Assignment Task:
Task:
INSTRUCTIONS
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This assignment deals with the following assessment criteria:
Unit root testing
Cointegration
ECM
Model statement
Response characteristics and forecasting
Question 1: (10 marks)
1.1Discuss the different components (trends or variations) of a time series (4)
1.2Explain the difference between stationary and non-stationary stochastic processes(3)
1.3In your own words explain what a weakly dependent time series is and how this can impact the modelling process. (3)
Question 2: (17 marks)
For the remainder of this assignment you will be required to build an econometric model to track the development of the JSE All share index.
According to theory, the share price of a company is negatively correlated to changes in interest rates. Also share prices are often extremely sensitive to changes in the exchange rate as well as commodity prices.
The quarterly data is provided in the Excel file: ECS4863 2021 Assignment 02 data, which is available on myUNISA.
Variable names and description:
ALSI= JSE: All Share index – Price index (Index)
TBILL= South Africa Treasury Bill rate (percent per annum)
ZAR= SA Rand to US Dollar exchange rate (quarterly averages)
GOLD= Gold price (USD/oz)
M3 = M3 Money supply (Current prices, R Millions)
2.1Provide a graph of the All Share Index. Briefly discuss the main trends (and possible reasons) you observe.(2)
2.2Calculate and provide a graph depicting the gold price in both US Dollars and Rands. Discuss the differences observed(3)
2.3Complete the following table: (4)
Remember to generate the logs of all the relevant variables, prior to conducting the tests. Clearly indicate the statistical significance of your findings by using stars (*) next to the results.
Variable Model Lags ADF test statistic
LALSI Trend and Intercept
Intercept
None LTBILL Trend and Intercept
Intercept
None DLALSI Trend and Intercept
Intercept
None DLTBILL Trend and Intercept
Intercept
None * Statistically significant at the 10% level** Statistically significant at the 5% level*** Statistically significant at the 1% level
D, indicates the number of differences.
2.4Based on your findings in the table above, comment on the order of integration of the ALSI and TBILL variables. (2)
2.5Estimate the following long-run cointegration equation (Remember to include an intercept term) (2)
ALSI = f (TBILL, ZAR)
Copy/paste your ‘EViews Estimation output’ window here (include all
information)
2.6Interpret the coefficients of the long-run equation. Do they correspond to your a priori expectations in terms of their signs? (2)
2.7 Test for cointegration between the variables. Generate the residual series with the command GENR: RESALSI = RESID. Perform a unit root test on RESALSI and report your answers in the table below(1)
Model Lags p-value
RESALSI 2.8 Can we conclude that the variables in the long-run equation are cointegrated? Explain. (1)
Question 3: (15 marks)
3.1 In this question you have to build an ECM for the All Share price index, using the equation as specified below (Note the differences and lags).(4)
D(LNALSI) = C(1)*D(LNTBILL(-1)) + C(2)*D(LNZAR(-1)) + C(3)*D(LNM3) +
C(4)*D(LNGOLD) + C(5)*RESALSI(-1) + Constant
Copy/paste your ‘EViews Estimation output’ window here (include all
information)
3.2Evaluate the ECM statistically. Also, comment on the number of lags included, and whether this makes sense in terms of your a priori expectations. (3)
Test Test Statistics p-value Conclusion
Jarque-BeraJB = Ljung-Box Q LBQ(6)= Breusch-Godfrey LM TEST nR²(2) = ARCH-LM nR²(2) = White nR² (no CT) = Ramsey RESET LR(1) = 3.3 Perform the required diagnostic and stability tests on the residuals of the ECM. Complete the table. (6)
3.4 Given your conclusions on the diagnostic check of the ECM, do you think that this is an acceptable model? (Please provide reasons, no marks will be awarded for only stating yes/no). (2)
Question 4: (8 marks)
In this question you have to create a model in EViews to solve the equation (i.e. put the long-run and short run components together).
4.1 Provide your model statement (2 marks), and a copy of the graph depicting the actual and modelled values (2 marks).(4)
4.2Apply a permanent shock to the TBILL variable. You can decide the size of your shock as well as the year during which it is implemented.
Post a graph of the shocked versus un-shocked variable. (make sure to clearly indicate your decisions in terms of the size and date of the shock applied)(4)
[Total = 50 marks]
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