2. Example- Real GDP (2000 Prices) Seasonally Adjusted
(1) Plot Time Series - Non-Stationary
(i.e. time varying mean and correlogram non-zero)
GDP
Y
100
75
50
1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 Time
1.00
r ACF-Y
0.75
0.50
0.25
0 5 10
k
2
4. Unit Root Testing
(1) Plot First Difference of Time Series - Stationary
(i.e. constant mean and correlogram zero)
3
DY
2
1
0
-1
1955 1960 1965 1970 1975 1980 1985 1990 1995 2000
Time
1.0
r ACF-DY
0.5
0.0
-0.5
0 5 10 k
4
5. Informal Procedures to identify non-stationary processes
(2) Diagnostic test - Correlogram
Correlation between 1980 and 1980 + k.
For stationary process correlogram dies out rapidly.
Series has no memory. 1980 is not related to 1985.
0.50
whitenoise
0.25
0.00
-0.25
0 50 100 150 200 250 300 350 400 450 500
1.0
ACF-whitenoise
0.5
0.0
-0.5
0 5 10
5
7. What is a Spurious Regression?
A Spurious or Nonsensical relationship may
result when one Non-stationary time series is
regressed against one or more Non-stationary
time series
The best way to guard against Spurious
Regressions is to check for “Cointegration” of
the variables used in time series modeling
8. Symptoms of Likely Presence of Spurious
Regression
• If the R2 of the regression is greater than the
Durbin-Watson Statistic
• If the residual series of the regression has a Unit
Root
9.
10. What is a “Unit Root”?
If a Non-Stationary Time Series Yt has
to be “differenced” d times to make it
stationary, then Yt is said to contain
d “Unit Roots”. It is customary to
denote Yt ~ I(d) which reads “Yt is
integrated of order d”
11. Unit Root Testing: Formal Tests to
Establish Stationarity of Time Series
• Dickey-Fuller (DF) Test
• Augmented Dickey-Fuller (ADF) Test
• Phillips-Perron (PP) Unit Root Test
• Dickey-Pantula Unit Root Test
• GLS Transformed Dickey-Fuller Test
• ERS Point Optimal Test
• KPSS Unit Root Test
• Ng and Perron Test