Stock Market Prediction - Amazon & Google
Nilosree Sengupta
2021-06-14
Amazon
Data Fetching :
Stock data for two companies, Amazon (AMZN) and Google (GOOGL), are fetched from Yahoo Finance for the period from January 1, 2010, to June 14, 2021.
Fetching Amazon stock data
require(xts)
require(quantmod)
getSymbols.warning4.0=FALSE
AMZN <- getSymbols(Symbols = "AMZN", src = "yahoo",
from = "2010-01-01", to = "2021-06-14", auto.assign = FALSE)
tail(AMZN)AMZN.Open AMZN.High AMZN.Low AMZN.Close AMZN.Volume AMZN.Adjusted
2021-06-04 160.6000 161.0500 159.9405 160.3110 44994000 160.3110
2021-06-07 159.8665 160.4000 158.6100 159.9005 44316000 159.9005
2021-06-08 161.1305 163.9765 160.9005 163.2055 68334000 163.2055
2021-06-09 163.6435 164.8790 163.5350 164.0575 49110000 164.0575
2021-06-10 164.1005 167.5500 164.0575 167.4825 69530000 167.4825
2021-06-11 167.4825 168.3290 166.6725 167.3415 56348000 167.3415Fetching Google stock data
require(xts)
require(quantmod)
getSymbols.warning4.0=FALSEGOOGL <- getSymbols(Symbols = "GOOGL", src = "yahoo",
from = "2010-01-01", to = "2021-06-14", auto.assign = FALSE)
tail(GOOGL) GOOGL.Open GOOGL.High GOOGL.Low GOOGL.Close GOOGL.Volume GOOGL.Adjusted
2021-06-04 118.4635 119.9515 118.1205 119.6785 24458000 119.6785
2021-06-07 119.4720 120.2255 119.0500 120.1150 24120000 120.1150
2021-06-08 120.6005 120.9760 119.7390 119.9220 24240000 119.9220
2021-06-09 120.5715 120.6440 119.8450 120.3970 17942000 120.3970
2021-06-10 120.3460 121.8000 120.1890 121.7565 25904000 121.7565
2021-06-11 122.0000 122.0860 120.9480 121.5100 21958000 121.5100Data Preprocessing:
The closing prices of the stocks were extracted and converted into logarithmic returns. The differencing technique was applied to obtain the differenced log returns.
Data preprocessing for Amazon
AMZN_closing <- Cl(to.daily(AMZN))
AMZN_dc <- Cl(to.monthly(AMZN))
AMZN_log <- log(AMZN_closing)
AMZN_diff <- diff(AMZN_log, lag = 1)
anyNA(AMZN_diff)
colSums(is.na(AMZN_diff))
AMZN_diff <- AMZN_diff[!is.na(AMZN_diff)]Data preprocessing for Google
GOOGL_closing <- Cl(to.daily(GOOGL))
GOOGL_dc <- Cl(to.monthly(GOOGL))
GOOGL_log <- log(GOOGL_closing)
GOOGL_diff <- diff(GOOGL_log, lag = 1)
anyNA(GOOGL_diff)
colSums(is.na(GOOGL_diff))
GOOGL_diff <- GOOGL_diff[!is.na(GOOGL_diff)]Plottings:
Several plots were generated to visualize the data. For both AMZN and GOOGL, plots of the log returns and differenced log returns were created. These plots provide insights into the volatility and trends present in the stock prices.
Plottings for Amazon
plot(AMZN_log, main = "AMZN log returns")
plot(AMZN_diff, type = "l", main = "AMZN diff") 
Plottings for Google
plot(GOOGL_dc)
plot(GOOGL_log, main = "GOOGL log returns")
plot(GOOGL_diff, type = "l", main = "GOOGL diff")
ACF & PACF:
Autocorrelation function (ACF) and partial autocorrelation function (PACF) plots were generated for the differenced log returns of both AMZN and GOOGL. These plots help identify the potential order of autoregressive and moving average terms in the ARIMA models.
