1. Introduction to Time Series
Is it Time Series Data?
Is it Cross Sectional Data?
Is it Panel (Pooled Data)?

2. About Data Qualitative Data Quantitative Data Qualitative Surveys
Primary Data: Questionnaire Research
Secondary Data: Existing Data from records

3. On Data More! Time Series Data
Monthly, Annually, Quarterly, Weekly, Daily
Cross Sectional Data
Questionnaire Data
Data for variables based on a single period
Panel Data
As a combination of time series and cross-sectional data

4. On the types of Data More !
Years
GDP (m.$)
M2 /GDP
1996
115,2
0,55
1997
116,4
0,56
1998
117,8
1999
115,4
0,60
2000
119,5
0,70
2001
120,0
0,71
2002
124,1
2003
125,9
0,72
2004
132,4
0,74
Time Series Data for a particular country

5. On the types of Data More
Country
GDP (m.$)
(Year: 2004)
M2 /GDP
Albania
215,2
0,55
Belgium
206,4
0,56
Denmark
217,8
Estonia
115,4
0,60
Finland
119,5
0,70
Germany
920,0
0,71
Holland
224,1
Ireland
150,9
0,72
Litvania
132,4
0,74
Crosssectional Data for GDP and M2 by country for 2004

6. On the types of Data More
Country
Years
GDP (m.$)
(Year: 2004)
M2 /GDP
Albania
2002
215,2
0,55
2003
206,4
0,56
2004
217,8
Belgium
215,4
0,60
219,5
0,70
220,0
0,71
Denmark
224,1
250,9
0,72
232,4
0,74
Panel
Data

7. Econometrics  Economic Measurement
What is Econometrics?
Econometrics  Economic Measurement
Mathematical Economics
Economics
Mathematics
Econometrics
Mathematical Statistics
Statistical Economics
Statistics

8. Methodology of Econometrics
1. Statement of theory or hypothesis
2. Specification of the mathematical model of the theory
3. Specification of the econometric model of the theory
4. Obtaining the data
5. Estimation of the parameters of the econometric model
6. Hypothesis Testing
7. Forecasting or Prediction
8.Using the model for control or policy purposes

9. Stationarity
Empirical work based on time series data assumes that the underlying time series is stationary.
Otherwise, are econometric results spurious or non-sense?
Then, what is Stationarity?

10. Definition of “Stationarity”
A time series might be equal to its value plus a purely random shock (or error term). Thus, this means a random walk phenomenon (Especially in financial time series).
Thus, the relationship between two series need to be the one with “stationarity” charactetistic.

11. A Stationary Stochastic Process
A random or stochastic process is a collection of random variables ordered in time.
Thus, a type stochastic process is the so-called stationary stochastic process.

12. Specification of Stationarity
Mean : E (Yt) = µ
Variance : var (Yt) = E (Yt - µ)2 = 2
Covariance: k = E[(Yt - µ)(Yt+k - µ)]
In short, if a time series is stationary, its mean, variance and autocovariance (at various lags) remain the same no matter at what point we measure them; they are time invariant.
Such a time series will tend to return to its mean (mean reversion) and fluctuations (its variance) around this mean will have a broadly constant amplitude.

13. Tests of Stationarity 1. Graphical Analysis
2. Autocorrelation Function (ACF) and Correlogram
3. The Unit Root Tests (The main Focus of “all the tests of Stationarity”)

14. 1. Graphical Analysis of Stationarity
Here GDP is increasing, that is, showing an upward trend, suggesting perhaps that the mean value of the GDP has been changing. This suggests that may be GDP is non-stationary. This ituitive feel is the starting point of more formal tests of stationarity.

15. 2. Autocorrelation Function (ACF) and Correlogram

16. 3. The Unit Root Test
This is a test of stationarity (or nonstationarity) that has become widely popular over the past several years (Gujarati, 2003).
The starting point is the unit root (stochastic) process with:
A white noise error term
-1 ≤ p ≤ 1
When p = 1, the above equation becomes a random walk model without drift, which is a non-stationary stochastic process.

17. Contiuned with manipulation:
This shows that since ut is a white noise error term, it is stationary, which means that the first differences of a random walk time series are stationary.

18. Continued
In practice, we estimate the above equation and test the null hypothesis that  = 0. If  = 0, then p = 1, that is we have a unit root in Y variable. This means it is NOT stationary.
When  < 0, then, p < 1 and Y is STATIONARY. Since  = (p-1), for stationarity p must be less than one. For this to happen  must be negative.

19. Question: Which test to use for Unit Root?
The estimated t value of Yt-1 does follow the t distribution even in large samples: It does not have an symptotic normal distribution.
So? What is the alternative?

20. a. Dickey-Fuller (DF) Test (1979)
DF has shown that under the null hypothesis that =0, the estimated t value of the coefficient of Yt-1 follows the  (tau) statistic.
DF have computed the critical values of  statistic on the basis of Monte Carlo simulations.
In the literature tau test is known as the DF test.

21. DF Test
A random walk process may have no drift, or it may have drift or it may have both deterministic and stochastic trends. To allow for the various possibilities, the DF test is estimated in three different forms (under three different null hypotheses).

22. DF Test Yt is a random walk: Yt is a random walk with drift:
Yt is a random walk with drift around a stochastic trend:
In each case, the null hypothesis is that =0; that is, there is a unit root – the time series is non-stationary. It is extremely important to note that the critical values of the tau test to test the hypothesis that =0, are different for each of the preceeding three specifications of the DF test.

23. b. The Augmented Dickey-Fuller (ADF) Test (1981)
In conducting the DF test, it was assumed that the error term ut was uncorrelated.
But in case the ut is correlated, DF have developed a test, known as ADF test.
The test is conducted by “augmenting” the preceeding three equations by adding the lagged values of the dependent variable Yt .

24. The ADF Test
The ADF test consists of estimating the following regression:

25. The Phillips-Perron (PP) Unit Root Tests (1988)
Phillips and Perron (1988) procedures, which compute a residual variance that is robust to auto-correlation, are applied to test for unit roots as an alternative to ADF unit root test.

26. Walter Enders’ (1995) suggestion for Unit Root Tests:

27. Walter Enders’ (1995) suggestion for Unit Root Tests:
Start to test unit roots from the most general model (with drift+trend) to the most specific (without drift and trend) model.
Then, compare results. If in any model, the null hypothesis is accepted, =0, then, there is a unit root. The series is non-stationary.

28. A Professional Table for Unit Roots: Developed by Salih KATIRCIOGLU

29. The Question is:
There must be a lag level for testing unit roots. So, which lag level to select in running unit root tests?
Two popular tests: Akaike Information Criterion (AIC) and Schwartz Information Criterion (SIC).
These lag tests will be introduce in the application session.
EVIEWS 5.1 does these tests automatically.

30. Power of Test
Most tests of the DF type have low power; that is, they tend to accept the null of unit root more frequently than is warranted. That is, these tests may find a unit root even when none exists.
There are some reasons for low power, please refer to Gujarati (2003): p. 819.

31. c. KPSS Test for Unit Root
To confirm the test results obtained from the ADF and PP tests, Kwiatkowski Phillips, Schmidt and Shin’s test (1992) (KPSS) is suggested to eliminate a possible low power against stationary near unit root processes which occurs in the ADF and PP tests.
The KPSS test complements the ADF and PP tests in which the null hypothesis of KPSS test is that a series is stationary. This means that a stationary series is likely to have insignificant KPSS statistics and significant ADF and PP statistics.

32. Now is the Application Time of Unit Root Tests