OVERVIEWEco 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 TOGETHERY = T

ADDING THE PARTS TOGETHERY = T + C

ADDING THE PARTS TOGETHERY = T + C + S

ADDING THE PARTS TOGETHERY = T + C + S + I

TRUE DATA GENERATING PROCESSCosine Wave

a=amplitude=50, phase=0, period=20Monthly Data (obs = 100)

)cos(1 taty ot

)100,0(Niidt

3146.020/2 w

150,,125,75,0,3146.0,50,4,50 12321 ao

tttt DDD 12,123,32,2

FITTED MODELSee SAS program – Decomposition.sas

-100

-50

0

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100

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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

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 detectGood 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 FUNDOING 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 macro econometrics 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 simultane ously 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 andGwilym 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.

• ½ Share of 2003 Nobel Prize in Economics http://nobelprize.org/nobel_prizes/economics/laureates/2003/

• http://www.econbrowser.com/archives/2009/05/clive_w_j_grang.html

• http://en.wikipedia.org/wiki/Clive_Granger

• A WAY TO GAIN MORE ACCURACY IN FORECASTING