ACF and PACF for Amazon
require(astsa)
acf2(AMZN_diff, max.lag = 30) [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
ACF -0.03 -0.01 -0.02 -0.02 0.01 -0.01 0.02 -0.05 0.02 -0.01 -0.01 -0.01 -0.02
PACF -0.03 -0.01 -0.02 -0.02 0.01 -0.01 0.02 -0.05 0.02 -0.01 -0.01 -0.02 -0.02
[,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
ACF -0.02 -0.03 0.03 0.02 0.02 0.01 -0.01 -0.02 -0.03 0.04 0 -0.02 -0.01
PACF -0.03 -0.03 0.02 0.02 0.02 0.01 0.00 -0.02 -0.03 0.03 0 -0.02 -0.01
[,27] [,28] [,29] [,30]
ACF 0.01 0 -0.03 -0.02
PACF 0.01 0 -0.03 -0.02
ACF and PACF for Google
require(astsa)
acf2(GOOGL_diff, max.lag = 30) [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
ACF -0.05 0.02 -0.01 0 -0.01 -0.04 0.06 -0.07 0.05 -0.01 -0.02 0.02 -0.04
PACF -0.05 0.02 -0.01 0 -0.01 -0.04 0.05 -0.06 0.04 0.00 -0.02 0.02 -0.04
[,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
ACF 0.01 -0.03 0.04 0.02 0.02 0.00 -0.03 0.00 -0.07 0.01 -0.02 -0.01 -0.04
PACF 0.00 -0.02 0.03 0.03 0.03 -0.01 -0.02 -0.01 -0.06 0.00 -0.01 -0.02 -0.04
[,27] [,28] [,29] [,30]
ACF 0.01 0.04 -0.04 -0.02
PACF 0.00 0.03 -0.02 -0.03
ARIMA Modeling:
ARIMA models were fitted to the differenced log returns of AMZN and GOOGL. The models were tested with different combinations of autoregressive (AR), integrated (I), and moving average (MA) terms. The SARIMA function from the “astsa” package was used for modeling.
ARIMA Model for Amazon
Res <- sarima(AMZN_diff,0,0,0)
AMZN_fit1 <- sarima(AMZN_diff,0,1,0)
AMZN_fit2 <- sarima(AMZN_diff,0,0,1)
AMZN_fit3 <- sarima(AMZN_diff,1,0,0)
Apply model
arima_log <- arima(AMZN_log, order = c(0,1,0))sarima(AMZN_log, 0,1,0)
ARIMA Model for Google
Res <- sarima(GOOGL_diff, 0, 0, 0)
G_fit1 <- sarima(GOOGL_diff, 0, 1, 0)
G_fit2 <- sarima(GOOGL_diff, 0, 0, 1)
G_fit3 <- sarima(GOOGL_diff, 1, 0, 0)
Apply model
sarima(GOOGL_log, 0, 1, 0)
Forecasting:
SARIMA models were used to forecast the log returns for the next 24 periods for both AMZN and GOOGL. These forecasts provide an estimate of the future behavior of the stock prices based on the historical data
Forecasting for Amazon
sarima.for(AMZN_log, n.ahead = 24,0,1,0)Time Series:
Start = 2881
End = 2904
Frequency = 1
[1] 5.121155 5.122273 5.123391 5.124509 5.125627 5.126745 5.127863 5.128981
[9] 5.130099 5.131217 5.132334 5.133452 5.134570 5.135688 5.136806 5.137924
[17] 5.139042 5.140160 5.141278 5.142396 5.143514 5.144632 5.145750 5.146868
$se
Time Series:
Start = 2881
End = 2904
Frequency = 1
[1] 0.01976214 0.02794788 0.03422903 0.03952428 0.04418949 0.04840716 0.05228571
[8] 0.05589577 0.05928642 0.06249337 0.06554360 0.06845806 0.07125341 0.07394315
[15] 0.07653844 0.07904856 0.08148139 0.08384365 0.08614117 0.08837897 0.09056150
[22] 0.09269265 0.09477589 0.09681431
require(forecast)
summary(arima_log)Call:
arima(x = AMZN_log, order = c(0, 1, 0))
sigma^2 estimated as 0.0003918: log likelihood = 7207.44, aic = -14412.87
Training set error measures:
ME RMSE MAE MPE MAPE MASE
Training set 0.001118256 0.01979033 0.01377054 0.03204543 0.4547713 0.9997007
ACF1
Training set -0.02780339Forecasting for Google
sarima.for(GOOGL_log, n.ahead = 24, 0, 1, 0)
require(forecast)
summary(arima_log)arima(x = AMZN_log, order = c(0, 1, 0))
sigma^2 estimated as 0.0003918: log likelihood = 7207.44, aic = -14412.87
Training set error measures:
ME RMSE MAE MPE MAPE MASE
Training set 0.001118256 0.01979033 0.01377054 0.03204543 0.4547713 0.9997007
ACF1
Training set -0.02780339Summary Statistics:
Summary statistics were calculated for the ARIMA model fitted to the log returns of AMZN. The mean error (ME), root mean squared error (RMSE), mean absolute error (MAE), mean percentage error (MPE), mean absolute percentage error (MAPE), mean absolute scaled error (MASE), and the first-order autocorrelation coefficient (ACF1) were reported