Week 11 Tutorial: VAR (Vector
Auto regressions) - Illustration
Introduction
Vector Autoregression (VAR) is a
generalisation of the autoregressive (AR)
models. You can think of combining more
than 1 AR models together (in this sense,
there will be more tha
EF3451EconomicandBusinessForecasting
FredYKwan
Fall201314
Volatility Modeling1
1. Independence versus no correlation
(Definition) Two random variables X and Y are independent if their joint
probability distribution function (pdf) f ( x, y ) can be written
EF3451EconomicandBusinessForecasting
FredYKwan
Fall201314
Forecasting with VAR1
1. Vector Autoregressions
VAR = Vector AutoRegression
A natural generalization of the AR model to multiple time series.
Example: Two time series cfw_ y1t , y2t , t = 1, 2,., T
EF3451EconomicandBusinessForecasting
FredYKwan
Fall201314
Evaluating and Combining Forecasts1
1. Is my forecast optimal?
Ask this question not just for curiosity but for practical reason.
If the answer is no, in principle we should be able to improve our
EF3451EconomicandBusinessForecasting
FredYKwan
Fall201314
Stochastic trend and ARIMA1
1. Deterministic versus stochastic level
A constant level is a trend with zero slope.
yt = 1, t = 0,1, 2,.
(1.1)
yt = yt 1 ,
(1.2)
y0 = 1, t = 1, 2,.
yt = 0,
y0 = 1, t =
EF3451 Economic and Business Forecasting
Fred Y Kwan
Fall 2013-14
A complete ARMA example 1
US monthly liquor sales, 1967M1 1994M12.
Very strong seasonality sales peak every year during the Christmas season.
Variance stabilization by taking natural logari
Using E-view to run
regression
Exercise
Urban = live in urban =
1
C = Constant
Educ = year of
education
Exper = year of
working
Feduc = year of
fathers education
Lwage = natural
log of wage
Meduc = year of
mothers education
Enter command:
lwage educ expe
EF3451 Economic and Business Forecasting
Fred Y Kwan
Fall 2013-14
Forecasting with ARMA models 1
1. The behavior of forecasts
Figure 1 shows the Canadian employment index and long horizontal forecasts
from MA(4) and AR(2) models.
Estimation period: 1962Q1
EF3451EconomicandBusinessForecasting
FredYKwan
Fall201314
Identification of ARMA models1
1. Introduction
Any covariance stationary time series has an MA() representation (Wolds
theorem).
Thus, the key to successful time series modeling and forecasting is
Model Selection
Akaike information
Criterion (AIC)
Schwarz Criterion (SC)
Akaike information Criterion
(AIC)
Let N be the sample size and K be the
number of X variables,
If you add a lot of X variables into your
model, the first term will drop, but the
se
EF3451EconomicandBusinessForecasting
FredYKwan
Fall201314
Characterizing Cycles1
1. Time series decomposition
Conceptually a time series consists of three components:
Time series = Trend + Seasonals + Cycles
(1.1)
Here we will focus on the third component
Review on Conditional
Probability
Population Regression
Conditional
Probability
Salary
Primary
Secondar
y
Tertiary
Education
Marginal Probability
Joint Distribution of Weather Conditions and
Commuting Times
Rain (X = No Rain (X = f(y)
0)
1)
Long commute (
EF3451EconomicandBusinessForecasting
FredYKwan
Fall201314
Introduction to Forecasting
1. Why do you need to learn forecasting?
The importance of forecasting is self evident after all we forecast all the time in
daily life.
Governments, policy organization
EF3451EconomicandBusinessForecasting
FredYKwan
Fall201314
Addendum to EViews Illustrated Ch 1
'
File: nyse1.prg
'
Batch file for "EViews illustrated" Chapter 1.
'
Last update: 9 September 2013.
%path = @runpath
' get current directory
cd %path
' change to