1 Project I Project I Econ 240c Spring 2006 Econ 240c Spring 2006
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Project IProject I
Econ 240c Spring 2006Econ 240c Spring 2006
22
IssuesIssues Parsimonious modelsParsimonious models 2006: March or April 9.3 wks or 8.9 wks2006: March or April 9.3 wks or 8.9 wks TrendTrend Residual seasonalityResidual seasonality Forecasts: sharp peaks or broad peaks?Forecasts: sharp peaks or broad peaks? Model selectionModel selection The labor marketThe labor market
TrendTrend Broad peaksBroad peaks
33
∆ ∆ durationduration : ar(1) ar(4) ar(24) ar(36): ar(1) ar(4) ar(24) ar(36) : ma(1) ma(4) ma(24) ma(36): ma(1) ma(4) ma(24) ma(36) : ar(1) ar(2) ma(1) ma(2): ar(1) ar(2) ma(1) ma(2)
44
∆ ∆ lndurationlnduration : ma(1) ma(4) sma(24) sma(36): ma(1) ma(4) sma(24) sma(36) : ma(1) ma(4) ar(24) ar(36): ma(1) ma(4) ar(24) ar(36) : ar(1) ar(2) ma(1) ma(2): ar(1) ar(2) ma(1) ma(2) : ar(1) ma(1) ma(2) ma(3): ar(1) ma(1) ma(2) ma(3)
55
OutlineOutline
Duration Model: trend and arma error, p.6Duration Model: trend and arma error, p.6 Dduration model: arma(2,2), p. 29Dduration model: arma(2,2), p. 29
66
Duration in LevelsDuration in Levels TrendTrend Duration = a + b*t +arma errorDuration = a + b*t +arma error IdentificationIdentification EstimationEstimation Model VerificationModel Verification Within Sample Forecasting, a Test of the Within Sample Forecasting, a Test of the
ModelModel ForecastsForecasts
77
2
4
6
8
10
12
14
70 75 80 85 90 95 00 05
DURATION
88
99
-4
-2
0
2
4
6
2
4
6
8
10
12
14
70 75 80 85 90 95 00 05
Residual Actual Fitted
Trend Model: Duration
1010
0
10
20
30
40
4 5 6 7 8 9 10 11 12
Series: DURATIONSample 1967:07 2006:04Observations 466
Mean 7.097639Median 6.900000Maximum 12.30000Minimum 4.000000Std. Dev. 1.651788Skewness 0.304644Kurtosis 2.365030
Jarque-Bera 15.03663Probability 0.000543
1111
1212
1313
1414
-2
-1
0
1
2
2
4
6
8
10
12
14
70 75 80 85 90 95 00 05
Residual Actual Fitted
ARMA-Trend Model for Duration
1515
1616
1717
Conditional Conditional Heteroskedasticity?Heteroskedasticity?
1818
1919
0
10
20
30
40
50
60
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Series: ResidualsSample 1967:09 2006:04Observations 464
Mean 0.002033Median 0.009195Maximum 1.667878Minimum -1.540585Std. Dev. 0.410532Skewness 0.140254Kurtosis 5.762284
Jarque-Bera 149.0387Probability 0.000000
Rewsiduals from ARMA Trend Model
2020
Within Sample TestWithin Sample Test
2121
6
7
8
9
10
11
05:05 05:07 05:09 05:11 06:01 06:03
DURATIONF ± 2 S.E.
Forecast: DURATIONFActual: DURATIONSample: 2005:05 2006:04Include observations: 12
Root Mean Squared Error 0.242936Mean Absolute Error 0.196195Mean Abs. Percent Error 2.213545Theil Inequality Coefficient 0.013909 Bias Proportion 0.009928 Variance Proportion 0.618213 Covariance Proportion 0.371859
2222
2323
Quick Menu, ShowQuick Menu, Show
2424
2
4
6
8
10
12
14
70 75 80 85 90 95 00 05
DURATIONTEST
TEST+2*SEFTEST-2*SEF
Forecast: 2005.05-2006.04, ARMA Trend model
2525
Forecast: 2006.05-Forecast: 2006.05-2007.122007.12
5
6
7
8
9
10
11
12
06:07 06:10 07:01 07:04 07:07 07:10
DURATIONFF ± 2 S.E.
