Relational Operators

It compares two numerical expressions and return a Boolean variable: either 0 (FALSE) or 1 (TRUE). The following table shows the six commonly used relational operators

Precedence of relational operators is lower than arithmetic operators. To avoid confusion, it is good practice to use brackets to control ordering. For example, if we write 2 + 2 1 + 3, then the software we do the arithmetic operators first. This implies we have 4 4, which implies a false statement

Logical Operators

In practice, we often use two or more conditions to decide what to do. For example, scholarship is often given if the candidate has done well in both academic and extra-curricular activities.

To combine different conditions, there are three logical operators: (1) &&, (2) ||, and (3) !.

First, && is similar to AND in English, that is, A && B is true only if both A and B are true. Second,  is similar to OR in English, that is, A || B is false only if both A and B are false. Third, ! is similar to NOT in English, that is, !A is true only if A is false.

Different relational operators, the precedence of logical operators can be high. While and and or operators are lower in precedence than relational operators, not has a very high precedence and almost always evaluated first. - Hence, it is always a good practice to use brackets to control operation ordering.

Application: Checking Data Type

One important usage of conditional statement is to check whether the data for calculation is correct.

Very often, we only want to execute the code if the data point exists. We can use is.na(). It will return true if it is NA; otherwise false.

if(!is.na(x)){
  do.something
}

Another related function is to check if the data type is number. The function is.numeric() returns true if it is numerical variable; otherwise false.

Application: Missing data

Note that R reports error if there is an NA in the statement.

x <- NA
x > 0

## [1] NA

Very often, we want to set ignore those case with missing data (NA). Then we will use isTRUE

x <- NA
isTRUE(x > 0)

## [1] FALSE

While loop

The syntax of while loop is as follows:

while (condition){
  keep doing when condition holds
}

The following example shows how to calculate the sum of all integers from 1 to 10.

n <- 10
i <- 1
sum <- 0
while (i <= n){         # i is the control variable     
  sum <- sum + i        # accumulate i into sum
        i <- i + 1      # increment i by 1
  }

For Loop over integers

Loops that are based on the value of an integer variable. It increases by the same amount each time, and ends when the variable reaches a specified value

The syntax for a for loop is simple.

m <- 1
n <-10
for (i in m:n){
  run as long as condition holds
}

Loop over vectors

We can define a vector and construct a for loop that executes for each element in the vector:

students <- c("Amy", "Tom")
for (student in students){
   cat(student,"\n")
}

## Amy 
## Tom

Example: Technical Indicators

A n-day simple moving avaerage (n-day SMA) is arithmetic average of prices of past n days:

\[ SMA_t(n) = \frac{P_t+\ldots+P_{t-n+1}}{n}\]

The following is an SMA function:

mySMA <- function (price,n){
  sma <- c()
  sma[1:(n-1)] <- NA
  for (i in n:length(price)){
    sma[i]<-mean(price[(i-n+1):i])
  }
  return(sma)
}
mySMA(1:10,5)

##  [1] NA NA NA NA  3  4  5  6  7  8

An n-day exponential moving avaerage (n-day EMA) is exponential average of prices where weighting of more recent prices carry higher weights. The first EMA is similar to SMA and the updating formula is simple.

\[ EMA_t(n) = \beta P_t +(1-\beta) EMA_{t-1}(n)\]

where \(\beta =\frac{2}{n+1}\), \(n\) is number of days and \(P_t\) is price of time \(t\).

This is an EMA function:

myEMA <- function (price,n){
  ema <- c()
  ema[1:(n-1)] <- NA
  ema[n]<- mean(price[1:n])
  beta <- 2/(n+1)
  for (i in (n+1):length(price)){
    ema[i]<-beta * price[i] + 
      (1-beta) * ema[i-1]
  }
  return(ema)
}
myEMA(1:10,5)

##  [1] NA NA NA NA  3  4  5  6  7  8

An n-day relative strenght index (RSI) is normalized n-day relative strength (RS) that is ratio of days of stock price has gone up to the days of stock price have gone down.

