is the us economy recovering?
DESCRIPTION
Is The Us Economy Recovering?. Angela Sordello Christopher Friedberg Can Shen Hui Lai Hui Wang Fang Guo . Outline. Introduction Original Data Pre Whitening Comparison of Models Modeling Model Validation - PowerPoint PPT PresentationTRANSCRIPT
IS THE US ECONOMY
RECOVERING?Angela Sordello
Christopher Friedberg
Can Shen
Hui LaiHui Wang
Fang Guo
OUTLINE
Introduction Original Data Pre Whitening Comparison of Models Modeling Model Validation Forecasting Conclusion
GROSS PRIVATE DOMESTIC INVESTMENT
Gross Private Domestic Investment (GPDI) is a measure of fixed investment and the change in private inventories
Used as an indicator to assess the state of the economy
We wanted to see if the United States economy is still in a recession
ORIGINAL DATA St. Louis Federal Reserve Bank The data is quarterly and has been seasonally
adjusted GDPI is measured in billions of US dollars
ORIGINAL DATA
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Series: GPDISample 1947Q1 2010Q1Observations 253
Mean 677.0980Median 443.5000Maximum 2352.100Minimum 32.40000Std. Dev. 688.1904Skewness 0.952415Kurtosis 2.664464
Jarque-Bera 39.43595Probability 0.000000
Histogram of original data
Correlogram of original data
UNIT ROOT TESTNull Hypothesis: GPDI has a unit rootExogenous: ConstantLag Length: 1 (Automatic based on SIC, MAXLAG=15)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -0.051649 0.9519Test critical values: 1% level -3.456302
5% level -2.87285710% level -2.572875
*MacKinnon (1996) one-sided p-values.
PRE WHITENING: LOGARITHMIC TRANSFORMATION
Null Hypothesis: LNVAL has a unit rootExogenous: Constant
Lag Length: 1 (Automatic based on SIC, MAXLAG=15)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -1.402074 0.5812
Test critical values: 1% level -3.456302
5% level -2.872857
10% level -2.572875
*MacKinnon (1996) one-sided p-values.
PRE WHITENING CONTINUED :FIRST DIFFERENCE
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DLNVAL
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Series: DLNVALSample 1947Q1 2010Q1Observations 252
Mean 0.015703Median 0.017661Maximum 0.232193Minimum -0.184770Std. Dev. 0.056848Skewness -0.255340Kurtosis 5.578477
Jarque-Bera 72.54805Probability 0.000000
Line graph Histogram
PRE WHITENING CONTINUED :FIRST DIFFERENCE
Null Hypothesis: DLNVAL has a unit root
Exogenous: ConstantLag Length: 0 (Automatic based on SIC, MAXLAG=15)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic
-12.67345 0.0000
Test critical values:
1% level
-3.456302
5% level
-2.872857
10% level
-2.572875
*MacKinnon (1996) one-sided p-values.
COMPARISONS OF MODELS
AIC Std.ar1 ma1 ma4 -3.16465 0.054171ar1 ma1 ar4 -3.18318 0.052654ar1 ma4 -3.15211 0.054871ma1 ma4 -3.1329 0.055395ar1 ar4 -3.17636 0.053344ma1 ar4 -3.16707 0.053945ar1 -3.14968 0.055969ma1 -3.13432 0.056211ar1 ma1 -3.14513 0.056056
MODELINGDependent Variable: DLNMethod: Least SquaresSample (adjusted): 1948Q2 2010Q1Included observations: 248 after adjustmentsConvergence achieved after 8 iterationsBackcast: 1948Q1
Variable Coefficient Std. Error t-Statistic Prob.
