Transcript OVERVIEW Eco 5375 Economic and Business Forecasting

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)
yt   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
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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.
• ½ Share of 2003 Nobel Prize in Economics
http://nobelprize.org/nobel_prizes/economics/lau
reates/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