Financial Econometrics - Assignment Example

Econometrics Log of Real Personal Disposable Income (Lrpdi) The graph above is a time series plot for the log of real personal disposable income. This series shows an upward trend. This implies that this variable has an upward trend across the years. This data is non-stationary since it is increasing with the change of time.
The graph above shows autocorrelation of Lrpdi. ACF is significant across the years. However, at year 1 it is quite high but it has a decreasing uniform trend across the years; implying that the data is not stationary.
The above plot shows the partial autocorrelation of Lrpsi. PACF is generally small in most of the years. Thus, the series has a significant autocorrelations across the years. However, compared to other years, lag 1, 5, 11 and 31 have larger partial autocorrelations.
DLrpdi
The above plot represents the difference in log of real personal disposable income. This data shows a stationary trend whereby the data points assume a straight line. Moreover, the graph shows that the data have a constant mean and variance. This implies that the first difference of the series achieves stationarity.
The above graph represents the autocorrelations of DLrpdi series whereby all the years show significance autocorrelations. However, compared to other years, year 4 and year 10 have larger autocorrelations due to large variations.
Log of real personal consumption (Lrc)
The above graph is a representation of the log of real personal consumption data over time. This series shows an upward trend. This implies that this variable has an upward trend across the years. This data is non-stationary since it is increasing with the change of time.
The graph above shows autocorrelation of Lrc. ACF is significant across the years. At lag 1 it is quite high and it has a decreasing uniform trend across the years; implying that the data is not stationary.
The above graph represents the partial autocorrelation of Lrc series whereby all the years show significance autocorrelations. However, compared to other years, year1, year 3 and year 4 have larger autocorrelations due to large variations.
DLrc
The above plot represents the difference in log of real personal consumption. This data shows a stationary trend whereby the data points assume a straight line. Moreover, the graph shows that the data has a constant mean and variance. This implies that the first difference of the series achieve stationarity.
The above plots are for ACF and PACF for DLrc respectively. The graphs show that both the autocorrelation and partial autocorrelations for the years are significant.
Augmented Dickey-Fuller Test
The test for Lrpdi gives the following results at lag 0 and lag 1:

Thus, since the p-values at both lag 0 and lag 1 is more than 0.05, we fail to reject the null hypothesis which states that the log real personal disposable income shows a unit root.
The test for Lrc at lag 0 and lag 1 give the following results:

Therefore, since the p-value at both lag 0 and lag 1 is more than 0.05 in the above tests, we fail to reject the null hypothesis which states that the log real personal consumption shows a unit root.
The test for Ls at lag 0 and lag 1 give the following results:
Therefore, since the p-values at lag 0 and lag 1 is less than 0.05 in the above tests, we fail to accept the null hypothesis which states that the difference in the Lrpdi and Lrc show a unit root; the difference does not show a unit root.
When we test Ls from 1947 to 1980, we obtain the following results:
From the above results, the p-value is less than 0.05. Thus, we fail to accept the null hypothesis and conclude the difference in the Lrpdi and Lrc do not show a unit root.
When we test Ls from 1980 to 2009, we obtain the following results:
From the above output, the p-value is more than 0.05. Thus, we fail to reject the null hypothesis and conclude that the difference in the Lrpdi and Lrc show a unit root.
Univariate model
From the above output, ARIMA(2,0,0), the coefficient of the AR(1) is 0.0097 and that of AR(2) is 0.28186. Thus, the coefficient at AR(2) is highly significant which implies that AR(2) is the most appropriate alternative univariate model.
REFERENCES LIST
BECKETTI, S. (2013). Introduction to Time Series Using Stata. College Station, TX: Stata
Press.
BOX, G. E. P., G. M. JENKINS, AND G. C. REINSEL. (2008) .Time Series Analysis:
Forecasting and Control. 4th ed. Hoboken, NJ: Wiley.
DICKEY, D. A., AND W. A. FULLER. (1979). Distribution of the estimators for autoregressive
time series with a unit root. Journal of the American Statistical Association vol.74, p. 427–431.
FULLER, W. A. (1996). Introduction to Statistical Time Series. 2nd ed. New York: Wiley.
HAMILTON, J. D. (1994). Time Series Analysis. Princeton: Princeton University Press.
MACKINNON, J. G. (1994). Approximate asymptotic distribution functions for unit-root and
cointegration tests. Journal of Business and Economic Statistics vol.12, p. 167–176.
NEWTON, H. J. (1988). TIMESLAB: A Time Series Analysis Laboratory. Belmont, CA:
Wadsworth Read More