This is an RSI function:

myRSI <- function (price,n){
  U <- rep(0,length(price))
  D <- rep(0,length(price))
  rs <- rep(NA,length(price))
  rsi <- rep(NA,length(price))
  for (i in 2:length(price)){
    if (price[i]>price[(i-1)]){
      U[i] <- 1
    } else if (price[i]<price[(i-1)]){
      D[i] <- 1
    }
    if (i>n){
      if (sum(D[(i-n+1):i])==0){
        rsi[i] <- 100
      } else{
        rs[i] <- sum(U[(i-n+1):i])/
          sum(D[(i-n+1):i])
        rsi[i] <- rs[i]/(rs[i]+1)*100
      }
    }
  }
  return(rsi)
}
myRSI(sample(4:10,20,replace=TRUE),6)

##  [1]       NA       NA       NA       NA       NA       NA 50.00000
##  [8] 40.00000 20.00000 33.33333 33.33333 20.00000 40.00000 60.00000
## [15] 75.00000 50.00000 66.66667 75.00000 50.00000 33.33333

apply

We will to apply a function to each row or each column on a matrix. It will apply a function by-column (=2) or by-row (=1).

x <- matrix(1:9, nrow = 3, ncol=3)
x

##      [,1] [,2] [,3]
## [1,]    1    4    7
## [2,]    2    5    8
## [3,]    3    6    9

apply(x,1,mean) # average each row

## [1] 4 5 6

apply(x,2,mean) # average each column

## [1] 2 5 8

sapply and lapply

Sometimes, we will apply a function repeatedly on each element of a vector (or a list). Then sapply is more convenient then a for loop.

Consider the following for loop that returns the square of each element

x <- c(1,3,5)
for (i in 1:length(x)) {
  x[i] <- x[i]^2
}
x

## [1]  1  9 25

We can do the same using sapply() with much cleaner code.

x <- c(1,3,5)
x <- sapply(x, function(x) x^2)
x

## [1]  1  9 25

lapply() is the same as sapply() but we end up with a list instead of vector. We can use unlist to get back the same result as sapply().

x <- c(1,3,5)
x <- lapply(x, function(x) x^2)
x

## [[1]]
## [1] 1
## 
## [[2]]
## [1] 9
## 
## [[3]]
## [1] 25

x <- unlist(x)

On vector

For example, 2-day moving average is \[EMA_{t}=\frac{1}{3}p_{t}+\frac{2}{3}EMA_{t-1}\].

The following example shows the final 2-day EMA with initial EMA being 5.

price <- 1:10
ema <- 5
for (i in 1:length(price)) {
 ema <- (ema + 2*price[i])/3 
}
ema

## [1] 9.500093

The following example use Reduce to simplify the code.

price <- 1:10
initial <- 5
ema <- Reduce(function(x,y){(x+2*y)/3},price,initial)
ema

## [1] 9.500093

On list

The following example shows how we can combine data sets.

HI <- data.frame(stock=c(1,2), high=c(7,8))
LO <- data.frame(stock=c(1,2), low=c(1,2))
OP <- data.frame(stock=c(1,2), open=c(3,6))
CL <- data.frame(stock=c(1,2), close=c(5,5))
df <-merge(HI,LO)
df <-merge(df,OP)
df <-merge(df,CL)
df

##   stock high low open close
## 1     1    7   1    3     5
## 2     2    8   2    6     5

Since merging is one by one on the data.frame, we just need to create a list of data.frame.

HI <- data.frame(stock=c(1,2), high=c(7,8))
LO <- data.frame(stock=c(1,2), low=c(1,2))
OP <- data.frame(stock=c(1,2), open=c(3,6))
CL <- data.frame(stock=c(1,2), close=c(5,5))
df <- Reduce(function(x,y) {merge(x,y)}, list(HI, LO, OP, CL))
df

##   stock high low open close
## 1     1    7   1    3     5
## 2     2    8   2    6     5

Timing code

To get the current time, we may use Sys.time(). Put this at the beginning and the end of the code. Then the difference is the run time.

t1 <- sys.time()
#…run code here …#
t2 <- sys.time()
t2-t1

Suppress annoying message

R tends to give a lot of warning and messages when you run a long code. Sometimes you want to suppress them to keep your console window clean.

suppressMessage(…)
suppressWarnings(…)

All files names in a folder

The function list.files will find all files in a folder.

# full.names = TRUE for full path
filenames <- list.files(path = "./folder/", full.names = TRUE)

Using Reduce() and lapply() we can read all csv files from the folder, and merge them together

setwd("C:/path")
file.names <-list.files(path = ".", 
                        pattern="*.csv",
                        full.names = TRUE)
file.list <- lapply(file.names, 
                    function(x){
                      read.csv(file = x,
                               header = TRUE,
                               stringsAsFactors = FALSE)})
df<-Reduce(function(x,y) {merge(x, y, all=TRUE)},
           file.list)