NỘI DUNG
Giới thiệu
Phương pháp luận Box-Jenkins
Mô hình AR(p)
Mô hình MA(q)
Mô hình ARMA(p,q)
Mô hình ARIMA(p,d,q)
Mô hình SARIMA
Ví dụ minh họa
Ln(Yt)
Stationary Seasonal
Yt
Nonstationary
p, q
AR(p)
MA(q)
ARMA(p,q)
Practical
ARMA(p,q)
Diagnostic Checking
∆LnYt
Stationary
NonStationary
∆2LnYt
Seasonal
difference
p, q, P, Q
Holt-
Winters
SARIMA
Comparison
BOX-JENKINS
METHODOLOGY
Step 1
Calculate the
ACF and PACF of the raw data, and check whether the
series is stationary or not. If the series is stationary go to step 3,
if not go to step 2.
Step 2
Take the
log and the 1st diff.of
the raw data and calculate the ACF and
PACF for the first
logarithic differenced series.
Step 3
Examine the graphs of the
ACF and PACF
and determine which models would
be good starting points.
Step 4
Estimate those models.
Step 5
Diagnostic checking for each of these estimated models:
a)
Check to see if the parameter of the longest lag is significant. If
not, then you probably have too many parameters, and should decrease
the order of p and/or q.
b)
Check the ACF and PACF of the errors. If the model has at least
enough parameters, then all ACFs and PACFs will be insignificant.
c)
Check the AIC and SBC together with the adj-R2 of the estimated
models to detect which model is the parsimonious one (i.e., the one
that minimizes AIC and SBC and has the highest adj-R2).
d)
Check the RMSE and compare the fitted – actual value graphs
(especially at turning points).
If the series is highly volatile (e.g., stock prices, gold prices, and
other commodity prices), we sometimes check whether the ARCH effects
exist. If yes, we should apply the ARCH/
GARCH models for the data.
Step 6
If changes in the original model are needed, go back to step 4.
BOX-JENKINS METHODOLOGY
AUTOREGRESSIVE (AR) MODEL
Giả sử Yt là một chuỗi dừng
Mô hình AR(p) có dạng sau đây:
Yt = B0 + B1Yt-1 + … + BpYt-p + ut (1)
ut: white noise error term
Độ trễ p được xác định theo lối
thực nghiệm, dựa vào các tiêu
chí như AIC, hoặc theo PACF!
PACF? Partial AutoCorrelation Function
