Project 3
Jeffrey Wang
2022-12-25
Time series project III. - Stock price prediction
In this project, I used ARIMA and ETS model to predict Novartis’s stock price, using the stock price in 2015.
#Set the language used in the output
Sys.setlocale("LC_TIME","C")## [1] "C"#Load in the library needed
library(quantmod)## Loading required package: xts## Loading required package: zoo##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric## Loading required package: TTR## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zooGet the historical stock price from Yahoo finance
novartis = getSymbols("NVS", auto.assign = F,
from = "2015-01-01", to = "2016-01-01")
plot(as.ts(novartis$NVS.Open))
Overall, the line plot shows that the stock price has a clear trend pattern, but the seasonal pattern is unclear.
#Accomandate with finacial data's irregularly spaced
chartSeries(novartis,type = 'line')
This plot shows the price skipping the sotck market close days, and below is the transaction volumes.
library(forecast)
ggtsdisplay(novartis$NVS.Open)
From the ACF plot, there’s a clear auto-correlated pattern. But it’s hard to find the cut point for setting the AC parameter for arima models. On the other hand, based on the PACF plot, the is a clear cut-point when lag equals 1, thus the p should be equal to 1.
Model construction
#ARIMA model
novartsarima = auto.arima(novartis$NVS.Open,
stepwise = T,
approximation = F,
trace =T)##
## ARIMA(2,1,2) with drift : 789.8915
## ARIMA(0,1,0) with drift : 789.3865
## ARIMA(1,1,0) with drift : 787.3966
## ARIMA(0,1,1) with drift : 786.4334
## ARIMA(0,1,0) : 787.4521
## ARIMA(1,1,1) with drift : 786.4954
## ARIMA(0,1,2) with drift : 786.4976
## ARIMA(1,1,2) with drift : 788.4009
## ARIMA(0,1,1) : 784.5149
## ARIMA(1,1,1) : 784.6786
## ARIMA(0,1,2) : 784.5871
## ARIMA(1,1,0) : 785.468
## ARIMA(1,1,2) : 786.4657
##
## Best model: ARIMA(0,1,1)novartsarima## Series: novartis$NVS.Open
## ARIMA(0,1,1)
##
## Coefficients:
## ma1
## -0.1553
## s.e. 0.0682
##
## sigma^2 = 1.317: log likelihood = -390.23
## AIC=784.47 AICc=784.51 BIC=791.52The auto arima function gave us the most suitable model, which is ARIMA(0,1,1), however, this model didn’t account for any auto-correlated relationship in our data, and it’s worthwhile to take a look at the model including auto-correlated relationship since we did capture it in the PACF plot.
#ARIMA model 2: with autoregressive part
novartsarima2 = Arima(novartis$NVS.Open, order = c(1,1,1))
novartsarima2## Series: novartis$NVS.Open
## ARIMA(1,1,1)
##
## Coefficients:
## ar1 ma1
## 0.5904 -0.7247
## s.e. 0.3136 0.2723
##
## sigma^2 = 1.312: log likelihood = -389.29
## AIC=784.58 AICc=784.68 BIC=795.16Here’s the summary of the arima(1,1,1) model, the AIC was slightly higher but still close to that of what the auto arima function picked for us.
#Forecast using the 2 arima
plot(forecast(novartsarima, h = 20))
plot(forecast(novartsarima2, h = 20))
The difference between the predicted price of the two models is little. The only difference is the confidence interval, arima(0,1,1) has a larger confidence interval. And that’s because ARIMA model assumed that the last observation is indicative of the next one. Prior observations don’t matter much.
#ETS
novartisets = ets(novartis$NVS.Open)
plot(forecast(novartisets, h = 20))
The result of the ETS model was also similar to the previous two models.
Convert to a regular time series
Since the stock market closes during holidays and weekends, the stock price is not regularly spaced. Fixing this issue could bring us a more robust result.
- First, transform the data into a data frame format
- Create a df column of complete dates in 2015
- Merge the two, and find out which days are missing
- Remove weekends, since there should not be any transactions on weekends.
- For the rest missing values, impute them
#1. Conversion to dataframe
novartis = as.data.frame(novartis)
# Adding the rownames as date
novartis$Date = rownames(novartis)
novartis$Date = as.Date(novartis$Date)
head(novartis)## NVS.Open NVS.High NVS.Low NVS.Close NVS.Volume NVS.Adjusted
## 2015-01-02 83.18101 83.37814 82.44624 82.66129 807872 62.11983
## 2015-01-05 83.71864 83.73656 82.59856 82.84050 1537848 62.25450
## 2015-01-06 82.77778 83.09140 81.52330 82.14158 1316992 61.72925
## 2015-01-07 81.85484 82.70609 81.76524 82.50000 1598447 61.99861
## 2015-01-08 84.38172 85.72581 84.22939 85.36739 2156782 64.15344
## 2015-01-09 86.43369 86.74731 85.77957 86.12903 2206890 64.72582
## Date
## 2015-01-02 2015-01-02
## 2015-01-05 2015-01-05
## 2015-01-06 2015-01-06
## 2015-01-07 2015-01-07
## 2015-01-08 2015-01-08
## 2015-01-09 2015-01-09#2. Creating the date column of complete dates in 2015
mydates = seq.Date(from = as.Date("2015-01-01"),
to = as.Date("2016-01-01"),
by = 1)
# Converting to a df (required for the merge)
mydates = data.frame(Date = mydates)#3. Merge novartis with 'mydates'
mydata = merge(novartis, mydates, by = "Date", all.y = T) #Default is full join# 3.9 Removing initial days to start on monday, since 1/1/2015 is Thursday
mydata = mydata[5:366,]#4. Removing wekends,
## Sundays
mydata = mydata[-(seq(from = 7, to = nrow(mydata), by = 7)),]
## Saturdays
mydata = mydata[-(seq(from = 6, to = nrow(mydata), by = 6)),]#5. Impute with last observation
mydata = na.locf(mydata)Which days are the ones best to buy or sell?
After preprocessing the data, now it’s time to look at the price pattern and find the best sell/buy date for Novartis stock.
# Putting the closeprice into a weekly time series
highestprice = ts(as.numeric(mydata$NVS.High),
frequency = 5)# Various plots
seasonplot(highestprice, season.labels = c("Mon", "Tue", "Wed", "Thu", "Fri"))
monthplot(highestprice)
monthplot(highestprice, base = median, col.base = "red")
plot(stl(highestprice, s.window = "periodic"))
From the season plot, the stock price did not show a clear seasonal pattern - there’ probably not a specific day of the week to sell or buy the stock overall. Though, we did see a lower price on Wednesdays.
# Comparison with the low prices
lowestprice = ts(as.numeric(mydata$NVS.Low),
frequency = 5)
monthplot(lowestprice, base = median, col.base = "red")
monthplot(highestprice, base = median, col.base = "red")
It seems the same for the low-price pattern. The seasonal pattern was not clear, so buying/selling stock on a specific day is probably not a good strategy. But Wednesday could be the one day to buy the stock since on average the price is slightly lower compared to other days.