Kim 2 ML

Starting off as a muggle that naïve to the Math's and Data Science world.

Day 64

Volatile Model (ARCH & GARCH)

Technique to address irregular fluctuation that cannot be handle by typical time series model such as ARIMA, Moving Average, Exponential Smoothing & others.

R

Import data. (download from https://finance.yahoo.com/quote/005930.KS/history)

X005930_KS <- read_csv("005930.KS.csv")
samsung <- ts(X005930_KS$`Adj Close`)

Check order of differencing.

ndiffs(samsung)

Result:

Stationary check after differencing.

library(tseries)
adf.test( diff(samsung, 1) )

Result:

Check stationary and ARIMA hyperparameter.

tsdisplay( diff(samsung, 1) )

Result:

Train an ARIMA model.

samsung_arima_010 <- Arima(
                      samsung,
                      order=c(0,1,0)
                    )

Check if model adequate.

checkresiduals( samsung_arima_010 )

Result:

Check ARCH effect

library(rugarch)
library(FinTS)
return_samsung <- diff( samsung , 1)

ArchTest( return_samsung )

Result:

Explanation:

p-value = 0.04753 < 0.05, this show the model has ARCH effect.

Check residual after ARIMA, to identify ACF&PACF for residual square.

tsdisplay( samsung_arima_010$residuals^2 )

Result:

Train an ARCH model.

garchSpec <- ugarchspec(
  variance.model = list(model="sGARCH", garchOrder=c(1,0)),
  mean.model = list(armaOrder=c(0,0)),
  distribution.model = "std"
)
garchFit <- ugarchfit(
  spec = garchSpec,
  data = return_samsung
)
garchFit

Result:

Explanation:

Note that variance.model = list(model="sGARCH", garchOrder=c(1,0)), means that we are training a ARCH model as the value c(1, 0) equivalent to GARCH(p, q). p meant for PACF on residual square, and q meant for ACF on residual square.
If p = q = 0, it actually mean the residual are simply white noise.

Import data. (download from https://finance.yahoo.com/quote/AAPL/history)

AAPL <- read_csv("AAPL.csv")
AAPL <- ts(AAPL$`Adj Close`)

Check stationary and ARIMA hyperparameter.

library(tseries)
adf.test( diff(AAPL, 1) )

Result:

Check stationary and ARIMA hyperparameter.

tsdisplay( diff(AAPL, 1) )

Result:

Train an ARIMA model.

AAPL_arima <- Arima(
                    AAPL,
                    order=c(1,1,1)
                   )

Check residual after ARIMA, to identify ACF&PACF for residual square.

tsdisplay( AAPL_arima$residuals^2 )

Result:

Train an ARCH model.

AAPL_rTS <- ts(diff(AAPL, 1))
garchSpec <- ugarchspec(
  variance.model = list(model="sGARCH", garchOrder=c(1,1)),
  mean.model = list(armaOrder=c(1,1)),
  distribution.model = "std"
)
garchFit <- ugarchfit(
  spec = garchSpec,
  data = AAPL_rTS
)
garchFit

Result:

Confirm ARCH effect.

library(FinTS)
ArchTest(AAPL)
ArchTest(AAPL_rTS)

Result:

Forecast

forecast_garch <- ugarchforecast(garchFit)
forecast_garch

Result:

Kim Ng

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