1. DATA STATIONER AND
DATA NON STATIONER

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

3. These are Examples of
Non-Stationary Time Series
16000 12000 10000 9000
14000 8000
10000
8000
7000
12000
8000
6000 6000
10000
6000 5000
8000
4000 4000
4000
6000
3000
2000
4000 2000
2000
2000 0 0 1000
92 94 96 98 00 02 04 92 94 96 98 00 02 04 92 94 96 98 00 02 04 92 94 96 98 00 02 04
AUSTRALIA CANADA CHINA GERMANY
24000 45000 50000 7000
20000 40000 6000
40000
35000 5000
16000
30000
30000 4000
12000
25000 20000 3000
8000
20000 2000
10000
4000 15000 1000
0 10000 0 0
92 94 96 98 00 02 04 92 94 96 98 00 02 04 92 94 96 98 00 02 04 92 94 96 98 00 02 04
HONGKONG JAPAN KOREA MALAYSIA
7000 30000 12000 60000
6000 25000 10000
50000
5000
20000 8000
40000
4000
15000 6000
3000
30000
10000 4000
2000
20000
1000 5000 2000
0 0 0 10000
92 94 96 98 00 02 04 92 94 96 98 00 02 04 92 94 96 98 00 02 04 92 94 96 98 00 02 04
SINGAPORE TAIWAN UK USA

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

6. These are Examples of
Stationary Time Series
8000 6000 4000 6000
6000 4000 3000 4000
4000
2000 2000 2000
2000
0 1000 0
0
-2000 0 -2000
-2000
-4000 -4000 -1000 -4000
-6000 -6000 -2000 -6000
92 94 96 98 00 02 04 92 94 96 98 00 02 04 92 94 96 98 00 02 04 92 94 96 98 00 02 04
AUST CAN CHI GERM
12000 12000 12000 2000
8000 8000 8000
1000
4000 4000 4000
0
0 0 0
-1000
-4000 -4000 -4000
-2000
-8000 -8000 -8000
-12000 -12000 -12000 -3000
92 94 96 98 00 02 04 92 94 96 98 00 02 04 92 94 96 98 00 02 04 92 94 96 98 00 02 04
HONG JAP KOR MAL
3000 12000 5000 30000
4000
2000
8000 3000 20000
1000 2000
4000 10000
1000
0
0
0 0
-1000 -1000
-4000 -2000 -10000
-2000
-3000
-3000 -8000 -4000 -20000
92 94 96 98 00 02 04 92 94 96 98 00 02 04 92 94 96 98 00 02 04 92 94 96 98 00 02 04
SING TWN UKK US

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

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