ECONOMICAL ANALYSIS

Economical Analysis

Economical Analysis

1. The file coursework2.xls contains the 100 values of a simulated series entitled Y2. Use this series to perform the following tasks.

i) Plot the sequence against time. Does the series appear to be stationary?

Correlogram of Y2

From the line graph it is clear that the data is stationary. The sequence of the series is plotted against time in order to identify the data pattern in term of stationary or non-stationary. Hence, if the data is found to be stationary it means that the statistics such as standard deviation, mean, relevant to the particular data do not have the tendency to change over time (Brooks, Wang; 2008). One can clearly assume the straight line through which the data has passed over the period of time. Hence, it can be concluded here that the data series appears to be stationary. The pattern of line shown in the graph below shows that the relevant series of data has the stationary pattern as it is clear from the signal consistency in the line graph below.

ii) Report the SACF, SPACF and Ljung-Box portmanteau statistics up to k=24. Plot the SACF and SPACF.

Sample: 1 100

Included observations: 100

Autocorrelation

Partial Correlation

OBS

AC 

 PAC

 Q-Stat

 Prob

  ******|. |

  ******|. |

1

-0.834

-0.834

71.729

0.000

       .|**** |

      **|. |

2

0.597

-0.328

108.77

0.000

     ***|. |

       *|. |

3

-0.440

-0.194

129.12

0.000

       .|** |

       .|. |

4

0.350

-0.015

142.12

0.000

      **|. |

       *|. |

5

-0.319

-0.140

153.03

0.000

       .|** |

       .|* |

6

0.332

0.089

164.96

0.000

      **|. |

       .|. |

7

-0.337

0.000

177.43

0.000

       .|** |

       .|. |

8

0.317

0.014

188.55

0.000

      **|. |

       .|. |

9

-0.276

0.017

197.09

0.000

       .|* |

       *|. |

10

0.179

-0.199

200.72

0.000

       *|. |

       .|. |

11

-0.084

-0.046

201.53

0.000

       .|. |

       .|. |

12

0.038

-0.021

201.69

0.000

       .|. |

       *|. |

13

-0.053

-0.113

202.02

0.000

       .|. |

       *|. |

14

0.073

-0.082

202.65

0.000

       *|. |

       *|. |

15

-0.090

-0.066

203.62

0.000

       .|* |

       .|. |

16

0.101

0.017

204.86

0.000

       *|. |

       .|* |

17

-0.068

0.099

205.43

0.000

       .|. |

       .|. |

18

-0.002

-0.061

205.43

0.000

       .|. |

       .|. |

19

0.049

-0.061

205.73

0.000

       .|. |

       .|. |

20

-0.055

0.002

206.11

0.000

       .|. |

       .|. |

21

0.027

-0.057

206.21

0.000

       .|. |

       *|. |

22

-0.002

-0.106

206.21

0.000

       .|. |

       .|. |

23

0.006

-0.005

206.21

0.000

       .|. |

       .|. |

24

-0.034

-0.045

206.37

0.000

SACF and SPACF of the series are obtained and are mentioned in the table above. The correlogram for the series shows that there are 5-6 spikes in ACF, whereas in PACF 1-2 spikes are visible for analysis. This suggests that we might have up to MA (3) and AR (1) specifications. Concerning both ACF and PACF are decaying towards 0 exponentially, this series is of high probability to follow an ARMA (p,q) process. So, the possible models are the ARMA (1, 3), ARMA (1, 2) or ARMA (1, 1) models. We then estimate the three possible models. The command for estimating the ARMA (1, 3) models in EViews is:

Ls Y2 c ar(1) ma(1) ma(2) ma(3)

Similarly, for the ARMA (1, 2), it is:

Ls Y2 c ar(1) ma(1) ma(2)

And for the ARMA (1, 1) it is:

Ls Y2 c ar(1) ma(1)

iii) Identify an ARMA model for this series, explaining carefully all the steps in your argument. [You can consider and examine several tentative models.]

Now, as discussed earlier that the values of autocorrelation function and partial autocorrelation functions shows that the model need to be tested against above three estimates. The details are mentioned below:

Regression results of an ARMA (1, 3) model

Dependent Variable: Y2

Method: Least Squares

Sample (adjusted): 2 100

Included observations: 99 after adjustments

MA Backcast: -1 1

Variable

Coefficient

Std. Error

t-Statistic

Prob.  

C

-0.003383

0.002145

-1.576805

0.1182

AR(1)

-0.608294

0.152224

-3.996034

0.0001

MA(1)

-0.793089

0.167206

-4.743191

0.0000

MA(2)

0.026588

0.240179

0.110701

0.9121

MA(3)

-0.233306

0.121575

-1.919023

0.0580

R-squared

0.796479

    Mean dependent var

-0.017301

Adjusted R-squared

0.787818

    S.D. dependent var

2.375139

S.E. of regression

1.094065

    Akaike info criterion

3.066863

Sum squared resid

112.5160

    Schwarz criterion

3.197930

Log likelihood

-146.8097

    Hannan-Quinn criter.

3.119893

F-statistic

91.96693

    Durbin-Watson stat

2.006227

Prob(F-statistic)

0.000000

Inverted AR Roots

     -.61

Inverted MA Roots

      1.00

    -.10-.47i

  -.10+.47i

Regression results of an ARMA(1,2) model

Dependent Variable: Y2

Method: Least Squares

Sample (adjusted): 2 100

Included observations: 99 after adjustments

Convergence achieved after 11 iterations

MA Backcast: 0 ...