Personal Savings as a Percentage of Disposable Personal Income Take Home II June 4 th, 2009 June 4 th, 2009 Marissa Pittman Morgan Hansen Eric Griffin Chris Stroud Eric Griffin Chris Stroud Yao Wang Yao Wang

Personal Savings Personal SavingsPersonal Savings The difference between household income (after taxes) and consumption expenditures.The difference between household income (after taxes) and consumption expenditures. Negative number implies debtNegative number implies debt Positive number implies savingsPositive number implies savings Household Income-Spending

Personal Savings As recently as April 2008, personal savings in the US totaled only 1.4 billion dollars In conjunction with the rapid collapse of the Economy in September 2008, personal savings has increased dramatically The latest number from April 2009 showed personal savings at $620.2 billion, the highest value in history.

Disposable Income Disposable IncomeDisposable Income Income (after taxes) that is available to you for saving or spendingIncome (after taxes) that is available to you for saving or spending

Expected Results Personal Savings (Semi-linear) Disposable Income (Exponential) Expect similar trends compared to the Personal Savings because decreasing and income is increasing

Savings as a Percentage of Disposable Income Why percentage and not net savings?  Normalizes the data set Different people make different amounts of moneyDifferent people make different amounts of money It is safe to assume someone making $100,000/year will be saving more than someone making $30,000/yearIt is safe to assume someone making $100,000/year will be saving more than someone making $30,000/year

Savings/Income This brings up our series, personal savings as a percentage of disposable income This ratio is also taken in order to account for inflation and the fact that incomes have been rising over time

Personal Savings as a Percentage of Disposable Personal Income Until the mid 1980s, people had been saving about 8-10 percent of their disposable income Starting in 1986 this number began trending downward due to easily obtainable credit (credit cards, lower mortgage rates, etc)

Personal Savings as a Percentage of Disposable Personal Income After the collapse of the economy in September this number began to shoot upward in conjunction with the increase in personal savings In April 2009 people were saving 5.7 percent of their disposable income which is the highest percentage since February 1995.

Trace of Personal Savings as a Percentage of Disposable Personal Income Appears to be random walkAppears to be random walk Hit peak in 1975 at 14.6%Hit peak in 1975 at 14.6% Has been steadily declining sinceHas been steadily declining since Hit low in 2005 at - 2.7% which meant people were spending more than they hadHit low in 2005 at - 2.7% which meant people were spending more than they had

Histogram of Personal Savings as a Percentage of Disposable Personal Income Multi-peakedMulti-peaked Large Jarque-Bera statisticsLarge Jarque-Bera statistics  Further evidence the data set is random walk

Correlogram of Personal Savings as a Percentage of Disposable Personal Income  The correlogram shows a slow decay in the autocorrelation  The PACF value at lag 1 is close to one  Both further indicators of a random walk

Unit Root Test of Personal Savings as a Percentage of Disposable Personal Income The unit root test returns a negative value that is not sufficiently more negative than the critical valuesThe unit root test returns a negative value that is not sufficiently more negative than the critical values Can’t reject null hypothesisCan’t reject null hypothesis  The time series is not stationary.

Differenced Trace of Personal Savings as a Percentage of Disposable Personal Income The trace of the differenced values looks to be white noiseThe trace of the differenced values looks to be white noise The peaks indicate some periods of heightened variance.The peaks indicate some periods of heightened variance.

Differenced Histogram of Personal Savings as a Percentage of Disposable Personal Income The histogram of the differenced values is kurtoticThe histogram of the differenced values is kurtotic It is single peaked which is a sign of stationarity but still not acceptableIt is single peaked which is a sign of stationarity but still not acceptable

Differenced Correlogram of Personal Savings as a Percentage of Disposable Personal Income Differencing the time saving has removed the autocorrelation trendsDifferencing the time saving has removed the autocorrelation trends The PACF at lag 1 value is no longer close to 1The PACF at lag 1 value is no longer close to 1 The spikes in PACF at lag 1 and lag 3 are evidence that an ARMA model of a AR(1) and AR(3) would be a good initial model estimationThe spikes in PACF at lag 1 and lag 3 are evidence that an ARMA model of a AR(1) and AR(3) would be a good initial model estimation

Differenced Unit Root Test of Personal Savings as a Percentage of Disposable Personal Income The unit root test of the differenced series returns a negative value that is sufficiently more negative than the critical valuesThe unit root test of the differenced series returns a negative value that is sufficiently more negative than the critical values Reject the null hypothesisReject the null hypothesis  Time series is stationary Dsaving does not contain a unit root.Dsaving does not contain a unit root.

