Time series refers to a set of observations on a particular variable recorded in time sequence. This time sequence or space can be hourly, daily, weekly, monthly, quarterly or yearly. The dataset that will be used is the daily-minimum-temperatures-in-me.csv you can download it from Kaggle. The libraries that will be used for the model in time series are series and forecast.

1. Time Series Analysis Using ARIMA Model For
Forecasting In R (Practical)
By
Laud Randy Amofah
February 2020
Time series refers to a set of observation on a particular variable recorded in time sequence. This
time sequence or space can be hourly, daily, weekly, monthly, quarterly or yearly.
Why time series analysis
1. Its emphasis is to support in decision making
2. To fit a mathematical model and then proceed to forecast the future.
The tool that we will be using for the practical is the RStudio you can click on the link below and
download the RStudio setup and install it;
https://rstudio.com/products/rstudio/download/
The dataset that will be used is the daily-minimum-temperatures-in-me.csv you can download it
from Kaggle. Below is the link to download the daily minimum temperatures in me dataset;
https://www.kaggle.com/paulbrabban/daily-minimum-temperatures-in-melbourne

2. The libraries that will be used for the model in time series are tseries and forecast. The # tag
means comment
I think the above information is enough for us to start our practical. Now let’s launch our RStudio.
Figure 1 – RStudio
We start:
#Importing the necessary libraries for the model
library(tseries)
library(forecast)
#load the daily minimum temperatures in me data.
#NB: To copy the path press on the shift button and right click on the file to copy the path
temp=read.csv("C:UsersLENOVODesktopR tutorialsdaily-minimum-temperatures-in-
me.csv")
temp

3. Figure 2 – Temp output
#NB: In time series we need only the observation, so we open the daily-minimum-temperatures-in-
me.csv file
# and delete the date column or the first column that will left with observation column in the csv file
# after we are done we will save the file as dailytemperature so that it will not conflict with the first file.
###load the daily temperatures data.
temperature=read.csv("C:UsersLENOVODesktopR tutorialsdailytemperatures.csv", header =
TRUE)
temperature

4. Figure 3 – Temperature output
### we convert the data to time series
temperature <- ts(temperature, start = c(1981,1), frequency = 365)
plot.ts(temperature)

5. Figure 4 – Temperature plot output
###Test the data for stationarity using adf test
###H0: Unit root
adf.test(temperature)
Figure 5 – Testing for its stationary output

6. ###Difference the data to make it stationary
#NB: You only differeniate when the p-value is greater then 0.01
dtemperature=diff(temperature)
adf.test(dtemperature)
###Plotting ACF and PACF
acf(as.numeric(temperature), main="ACF OF DIFFERNCED TEMPERATURES")
pacf(as.numeric(temperature), main="PACF OF DIFFERNCED TEMPERATURES")
Figure 6 – AFC output

7. Figure 7 – PAFC output
###Plotting both the ACF and PACF together
par(mfcol=c(2,1))
acf(as.numeric(temperature), main="ACF OF DIFFERNCED TEMPERATURES")
pacf(as.numeric(temperature), main="PACF OF DIFFERNCED TEMPERATURES")

8. Figure 8 – ACF AND PAFC output
###Fit Integrated AR models
model1=arima(temperature,order = c(15,1,0))
summary(model1)
Figure 9 – Summary of AR model output

9. #######Diagnosing the model for Adequecy
###Obtained the residuals of the model
res1=model1$resid
###Test for zero mean
t.test(res1)
Figure 10 – Residuals of the model and testing for zero mean output
###Plot the PACF of the Residuals to check for Autocorrelation
pacf(as.vector(res1),lag=25, na.action=na.pass)
pacf(as.vector(res1^2),lag=25, na.action=na.pass)

10. Figure 11 – Checking for Autocorrelation in the residuals of the PACF output
###Test for Independence
Box.test(res1, type="Ljung-Box", lag=15)
tsdiag(model1)
Figure 12 – Testing for independence output

11. Figure 13 – Testing for independence output with plot diagram
#######Forecasting from the model Model for 10 days
pred<-predict(model1,n.ahead=10)
pred
Figure 14 – The 10 days predictions output

12. #######Plot the data and fitted values
plot.ts(temperature)
lines(fitted(model1),col="red")
lines(fitted(model1),col="blue")

13. Figure 15 – Plotting fitted line with plot diagram

14. plot(forecast(model1,10))
Figure 16 – 10 days Forecast output with plot diagram