Upload
dbmumbai
View
216
Download
0
Embed Size (px)
Citation preview
8/8/2019 Busiess For Casting Overview
1/25
OVERVIEW
Eco 5375
Economic and Business
Forecasting
Tom Fomby
301A LeeFall 2009
8/8/2019 Busiess For Casting Overview
2/25
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
8/8/2019 Busiess For Casting Overview
3/25
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.
8/8/2019 Busiess For Casting Overview
4/25
THREE MAJOR CONCEPTS
Time Series Decomposition
Identifying Useful Leading Indicators
Combination forecasting: Enhancedaccuracy
8/8/2019 Busiess For Casting Overview
5/25
TIME SERIES DECOMPOSITION
Y = T + C + S + I
T = trend
C = cycleS = seasonal
I = irregular
8/8/2019 Busiess For Casting Overview
6/25
Trend
8/8/2019 Busiess For Casting Overview
7/25
Cycle
8/8/2019 Busiess For Casting Overview
8/25
Seasonal
8/8/2019 Busiess For Casting Overview
9/25
Irregular
8/8/2019 Busiess For Casting Overview
10/25
ADDING THE PARTS TOGETHER
Y = T
8/8/2019 Busiess For Casting Overview
11/25
ADDING THE PARTS TOGETHER
Y = T + C
8/8/2019 Busiess For Casting Overview
12/25
ADDING THE PARTS TOGETHER
Y = T + C + S
8/8/2019 Busiess For Casting Overview
13/25
ADDING THE PARTS TOGETHER
Y = T + C + S + I
8/8/2019 Busiess For Casting Overview
14/25
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 .
8/8/2019 Busiess For Casting Overview
15/25
FITTED MODEL
See SAS program
Decomposition.sas
-100
-50
0
50
100
150
200
250
300
350
400
450
500
550
600
650
700
0 10 20 30 40 50 60 70 80 90 100
X=Time Y=Trend plus Cycle plus Seasonal plus Irregular= Predicted Value
8/8/2019 Busiess For Casting Overview
16/25
FOR ACCURATEFORECASTING
YOU NEED TO GET THECOMPONENTS RIGHT:
NEED TO DETERMINE THE
COMPONENTS THAT AREPRESENT AND THOSE THAT ARE
NOT
8/8/2019 Busiess For Casting Overview
17/25
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?
8/8/2019 Busiess For Casting Overview
18/25
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)
8/8/2019 Busiess For Casting Overview
19/25
A WAY TO GAIN MORE
ACCURACY IN FORECASTING
Y_combo = w1*forecast1 + w2*forecast2 Combination (Ensemble) forecasting
Idea from Bates and Clive Granger(1969)
8/8/2019 Busiess For Casting Overview
20/25
LETS HAVE FUN
DOING APPLIED
ECONOMETRICS!
8/8/2019 Busiess For Casting Overview
21/25
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)
8/8/2019 Busiess For Casting Overview
22/25
8/8/2019 Busiess For Casting Overview
23/25
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)
8/8/2019 Busiess For Casting Overview
24/25
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...
8/8/2019 Busiess For Casting Overview
25/25
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