ARMA Model 1 ARMA Model 1 returns significant t- stats on both terms.ARMA Model 1 returns significant t- stats on both terms. AR(1)=-7.28AR(1)=-7.28 AR(3)=-4.46AR(3)=-4.46 The constant is not significantThe constant is not significant C=-0.23C=-0.23

Correlogram of ARMA Model 1 The ARMA terms have removed the PACF spikes at lags 1 and 3 but the Q stats are still high.The ARMA terms have removed the PACF spikes at lags 1 and 3 but the Q stats are still high. The spike at lag 2 may be eliminated with a MA(2).The spike at lag 2 may be eliminated with a MA(2).

ARMA Model 2 ARMA Model 2 returns significant t- stats on all 3 terms.ARMA Model 2 returns significant t- stats on all 3 terms. AR(1)=-8.97AR(1)=-8.97 AR(3)=-4.43AR(3)=-4.43 MA(2)=-6.04MA(2)=-6.04 The constant is not significantThe constant is not significant C=-0.37C=-0.37 Durbin-Watson statistic is approximately 2.0, indicating no serial correlationDurbin-Watson statistic is approximately 2.0, indicating no serial correlation

Correlogram of ARMA Model 2 All spikes have now been eliminated and Q-stats are now lowAll spikes have now been eliminated and Q-stats are now low L looks orthogonal, with fairly low Q- statistics and high probabilitiesL looks orthogonal, with fairly low Q- statistics and high probabilities Model has now proven to be stationary and an accurate estimationModel has now proven to be stationary and an accurate estimation

Serial Correlation Test of Model 2 The low F- statistic also confirms that there’s no serial correlation. Probability is less than critical at 0.28

Actual, Fitted and Residual Plot of Model 2 The residuals are orthogonal Tracking the actual trace well Peaks still implicated heightened variance

Histogram of Residuals for Model 2 The residuals are still single peaked Although highly kurtotic with afat tail Could suggest existence of conditional heteroskedasticity

Trace of Squared Residuals for Model 2 The episodic variance shows some spikes This indicates that residuals are not homoskedastic  Heteroskedasticity is present

Correlogram of Squared Residuals for Model 2 The correlogram of squared residuals shows high Q-statistics There are some significant lags

ARCH Test of Model 2 The F-statistic is significant enough to reject the null hypothesis of homoskedasticity Consistent with former evidences  Heteroskedasticity exists

ARCH GARCH Estimation of Model 2 Added ARCH GARCH to account for heteroskedasticty of the residuals Z-statistics of coefficients showed the model to be significant

ARCH GARCH Correlogram for Model 2 Correlogram is orthogonal Lower Q-stats were achieved Probabilities are above 0.05

GARCH Actual, Fitted, and Residual Plot for Model 2 The residuals are orthogonal Tracking the actual trace well Still some variance but tracking is better

Histogram of Standardized Residuals for Model 2 Histogram is single peaked Kurtosis is still an issue but all other problems are resolved

Trace of GARCH for Model 2 Estimate of h(t) by making GARCH variance seriesEstimate of h(t) by making GARCH variance series

ARCH GARCH Test for Model 2 The F-statistic now is not significant to reject the null hypothesis of homoskedasticity The model we estimated above seems to be a good fit  Heteroskedasticity no longer exists

Forecast of Model 2 Non-recolored In sample forecast to test for accuracy

Forecast of Variance for Model 2 In sample variance Variance is increasing over time Leveling off

Forecast of Model 2 In Sample Recession causing shocks to data set People would continue to spend at high rates or save at low rates

Project Purpose As said before there is an increase in saving due to our recent recession Purpose of the project is to answer is if people will continue to save as the economy comes out of the recession

Forecast for Model 2 Non-recolored Out of sample forecast for the next year

Forecast of Variance for Model 2 Out of sample variance Variance is decreasing over time Leveling off

Out of Sample Forecast for Model 2 Stops going up and steadies Current trend of rising is going to cease

Final Results The results of our forecast indicate that in fact people will continue to save as the recession subsides This makes sense intuitively because credit conditions will remain tighter People will need to save more for larger down-payments on homes, cars, and other loans that are now required due to more stringent loan requirements.

Thank You!