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Quantitive methods - Assignment Example

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1. The Order of integration Essentially, the order of integration reflects the stationarity characteristics of a time series variable. For a series that is stationary in its levels, the order of integration is zero, written as I(0). For a variable that is non-stationary in its levels, but the series of first differences is stationary, the order of integration is one, denoted as I(0)…
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Download file to see previous pages We shall first conduct an informal graphical analysis to get a feel for what to expect and then move on to formal tests for stationarity. We start by looking at the time plots of the two given series. Figure 2: share price of Korean Airlines Figures 1 and 2 present the time plots. Evidently, both series exhibit a gradually rising trend and some moderate persistence properties. This reflects that neither of the series are stationary. They also seem to reflect similar patterns of persistent volatility. Now, we turn to look at the first differences of the two series. Figure 3: The Korean Stock Exchange stock price index in first differences Figure 4: price of Korean Airlines in first differences. From figures 3 and 4, we find that neither series exhibits any patterns or trends. They seem to fluctuate randomly around zero. Thus, both the series of 1st differences seem to be stationary around a zero mean. Thus our preliminary graphical analysis reflects that both the series are integrated of the first order. Formally to evaluate the validity of these claims, we run Augmented Dickey Fuller (ADF) tests on the levels and the 1st differences of the two series. ...
Augmented Dickey-Fuller Test Equation Dependent Variable: D(LKO) Method: Least Squares Date: 04/09/12 Time: 13:53 Sample (adjusted): 1/08/1997 12/14/2011 Included observations: 780 after adjustments Coefficient Std. Error t-Statistic Prob.   LKO(-1) -0.003394 0.003258 -1.041768 0.2978 C 0.024682 0.022454 1.099231 0.2720 R-squared 0.001393     Mean dependent var 0.001348 Adjusted R-squared 0.000109     S.D. dependent var 0.044155 S.E. of regression 0.044152     Akaike info criterion -3.399783 Sum squared resid 1.516653     Schwarz criterion -3.387836 Log likelihood 1327.915     Hannan-Quinn criter. -3.395188 F-statistic 1.085281     Durbin-Watson stat 2.039111 Prob(F-statistic) 0.297843 Table 1 above presents the results of running an ADF test on the lko series. The choice of optimal lag is automatic based on the Schwarz information criterion or SIC. Note that the null hypothesis is that the series has a unit root. The relevant portions have been highlighted for convenience. The t-statistic is smaller in absolute terms compared to the critical value, and the associated p-value is 0.74>0.05. Therefore, we fail to reject the null hypothesis. Thus, this implies that the series of levels of the lko is non-stationary. Now, we take first differences of the series and test its stationarity properties. This is done in table 2. Table 2: testing stationarity of the 1st differences of lko Null Hypothesis: D(LKO) has a unit root Exogenous: Constant Lag Length: 0 (Automatic based on SIC, MAXLAG=20) t-Statistic   Prob.* Augmented Dickey-Fuller test statistic -28.52751  0.0000 Test critical values: 1% level -3.438518 5% level -2.865035 10% level -2.568686 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent ...Download file to see next pagesRead More
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