2626
2727
Quick Menu, ShowQuick Menu, Show
2828
2
4
6
8
10
12
14
70 75 80 85 90 95 00 05
DURATIONFORECASTFF
FORECASTFF+2*SEFFFORECASTFF-2*SEFF
Forecast 2006.04-2007.12, ARMA trend Model
2929
Monthly Change in Monthly Change in DurationDuration
3030
-3
-2
-1
0
1
2
70 75 80 85 90 95 00 05
DDURATION
Monthly change in Duratio, DDURATION
3131
0
10
20
30
40
50
60
-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Series: DDURATIONSample 1967:08 2006:04Observations 465
Mean 0.008602Median 0.000000Maximum 1.600000Minimum -2.100000Std. Dev. 0.443695Skewness -0.556232Kurtosis 6.021120
Jarque-Bera 200.8168Probability 0.000000
3232
3333
3434
3535
3636
3737
3838
Dduration: ar(1) ar(2), Dduration: ar(1) ar(2), ma(1)ma(1)
3939
Dduration: ar(1) ar(2), Dduration: ar(1) ar(2), ma(2)ma(2)
4040
Model Model
4141
DiagnosticsDiagnostics
-2
-1
0
1
2
-3
-2
-1
0
1
2
70 75 80 85 90 95 00 05
Residual Actual Fitted
ARMA(2,2) Model for DDuration
4242
4343
4444
4545
4646
0
10
20
30
40
50
60
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Series: ResidualsSample 1967:10 2006:04Observations 463
Mean -0.001033Median 0.008725Maximum 1.657726Minimum -1.584772Std. Dev. 0.416357Skewness -0.111928Kurtosis 5.581513
Jarque-Bera 129.5305Probability 0.000000
Residuals from ARMA(2,2) Model of DDuration
4747
Within Sample ForecastWithin Sample Forecast
4848
-1.0
-0.5
0.0
0.5
1.0
05:05 05:07 05:09 05:11 06:01 06:03
DDURATIONF ± 2 S.E.
Forecast: DDURATIONFActual: DDURATIONSample: 2005:05 2006:04Include observations: 12
Root Mean Squared Error 0.357149Mean Absolute Error 0.242394Mean Abs. Percent Error 70.55898Theil Inequality Coefficient 0.901135 Bias Proportion 0.007489 Variance Proportion 0.843115 Covariance Proportion 0.149396
4949
5050
Quick menu, showQuick menu, show
5151
Within Sample ForecastWithin Sample Forecast
-3
-2
-1
0
1
2
70 75 80 85 90 95 00 05
DDURATIONTESTD
TESTD+2*SEFDTESTD-2*SEFD
5252
Out of Sample ForecastOut of Sample Forecast
5353
-1.0
-0.5
0.0
0.5
1.0
06:07 06:10 07:01 07:04 07:07 07:10
DDURATIONFF ± 2 S.E.
5454
5555
-3
-2
-1
0
1
2
70 75 80 85 90 95 00 05
DDURATIONDDURFORE
DDURFORE+2*SEFFDDDURFORE-2*SEFFD
Out of Sample Forecast for DDuration: 2006.05-2007.12
5656
5757
5858
5959
2
4
6
8
10
12
14
70 75 80 85 90 95 00 05
DURATIONDURFORE
DURFORE+2*SEFFDDURFORE-2*SEFFD
Out of Sample Forecast; 2006.05-2007.12
6060
2
4
6
8
10
12
14
70 75 80 85 90 95 00 05
DURATIONFORECASTFF
FORECASTFF+2*SEFFFORECASTFF-2*SEFF
Forecast 2006.04-2007.12, ARMA trend Model
2
4
6
8
10
12
14
70 75 80 85 90 95 00 05
DURATIONDURFORE
DURFORE+2*SEFFDDURFORE-2*SEFFD
Out of Sample Forecast; 2006.05-2007.12
6161
Fractional Change in Fractional Change in DurationDuration
6262
-0.3
-0.2
-0.1
0.0
0.1
0.2
70 75 80 85 90 95 00 05
DLNDURATION
Fractional change in duration
6363
IdentificationIdentification
6464
ModelModel
6565
Model verificationModel verification
6666
6767
6868
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