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title: “Time Series Analysis” author: “Cornelius Tanui” date: “January 19, 2020” output: html_document #_____________________________________________________________________________

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TIME SERIES ANALYSIS

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Loading Packages

library(readxl)
library(dplyr)

## 
## Attaching package: 'dplyr'

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

library(ggplot2)
library(scales)
library(forecast)

## Registered S3 method overwritten by 'xts':
##   method     from
##   as.zoo.xts zoo

## Registered S3 method overwritten by 'quantmod':
##   method            from
##   as.zoo.data.frame zoo

## Registered S3 methods overwritten by 'forecast':
##   method             from    
##   fitted.fracdiff    fracdiff
##   residuals.fracdiff fracdiff

library(ggTimeSeries)

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Loading Packages

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TimeSeriesData <- read_excel("C:/Users/User/OneDrive/CORY/DATA/TimeSeries.xlsx",
                         col_types = c("date", 
                                       "numeric", 
                                       "numeric", 
                                       "numeric", 
                                       "numeric",
                                       "numeric")) %>% as.data.frame()
class(TimeSeriesData)

## [1] "data.frame"

View(TimeSeriesData)
sapply(TimeSeriesData, class)

## $date
## [1] "POSIXct" "POSIXt" 
## 
## $open
## [1] "numeric"
## 
## $high
## [1] "numeric"
## 
## $low
## [1] "numeric"
## 
## $close
## [1] "numeric"
## 
## $volume
## [1] "numeric"

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Visualisation

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ggplot(TimeSeriesData, 
       mapping = aes(x = date)) + 
  geom_line(aes(y = low), 
            colour = "green",
            size = 1.5) +
  geom_point(aes(y = high), 
            colour = "red",
            size = 0.5) +
  labs(title = "Trend of Low and High Values of Stock",
       subtitle = "Red = 'High', Green = 'Low'",
       caption = "Data source: AMREC Africa") +
  theme(plot.title = element_text(hjust = 0.5, size = 14),    # Center title position and size
        plot.subtitle = element_text(hjust = 0.5),            # Center subtitle
        plot.caption = element_text(hjust = 0, face = "italic")) +
  xlab("Year") +
  ylab("Value") +
  theme_light()

#_____________________________________________________________________________ ## Data Cleaning #_____________________________________________________________________________

min(TimeSeriesData$date)

## [1] "1997-07-02 UTC"

max(TimeSeriesData$date)

## [1] "2016-05-31 UTC"

TimeSeriesData <- TimeSeriesData %>% arrange(date)

TimeSeries <- ts(TimeSeriesData$open, 
              start = c(1997, 7), 
              end = c(2016, 7),
              frequency = 12) 

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Plot

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plot(TimeSeries,
     xlim = c(1997, 2016),
     col = "red",
     lwd = 2)

#_____________________________________________________________________________ ## Decomposition #_____________________________________________________________________________

Decomposed <- decompose(TimeSeries)
#Decomposed

plot(Decomposed)

plot(Decomposed$x)

plot(Decomposed$seasonal)

plot(Decomposed$trend)

plot(Decomposed$random)

#mean(Decomposed$random, 
#     na.rm = TRUE)

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Exponential Smoothing Using Holt-Winters Method

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HW_Smoothing <- HoltWinters(TimeSeries,      # Smooth (remove trend)
                            beta=FALSE, 
                            gamma=FALSE, 
                            l.start=23.56)
plot(forecast(HW_Smoothing))

HW_Forecasts <- forecast:::forecast.HoltWinters(HW_Smoothing, 
                                     h=10)    # Forecast 10 years ahead 

forecast:::plot.forecast(HW_Forecasts)   # Plot the forecasts

Box.test(HW_Forecasts$residuals, 
         lag = 20, 
         type = "Ljung-Box") # A p-value less than 0.05 means the errors are white noise

## 
##  Box-Ljung test
## 
## data:  HW_Forecasts$residuals
## X-squared = 1.3012, df = 20, p-value = 1

plot.ts(HW_Forecasts$residuals)

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