2. ECO 6120 : Economic fluctuations
Understanding economic fluctuations: important empirical component in the analysis
Great contributions in the (Granger-Newbold, 1974, « spurious regressions»; Nelson and Plosser (1982) (Unit roots); Perron (1989) structural breaks.
The notion of stationarity is fundamental (Spurious regressions) 1: in general for macro-econometrics and 2 : persistence of shocks

3. Dependent Variable: LRY_CA
Method: Least Squares
Date: 10/27/03 Time: 10:41
Sample(adjusted): 1961:1 2000:1
Included observations: 157 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob. C
LRY_US
R-squared Mean dependent var
Adjusted R-squared S.D. dependent var
S.E. of regression Akaike info criterion
Sum squared resid Schwarz criterion
Log likelihood F-statistic
Durbin-Watson stat Prob(F-statistic)

5. Consequently: 1) you should know if the series are stationary
(using unit root tests) and 2) if non-stationary, you have to
make the series stationary (first differencing, HP filter)
or to use cointegration.

6. The traditional view
(artificial series)
Log (Y) Qt

9. Unit root tests
Suppose that we want to test if ln y tends to revert toward its trend
For this end, Nelson and Plosser (1982) propose to test:
Where εt is a mean zero disturbance uncorrelated with
the term between []
If b < 0, output tends to revert toward the trend
if b = 0, this is not the case (fluctuations have
a permanent component).

10. 4.54 is rewritten as:
There is however an important econometric complication
(Dickey et Fuller, 1979), the OLS estimate of b is biased towards negative values if chocks are persistent. The usual t test
cannot be used (see the detail discussion on page ).

11. Augmented Dickey-Fuller test on lry
Null Hypothesis: LRY has a unit root
Exogenous: Constant, Linear Trend
Lag Length: 1 (Automatic based on SIC, MAXLAG=13)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic
Test critical values: 1% level
5% level
10% level
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(LRY)
Method: Least Squares
Date: 10/23/03 Time: 14:51
Sample(adjusted): 1965:3 2002:4
Included observations: 150 after adjusting endpoints
Variable Coefficient Std. Error t -Statistic Prob.
LRY(-1)
D(LRY(-1)) C
@TREND(1965:1)

12. Augmented Dickey-Fuller test on Dlry
Null Hypothesis: D(LRY) has a unit root
Exogenous: Constant
Lag Length: 0 (Automatic based on SIC, MAXLAG=13)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic
Test critical values: 1% level
5% level
10% level
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(LRY,2)
Method: Least Squares
Date: 10/28/03 Time: 12:57
Sample(adjusted): 1965:3 2002:4

13. The Hodrick-Prescott (HP) filter (from EViews help)
This is a smoothing method that is widely used among macroeconomists to obtain a smooth estimate of the long-term trend component of a series. The method was first used in a working paper (circulated in the early 1980's and published in 1997) by Hodrick and Prescott to analyze postwar U.S. business cycles.
Technically, the Hodrick-Prescott (HP) filter is a two-sided linear filter that computes the smoothed series of by minimizing the variance of around , subject to a penalty that constrains the second difference of . That is, the HP filter chooses to minimize:
Where λ is the smoothing parameter or the penalty parameter that controls the smoothness of the series . (100, 1600, 14400)

14. (From EViews 4.0 Help)
To smooth the series using the Hodrick-Prescott filter, choose Procs/Hodrick-Prescott Filter....
First, provide a name for the smoothed series. EViews will suggest a name, but you can always enter a name of your choosing. Next, specify an integer value for the smoothing parameter, . The default values in EViews are set to be:
100 for annual data,
1,600 for quarterly,
and 14,400 for monthly
When you click OK, EViews displays a graph of the filtered series together with the original series.

15. The cyclical component is LRY-HPRY

17. Perron P. (1989): Unit roots can be explained by the presence
of one structural break in a stationary series.