School Papers

BE333- a country. Inflation also jumps and falls

BE333- Empirical Finance Coursework

Question 1

Seven time series were used in this case to
determine how they varied in the period that was provided. Graph for credit
spread or yield on Moody’s Aaa mins BBa debt indicated seasonal where high and
low were extended in the start of the period but eased towards the end. This is
opposite for dividend yield on S 500. There are visible dips and highs
but these were minimal in the start of the 1970 to 1985. The variations were
extreme from 1985 to 2005. These are typical trends of stocks where they
decline and rise several depending on news affecting specific stocks or general
economy of a country. Inflation also jumps and falls severally, with some
periods showing minimal changes and others extreme. Excess return on S
500 had close variations of highs and lows, an indication of possible multiple
effects on the same. All the graphs above show trends that are typical of time
series of economic nature where variations rise and fall seasonally depending
on prevailing factors.

 

 

Question
Two: Autocorrelogram

There is very weak correlation in the
images as shown the diagram above. With highest values ranging at around 0.105.
P-values are also very high compared to confidence limit. The implication here
is the null hypothesis that is there is no relationship is not rejected. AC and
PAC lags are all near zero, indicating there is no serial correlation. There
are no substantial and persistent autocorrelation in the residuals.

 

Question
Three

This is the test for normality where in a
perfectly normal series, skewness would be zero and kurtosis 3. The null
hypothesis is the data has s skewness of zero and excess kurtosis of zero. Alternative
hypothesis would mean the data is not normally distributed. Probability is
0.000, which is less than the confidence limit, implying that the null
hypothesis is not rejected. Thus, the data is normally distributed.

 

Question
Four

 

The aim of choosing the best order in the
process of equation estimation for the case of ARMA is to find best point of
integration. In the case of AR, the aim is to find the best order for
developing the equation. One of the criteria of doing this is to choose one
where there is no significant autocorrelation. The model should also have
lowest possible residual variance, if there are many with no autocorrelation
and finally, one that is easily understood.

In the model selection criteria below, (0,0)
has the least autocorrelation at 5.799306, compared to all provided. This
qualified it to be chosen as best order for this model.

 

In the
equation estimation below, one of the criteria given is AIC that has closely
similar value of 5.795139.

The graph below shows level of lags where
(0,0) is chosen as the lowest and therefore best for this model.

 

Question
Five.

 

Dependent
Variable: EXRET

 

 

Method:
Least Squares

 

 

Date:
12/03/17   Time: 00:34

 

 

Sample:
1966M01 2005M12

 

 

Included
observations: 480

 

 

 

 

 

 

 

 

 

 

 

 

Variable

Coefficient

Std.
Error

t-Statistic

Prob.  

 

 

 

 

 

 

 

 

 

 

CS_1

18.03872

10.62972

1.697008

0.0904

DY_1

12.01848

4.233788

2.838707

0.0047

I12_1

-41.65688

12.22205

-3.408339

0.0007

I12_2

34.50915

13.33280

2.588289

0.0099

I3_1

21.14607

13.28627

1.591573

0.1122

I3_2

-19.32246

12.13966

-1.591680

0.1121

INF_2

-12.20175

7.140983

-1.708693

0.0882

IP_2

0.342648

5.451389

0.062855

0.9499

MB_2

-15.72143

6.019613

-2.611702

0.0093

PE_1

-2.987798

2.423082

-1.233057

0.2182

TS_1

0.803668

3.957740

0.203062

0.8392

WINTER

0.848182

0.391702

2.165375

0.0309

 

 

 

 

 

 

 

 

 

 

R-squared

0.114137

    Mean dependent var

0.432739

Adjusted
R-squared

0.093316

    S.D. dependent var

4.382373

S.E. of regression

4.172895

    Akaike info criterion

5.719779

Sum
squared resid

8149.308

    Schwarz criterion

5.824124

Log
likelihood

-1360.747

    Hannan-Quinn criter.

5.760795

Durbin-Watson
stat

2.059292

 

 

 

 

 

 

 

 

 

 

 

 

 

Estimation
Equation:

=========================

EXRET =
C(1)*CS_1 + C(2)*DY_1 + C(3)*I12_1 + C(4)*I12_2 + C(5)*I3_1 + C(6)*I3_2 +
C(7)*INF_2 + C(8)*IP_2 + C(9)*MB_2 + C(10)*PE_1 + C(11)*TS_1 + C(12)*WINTER

 

Substituted
Coefficients:

=========================

EXRET =
18.0387199011*CS_1 + 12.0184818667*DY_1 – 41.6568827032*I12_1 +
34.5091473802*I12_2 + 21.1460691635*I3_1 – 19.3224561113*I3_2 –
12.2017462426*INF_2 + 0.342648443091*IP_2 – 15.7214334545*MB_2 –
2.98779768335*PE_1 + 0.803667639182*TS_1 + 0.848181739832*WINTER

 

 

 

 

 

 

Autocorrelagram

 

 

 

Dependent
Variable: EXRET

 

 

Method:
ARDL

 

 

 

Date:
12/03/17   Time: 00:44

 

 

Sample
(adjusted): 1966M02 2005M12

 

Included
observations: 479 after adjustments

 

Maximum
dependent lags: 12 (Automatic selection)

Model
selection method: Akaike info criterion (AIC)

Dynamic
regressors (0 lag, automatic): CS_1 DY_1 I12_1 I12_2 I3_1 I3_2

        INF_2
IP_2 MB_2 PE_1 TS_1 WINTER  

 

Fixed
regressors: C

 

 

Number of
models evalulated: 12

 

Selected
Model: ARDL(1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)

Note:
final equation sample is larger than selection sample

 

 

 

 

 

 

 

 

 

 

Variable

Coefficient

Std.
Error

t-Statistic

Prob.*  

 

 

 

 

 

 

 

 

 

 

EXRET(-1)

-0.039746

0.045242

-0.878523

0.3801

CS_1

20.12911

10.78879

1.865743

0.0627

DY_1

5.391993

6.074700

0.887615

0.3752

I12_1

-41.52241

12.23451

-3.393875

0.0007

I12_2

36.39865

13.39503

2.717325

0.0068

I3_1

19.32772

13.41259

1.441013

0.1503

I3_2

-20.10972

12.15937

-1.653846

0.0988

INF_2

-14.44179

7.287749

-1.981653

0.0481

IP_2

-2.191993

5.738492

-0.381981

0.7027

MB_2

-12.83998

6.388323

-2.009914

0.0450

PE_1

-12.15045

6.523265

-1.862633

0.0631

TS_1

-0.254958

4.041134

-0.063091

0.9497

WINTER

0.836493

0.394633

2.119670

0.0346

C

3.574303

2.392402

1.494023

0.1358

 

 

 

 

 

 

 

 

 

 

R-squared

0.119329

    Mean dependent var

0.432900

Adjusted
R-squared

0.094708

    S.D. dependent var

4.386954

S.E. of
regression

4.174048

    Akaike info criterion

5.724442

Sum
squared resid

8101.545

    Schwarz criterion

5.846370

Log
likelihood

-1357.004

    Hannan-Quinn criter.

5.772373

F-statistic

4.846636

    Durbin-Watson stat

2.000442

Prob(F-statistic)

0.000000

 

 

 

 

 

 

 

 

 

 

 

 

 

*Note:
p-values and any subsequent tests do not account for model

        selection.