Prac: ARCH & GARCH
We have know what is the AR, ARMA model. There are relationships between ARCH and AR, GARCH and ARMA. If we know the relationshps among them, it will be very helpful for understanding what we do in this practice.
The ARCH model is appropriate when the error variance in a time series follows an autoregressive (AR) model; if an autoregressive moving average (ARMA) model is assumed for the error variance, the model is a generalized autoregressive conditional heteroskedasticity (GARCH) model.
ARCH mdoel
The description for each column is like below.
D column is the original data.E column is the difference between original data and it's mean.F column is the square of column E.G column is the forcast of AR(4) model of F.H column is the square root of G.I column is the lower bound based H and bounds coefficient that defined by N27.J column is the upper bound based H and bounds coefficient that defined by N27.K column represents whether original data locats between the bounds defined by I and J.
N27 is the coefficient of bounds.N28 is the coverage rate calculated based on K column.
Based on the desciption of each column above, we could get the fomula for each below.
E2 = D2-N$12
F2 = E2^2
G6 = $N$7 + $N$3*F5 + $N$4*F4 + $N$5*F3 + $N$6*F2
H6 = SQRT(G6)
I6 = $N$12-$N$27*H6
J6 = $N$12+$N$27*H6
K6 = IF(AND(D6>I6,D6<J6),1,0)
GARCH mdoel
The description for each column is like below.
A column is the original data.B column is the forecasting based AR(3) model.C column is the difference between original data and AR(3).D column is the square of column C.E column is the GARCH model result.F column is the square root of E.G column is the lower bound.H column is the upper bound.
L19 is the coefficient of bounds.L20 is the coverage rate calculated for original dataset.
Based on the desciption of each column above, we could get the fomula for each below.
B5 = $L$4*A4 + $L$5*A3 + $L$6*A2 + $L$7
C5 = A5-B5
D5 = C5^2
E6 = $L$14*E5+$L$17*D5 +$L$15
F6 = SQRT(E6)
G6 = B6-$L$19*F6
H6 = B6+$L$19*F6
I6 = IF(AND(A6>G6, A6<H6),1,0)
L17 = $L$13-$L$14
L20 = SUM(I6:I793)/COUNT(I6:I793)