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Coursework Statistics

Autor:   •  November 11, 2015  •  Coursework  •  841 Words (4 Pages)  •  665 Views

Page 1 of 4

Question 4

1.

AR (1) model:

yt =c+φ1yt−1 +ut

C

φ1

Parameter

0.0290

0.9725

Standard error

0.0129

0.0089

2.

MA (3) model

yt =c+ut 1ut−1 2ut−2 3ut−3

We have c = 0.9310, θ1=1.5080, θ2=1.2488, θ3=0.6036

C

θ1

θ2

θ3

Parameter

0.9310

1.5080

1.2488

0.6036

Standard error

0.0546

0.0206

0.0305

0.0238

3.

ARMA (1,1) model

yt =c+φ1yt−1 1ut−1 +ut.

C

φ1

θ2

Parameter

0.0497

0.9506

0.4248

Standard error

0.0131

0.0082

0.0121

4. Model selection

Using AIC criteria

The number in the beginning of a row implies AR(x)

The number in the beginning of a row implies MA(x)

0

1

2

3

4

0

0.20004

-1.00435

-1.68537

-2.10825

-2.30147

1

-2.65224

-2.78593

-2.78893

-2.78839

-2.78985

2

-2.75376

-2.79040

-2.78932

-2.78707

-2.78706

3

-2.77491

-2.79119

-2.78892

-2.79788

-2.79566

4

-2.77704

-2.78986

-2.78759

-2.79668

-2.79384

ARMA(3,3) is the best.

Using SBIC criteria

The number in the beginning of a row implies AR(x)

The number in the beginning of a row implies MA(x)

0

1

2

3

4

0

0.20634

-0.99176

-1.66648

-2.08305

-2.26998

1

-2.63964

-2.76703

-2.76374

-2.75690

-2.75206

2

-2.73486

-2.76521

-2.75782

-2.74928

-2.74297

3

-2.74971

-2.75970

-2.75113

-2.75379

-2.74527

4

-2.74555

-2.75207

-2.74350

-2.74629

-2.73715

ARMA(1,1) is the best.

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