etc That improve the forecasting accuracy of the target variable y A WAY TO GAIN MORE ACCURACY IN FORECASTING Y combo w1 forecast1 w2 forecast2 Combination Ensemble forecasting Idea from Bates and Clive Granger 1969 LET S HAVE FUN DOING APPLIED ECONOMETRICS Ragnar Frisch Ragnar Frisch Jan Tinbergen Economics and the Development of Large Macroeconometric Models One of the most influential econometricians of the late 1920s and early 1930s was the Norwegian economist Ragnar Frisch 1895 1973 Frisch was a highly trained mathematician who made contributions to both macro and micro econometrics and played an important role in redirecting empirical economics away from the institutional approach and toward an econometric approach In fact it was he who coined the term econometrics Although Frisch made some important discoveries in microeconometrics he carried out a conclusive mathematical treatment of Working s identification problem and showed that the ordinary least squares estimator was biased it was his contribution to macroeconometrics that accounts for his importance Together with Jan Tinbergen he played an important role in creating the field of macroeconometrics by developing a macroeconometric model of the economy Frisch s primary work is found in his book Statistical Confluence Analysis by Means of Complete Regression Systems 1934 Here he argued that most economic variables were simultaneously interconnected in confluent systems in which no variable could be varied independently he worked out a variety of methods to handle these problems He and Jan Tinbergen shared the Nobel Prize in Economics in 1969 and were cited for having developed and applied dynamic models for the analysis of economic process See http nobelprize org nobel prizes economics laureates 1969 for more information THREE POPULAR DECOMPOSITION METHODS in chronological order George E P Box and Gwilym M Jenkins Time Series Analysis Forecasting and Control Holden Day 1970 http en wikipedia org wiki George E P Box http en wikipedia org wiki Gwilym Jenkins THREE POPULAR DECOMPOSITION METHODS in chronological order Andrew C Harvey Forecasting Structural Time Series Models and the Kalman Filter Cambridge University Press 1989 Implemented in Proc UCM in SAS http www econ cam ac uk faculty harvey THREE POPULAR DECOMPOSITION METHODS in chronological order Christopher Sims Seminal paper Macroeconomics and Reality Econometrica Jan 1980 pp 1 48 http www princeton edu sims http en wikipedia org wiki Christopher A Sims MULTIVARIATE TIME SERIES VECTOR AUTOREGRESSIONS VARs C Clive Granger Seminal Paper 1969 The Combination of Forecasts Operations Research Quarterly vol 20 pp 451 468 with J M Bates Share of 2003 Nobel Prize in Economics http nobelprize org nobel prizes economics laur eates 2003 http www econbrowser com archives 2009 05 cl ive w j grang html http en wikipedia org wiki Clive Granger A WAY TO GAIN MORE ACCURACY IN FORECASTING