C 0.015145 0.002791 5.426434 0.0000AR(1) 0.578654 0.127597 4.534997 0.0000AR(4) -0.253979 0.048822 -5.202175 0.0000MA(1) -0.430378 0.150243 -2.864547 0.0045
R-squared 0.133199 Mean dependent var 0.014791Adjusted R-squared 0.122542 S.D. dependent var 0.055381S.E. of regression 0.051877 Akaike info criterion -3.063875Sum squared resid 0.656665 Schwarz criterion -3.007206Log likelihood 383.9205 F-statistic 12.49830Durbin-Watson stat 2.031919 Prob(F-statistic) 0.000000
Inverted AR Roots .68-.46i .68+.46i -.39+.48i -.39-.48iInverted MA Roots .43
Regression with AR(1) MA(1) MA(4)
MODELINGCorrelogram Correlogram with residuals squared
MODELINGARCH Test:
F-statistic 7.160676 Probability 0.000951Obs*R-squared 13.69126 Probability 0.001064
Test Equation:Dependent Variable: RESID^2Method: Least SquaresDate: Time: 15:25Sample (adjusted): 1948Q4 2010Q1Included observations: 246 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
C 0.001859 0.000394 4.714357 0.0000RESID^2(-1) 0.159984 0.063446 2.521578 0.0123RESID^2(-2) 0.145641 0.063434 2.295939 0.0225
R-squared 0.055656 Mean dependent var 0.002669Adjusted R-squared 0.047883 S.D. dependent var 0.005322S.E. of regression 0.005193 Akaike info criterion -7.670838Sum squared resid 0.006553 Schwarz criterion -7.628090Log likelihood 946.5130 F-statistic 7.160676Durbin-Watson stat 2.036030 Prob(F-statistic) 0.000951
MODELINGDependent Variable: DLNMethod: ML - ARCH (Marquardt) - Normal distributionSample (adjusted): 1948Q2 2010Q1Included observations: 248 after adjustmentsConvergence achieved after 17 iterationsMA backcast: 1948Q1, Variance backcast: ONGARCH = C(5) + C(6)*RESID(-1)^2 + C(7)*GARCH(-1)
Coefficient Std. Error z-Statistic Prob. C 0.016106 0.003109 5.180012 0.0000
AR(1) 0.621096 0.208225 2.982814 0.0029AR(4) -0.158412 0.058175 -2.723025 0.0065MA(1) -0.457122 0.242386 -1.885925 0.0593
Variance Equation
C 0.000259 9.44E-05 2.741082 0.0061RESID(-1)^2 0.153163 0.037643 4.068873 0.0000GARCH(-1) 0.743574 0.060403 12.31026 0.0000
R-squared 0.118040 Mean dependent var 0.014791Adjusted R-squared 0.096082 S.D. dependent var 0.055381S.E. of regression 0.052654 Akaike info criterion -3.183176Sum squared resid 0.668149 Schwarz criterion -3.084006Log likelihood 401.7138 F-statistic 5.375835Durbin-Watson stat 2.027874 Prob(F-statistic) 0.000031
Inverted AR Roots .64+.38i .64-.38i -.33-.42i -.33+.42iInverted MA Roots .46
MODELINGCorrelogram Correlogram with residuals squared
MODELING
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Residual Actual Fitted
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Series: Standardized ResidualsSample 1948Q2 2010Q1Observations 248
Mean -0.047608Median 0.025543Maximum 2.756589Minimum -4.088392Std. Dev. 1.008087Skewness -0.673921Kurtosis 5.152086
Jarque-Bera 66.63087Probability 0.000000
ARCH Test:
F-statistic 0.335499 Probability 0.715312Obs*R-squared 0.677412 Probability 0.712692
Test Equation:Dependent Variable: STD_RESID^2Method: Least SquaresDate: Time: 15:27Sample (adjusted): 1948Q4 2010Q1Included observations: 246 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
C 1.035358 0.162525 6.370464 0.0000STD_RESID^2(-1) 0.030762 0.064084 0.480029 0.6316STD_RESID^2(-2) -0.043437 0.064055 -0.678121 0.4983
R-squared 0.002754 Mean dependent var 1.022628Adjusted R-squared -0.005454 S.D. dependent var 2.106837S.E. of regression 2.112575 Akaike info criterion 4.345812Sum squared resid 1084.503 Schwarz criterion 4.388560Log likelihood -531.5349 F-statistic 0.335499Durbin-Watson stat 1.998539 Prob(F-statistic) 0.715312
MODEL VALIDATION
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GPDIFORECASTGPDI
UPPERLOWER
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GPDIFORECASTGPDI
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FORECASTING
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VALUEVALUEF
LOWERUPPER
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LOWERUPPER
The GDPI is increasing.It is signaling the US economy is recovering.