Obtain the correlograms and examine the autocorrelations and partial autocorrelations for both e and r

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

Word limit:

The maximum word count for this exercise is 2000 words that includes everything between the start and completion of the answer, excluding tables, figures, foot - and endnotes, and appendices, but including any in-text citations. 

References and additional material:

In answering the questions below, you must consult the relevant chapters of the recommended book Introductory Econometrics for Finance by Chris Brooks and my lecture handouts, my Eviews based lab sheets and the help option in Eviews 

Data: 

Will be provided.

In answering the questions below, you may wish to consult the option in Eviews.

1.    For your series, in Eviews use the Genr option to calculate (i) the log of the price series, e.g. e=log (Adj Close), and (ii) the daily log returns (e.g. r=log(Adj Close)-log(Adj Close(-1))).

          i.    Examine the descriptive statistics for both e and r.  What do you conclude about the distributions of e and r?  Is e normally distributed?  Is r normally distributed?  Explain why/why not?

         ii.    Obtain the correlograms, and examine the autocorrelations and partial autocorrelations for both e and r.  What do you conclude about the behaviour of e and r?  Are they stationary/non-stationary?

        iii.    Are your conclusions about stationary/non-stationary of e and r confirmed by appropriate unit root tests?

2.    Estimate and select an appropriate ARMA (p,q) model for e.  In selecting your preferred model, use the information provided by: 

           i.    The estimated coefficients (and their t-statistics or p values)

          ii.    Serial correlation in the residuals

         iii.    Information criteria.

Produce a summary table similar to this.

(standard errors are in parenthesis)

        iv.    Carry out forecasts (Ex-post Out of sample) of the e series for the last 30 observations (fixed forecasting horizon) for the competing models (i.e. AR(1), AR(2) …. MA(1), …., ARMA(1,1), ….) and choose the best model using the following criterions.

AIC

SBC

LM(12)

RMSE

MAE

MAPE

THEIL

 

         v.    Carry out forecasts (Ex-post Out of sample) of the e series for the 30 observations (t+10, t+20, and t+30) using the chosen model from part 2(iv) [pay attention to the forecast summary statistics] and comment on your results.

        vi.     

Out of Sample Horizon

10 observations

20 observations

30 observations

 

Attachments:

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