1 Project I Econ 240c Spring 2006. 2 Issues Parsimonious models 2006: March or April 9.3 wks or...
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Transcript of 1 Project I Econ 240c Spring 2006. 2 Issues Parsimonious models 2006: March or April 9.3 wks or...
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Project IProject I
Econ 240c Spring 2006Econ 240c Spring 2006
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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
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∆ ∆ 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)
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∆ ∆ 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)
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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
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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
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70 75 80 85 90 95 00 05
DURATION
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99
-4
-2
0
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6
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Residual Actual Fitted
Trend Model: Duration
1010
0
10
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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
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1414
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Residual Actual Fitted
ARMA-Trend Model for Duration
1515
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Conditional Conditional Heteroskedasticity?Heteroskedasticity?
1818
1919
0
10
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30
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-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
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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
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Quick Menu, ShowQuick Menu, Show
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70 75 80 85 90 95 00 05
DURATIONTEST
TEST+2*SEFTEST-2*SEF
Forecast: 2005.05-2006.04, ARMA Trend model
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Forecast: 2006.05-Forecast: 2006.05-2007.122007.12
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06:07 06:10 07:01 07:04 07:07 07:10
DURATIONFF ± 2 S.E.
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Quick Menu, ShowQuick Menu, Show
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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
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70 75 80 85 90 95 00 05
DDURATION
Monthly change in Duratio, DDURATION
3131
0
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-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
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3333
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Dduration: ar(1) ar(2), Dduration: ar(1) ar(2), ma(1)ma(1)
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Dduration: ar(1) ar(2), Dduration: ar(1) ar(2), ma(2)ma(2)
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Model Model
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DiagnosticsDiagnostics
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-1
0
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-3
-2
-1
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70 75 80 85 90 95 00 05
Residual Actual Fitted
ARMA(2,2) Model for DDuration
4242
4343
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4646
0
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-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
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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
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DURATIONDURFORE
DURFORE+2*SEFFDDURFORE-2*SEFFD
Out of Sample Forecast; 2006.05-2007.12
6060
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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
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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
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