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IBM stock price forecast

Libraries

library(readr)
library(forecast)

In this exercise, I analyzed the IBM stock adjusted close price in the period of [2017-01-01/2021-12-10] to create a time series forecasting models (naïve , Seasonal naïve, ETS,ARIMA, Neural Network), then I checked which model returned the best forecasting results the test period of the last 7 month of the data period. Data from is Yahoo Finance .

Loading the Data

IBM <- read_csv("C:/Users/baaba/Desktop/MS. Applied Economic and Data analysis/ADEC7460.02 Fall 2021 Predictive AnalyticsForecasting [Fulton]/Module 6 VAR, Panel, HTS, Machine Learning 25 Nov -5 Dec/Assignment Homework Time Series/IBM.csv")

head(IBM)
summary(IBM)

plotting the data

IBM.ts <- ts(IBM$`Adj Close`
             , start = c(2016,01)
             , end = c(2021,12)
             , frequency = 12)

autoplot(IBM.ts)

Traingin Testing split

After loading data from Yahoo finance I split the data set into a training set from 2016,1 to 2021 and test set from 2021,6 to the end of data period.

# training sets   
train = window(IBM.ts, end = c(2021,5))
# testing sets
test = window(IBM.ts, start = c(2021,6)) # 7 months test set

Naïve Model

I generated a naive model and I checked the performance for the model forecasting on the test set. The naive model generated a MASE = 1.2720367 and a RMSE = 17.736403. Next we need to compare it with the other models.

naive.fit = naive(train)
naive.forecast = forecast(naive.fit, h = 7)
summary(naive.fit)

checkresiduals(naive.forecast)
accuracy(naive.forecast, test)

autoplot(IBM.ts) +
  autolayer(naive.forecast, series = "naive Forecast") +
  autolayer(test , series = "Actual price")

Seasonal naïve Model

Now I generated a Seasonal naive model and I checked the performance for the model forecasting on the test set. The Seasonal naive model generated a MASE = 1.009509 and a RMSE = 14.93724. the Seasonal naive model has worst RMSE and MASE than the naive model in this data, we will compare these models to check how good the next models are.

snaive.fit = snaive(train)
snaive.forecast = forecast(snaive.fit, h = 7)
summary(snaive.fit)

checkresiduals(snaive.forecast)
accuracy(snaive.forecast, test)

autoplot(IBM.ts) +
  autolayer(snaive.forecast, series = "snaive Forecast") +
  autolayer(test , series = "Actual price" )

ETS Model

In the subsequent model iteration, I generated a Error, Trend, Seasonal model and I checked the performance for the model forecasting on the test set. The ETS Model generated a MASE = 0.7658349 and a RMSE = 10.320349. Although the Seasonal naive model looks much better in the graph but the ETS model has better MASE and RMSE than the Seasonal naive model.

ETS.fit = ets(train)
ETS.forecast = forecast(ETS.fit, h = 7)
summary(ETS.fit)

checkresiduals(ETS.forecast)
accuracy(ETS.forecast, test)

autoplot(IBM.ts) +
  autolayer(ETS.forecast, series = "ETS Forecast") +
  autolayer(test , series = "Actual price")

ARIMA Model

Next I implemented, an ARIMA Model and I checked the performance for the model, and the model returned a MASE = 0.3730515 and a RMSE = 5.452839 , the ARIMA Model is better than the ETS model for this data.

ARIMA.fit = auto.arima(train)
ARIMA.forecast = forecast(ARIMA.fit, h = 7)
summary(ARIMA.fit)

checkresiduals(ARIMA.forecast)
accuracy(ARIMA.forecast, test)

autoplot(IBM.ts) +
  autolayer(ARIMA.forecast, series = "ARIMA Forecast") +
  autolayer(test , series = "Actual price")

Neural Network Model

Next I tried to use the Neural Network Model to see if it can generate better performance that the other models. For the Neural Network Model I got a MASE = 0.4623200 and RMSE = 7.424988 . the Neural Network Model performance for this data is lower than the ARIMA models.

library(forecast)
nn.fit = nnetar(train, lambda=0)


sim <- ts(matrix(0, nrow=20, ncol=5), start=end(train)[1]+1)
for(i in seq(5))
  sim[,i] <- simulate(nn.fit, nsim=20)
library(ggplot2)
ggplot2::autoplot(train) + forecast::autolayer(sim)


nn.forecast <- forecast(nn.fit, PI=TRUE, h=7)

checkresiduals(nn.forecast)
accuracy(nn.forecast, test)

autoplot(IBM.ts) +
  autolayer(nn.forecast, series = "Neural Network Forecast") +
  autolayer(test , series = "Actual price")

Conclusion

data.frame(Model = c("1.naive modlel", "2.snaive model", "3.ETS model", "4.ARIMA model", "5.Neural Network"), "RMSE" = c(8.048907,14.93724 ,10.320349,5.452839,9.559687), "MASE" = c(0.5629862,1.009509,0.7658349,0.3730515,0.6892889))

Ultimately, the ARIMA model returned the best results (MASE = 0.3730515 and RMSE = 5.452839), when we compare it to the actual test data, So we can choose the ARIMA model among these models to forecast the future IBM adjusted stock price.