Busiess For Casting Overview

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OVERVIEW

Eco 5375

Economic and Business

Forecasting

Tom Fomby

301A LeeFall 2009


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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 pastvalues of y and current and past values of x no matterthe explanation of the way x helps forecast the future

values of y.Use of out-of-sample forecasting experiments to gaugeforecasting accuracy


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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 ofits past values but also the current and past

values of some other variables x1, x2, etc.


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THREE MAJOR CONCEPTS

Time Series Decomposition

Identifying Useful Leading Indicators

Combination forecasting: Enhancedaccuracy


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TIME SERIES DECOMPOSITION

Y = T + C + S + I

T = trend

C = cycleS = seasonal

I = irregular


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Trend


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Cycle


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Seasonal


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Irregular


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ADDING THE PARTS TOGETHER

Y = T


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Y = T + C


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Y = T + C + S


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Y = T + C + S + I


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TRUE DATA GENERATING PROCESS

Cosine Wave

a=amplitude=50, phase=0, period=20

Monthly Data (obs = 100)

.! )cos(1 U[FF taty ot

)100,0(Niidt pI

3146.020/2 !! Tw

150,,125,75,0,3146.0,50,4,50 12321 !!!!!!!! KKKU[FF .ao

tttt DDD IKKK 12,123,32,2 .


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FITTED MODEL

See SAS program

Decomposition.sas

-100

-50

0

50

100

150

200

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350

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0 10 20 30 40 50 60 70 80 90 100

X=Time Y=Trend plus Cycle plus Seasonal plus Irregular= Predicted Value


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FOR ACCURATEFORECASTING

YOU NEED TO GET THECOMPONENTS RIGHT:

NEED TO DETERMINE THE

COMPONENTS THAT AREPRESENT AND THOSE THAT ARE

NOT


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THREE POPULAR

DECOMPOSITION METHODS

(in chronological order)

Deterministic Trend and Seasonal Dummy Variable Model withAutocorrelated 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 nicepictures of decomposition) while the second method is notdescriptive 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?


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MULTIVARIATE TIME SERIES:VECTOR AUTOREGRESSIONS

(VARs)

Christopher Sims (1980)

A Model to help detect

Good leading indicators (x1, x2, etc.)

That improve the forecasting accuracyof the target variable (y)


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A WAY TO GAIN MORE

ACCURACY IN FORECASTING

Y_combo = w1*forecast1 + w2*forecast2 Combination (Ensemble) forecasting

Idea from Bates and Clive Granger(1969)


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LETS HAVE FUN

DOING APPLIED

ECONOMETRICS!


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Ragnar Frisch

Ragnar Frisch, Jan Tinbergen Economics and the Development of LargeMacroeconometric Models

One of the most influential econometricians of the late 1920s and early 1930s was the Norwegianeconomist Ragnar Frisch (1895-1973). Frisch was a highly trained mathematician who madecontributions to both macro- and micro-econometrics and played an important role in redirectingempirical 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 ofWorking's identification problem and showed that the ordinary least squares estimator wasbiased), it was his contribution to macro-econometrics that accounts for his importance. Togetherwith Jan Tinbergen, he played an important role in creating the field of macroeconometrics bydeveloping a macroeconometric model of the economy. Frisch's primary work is found in his bookStatistical Confluence Analysis by Means of Complete Regression Systems (1934). Here heargued that most economic variables were simultane-ously interconnected in "confluent systems"in which no variable could be varied independently; he worked out a variety of methods to handlethese 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. Seehttp://nobelprize.org/nobel_prizes/economics/laureates/1969/ for more information.

THREE POPULAR DECOMPOSITION METHODS (in chronological order)


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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)


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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...


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Clive Granger

Seminal Paper (1969) The Combination ofForecasts, Operations Research Quarterly, vol.20, pp. 451 468 with J.M. Bates.

Share of 2003 Nobel Prize in Economicshttp://nobelprize.org/nobel_prizes/economics/laureates/2003/

http://www.econbrowser.com/archives/2009/05/c

live_w_j_grang.html http://en.wikipedia.org/wiki/Clive_Granger

A WAY TO GAIN MORE ACCURACY IN FORECASTING

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