Time Series Forecasting: Google stock price

Yul Young Park

08/24/2018

Time series data

Components of time series data

  • Seasonal component (S)
  • Trend-cycle component (T)
  • Remainder component ( R)

Composition types of the components

  • Additive: S + T + R
  • Multiplicative: S * T * R

Methods of time series forecasting

  • Moving average
  • Exponential filtering
  • Autoregressive integrated moving average (ARIMA)
  • Advanced methods (Neural network, Bagging, Bootstrapping, etc)

As an example, we demonstrate ARIMA model, and exponential filtering model is shown in Shiny App.

ARIMA model, as an example here

Three components of ARIMA model

  • Auto Regression (AR)
  • Differencing(Integrated)
  • Moving Average(MA)
library(quantmod)
library(forecast)
load("stock_data_google_2010_2016.RData")
weekly_GOOG <- to.weekly(GOOG[ "2013-01-01::2013-12-31"])
weekly_GOOG_closing <- Cl(weekly_GOOG)
ts1 <- ts(weekly_GOOG_closing, frequency=5)

autoplot(ts1) # seasonal component adj. excluded due to aperiodicity

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Parameter Selection & Fitting a model

ts1 %>% diff() %>% ggtsdisplay(main="Differenced data")

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fit <- Arima(ts1, order=c(6,3,7))
checkresiduals(fit)

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    Ljung-Box test

data:  Residuals from ARIMA(6,3,7)
Q* = 5.6726, df = 3, p-value = 0.1287

Model df: 13.   Total lags used: 16

ARIMA model: Forecasting and Accuracy

autoplot(forecast(fit))

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print(accuracy(fit))

                    ME     RMSE      MAE      MPE     MAPE      MASE
Training set 0.7272524 11.19919 7.544993 0.131336 1.699653 0.3099237
                     ACF1
Training set -0.006435246

References:

– https://otexts.org/fpp2/

– https://machinelearningmastery.com/time-series-forecasting/

– https://www.r-bloggers.com/forecasting-stock-returns-using-arima-model/