library(tidyverse)
## Warning: package 'tidyverse' was built under R version 4.0.2
## ── Attaching packages ──────────────────────────────────────── tidyverse 1.3.0 ──
## ✓ ggplot2 3.3.2 ✓ purrr 0.3.4
## ✓ tibble 3.0.1 ✓ dplyr 1.0.0
## ✓ tidyr 1.1.0 ✓ stringr 1.4.0
## ✓ readr 1.3.1 ✓ forcats 0.5.0
## ── Conflicts ─────────────────────────────────────────── tidyverse_conflicts() ──
## x dplyr::filter() masks stats::filter()
## x dplyr::lag() masks stats::lag()
cold <- read_csv('https://raw.githubusercontent.com/ywchiu/cdc_course/master/data/cold.csv')
## Parsed with column specification:
## cols(
## month = col_character(),
## cold = col_double()
## )
head(cold)
## # A tibble: 6 x 2
## month cold
## <chr> <dbl>
## 1 2004-01 0
## 2 2004-02 13
## 3 2004-03 8
## 4 2004-04 6
## 5 2004-05 6
## 6 2004-06 0
M <- ts(cold$cold, frequency = 12, start = c(2004,1))
plot(M)
#install.packages('TTR')
#??TTR
library(TTR)
## Warning: package 'TTR' was built under R version 4.0.2
M.SMA12 = SMA(M, n = 12)
M.SMA12
## Jan Feb Mar Apr May Jun Jul
## 2004 NA NA NA NA NA NA NA
## 2005 11.083333 11.833333 12.083333 12.666667 13.750000 14.083333 13.583333
## 2006 14.083333 12.750000 12.833333 12.666667 11.666667 12.666667 14.000000
## 2007 14.666667 15.666667 16.000000 16.333333 16.583333 16.416667 15.750000
## 2008 20.166667 21.500000 22.083333 22.250000 22.750000 22.833333 23.666667
## 2009 22.416667 22.500000 23.250000 23.500000 24.750000 24.916667 25.333333
## 2010 29.833333 29.583333 28.500000 28.916667 28.166667 27.916667 27.666667
## 2011 26.333333 26.833333 28.416667 28.666667 28.500000 29.500000 29.583333
## 2012 30.833333 30.916667 31.750000 31.833333 32.833333 32.916667 32.833333
## 2013 37.500000 38.000000 38.250000 38.916667 39.000000 38.500000 38.583333
## 2014 39.750000 40.333333 39.083333 39.333333 38.916667 39.083333 39.083333
## 2015 39.750000 39.583333 40.916667 41.416667 41.916667 42.333333 42.750000
## 2016 39.916667 36.666667 34.083333 31.416667 29.666667 28.083333 26.666667
## 2017 19.166667 23.416667 25.916667 28.750000 31.333333 33.416667 35.000000
## 2018 51.916667 53.333333 53.666667 52.833333 52.333333 52.083333 51.750000
## Aug Sep Oct Nov Dec
## 2004 NA NA NA NA 8.666667
## 2005 14.083333 13.833333 14.416667 15.000000 14.666667
## 2006 13.666667 14.083333 13.500000 13.500000 13.916667
## 2007 16.500000 17.416667 18.000000 18.750000 20.000000
## 2008 23.666667 23.416667 23.666667 23.750000 22.916667
## 2009 25.250000 26.250000 27.750000 28.500000 29.416667
## 2010 28.000000 27.500000 25.916667 24.500000 24.916667
## 2011 29.166667 29.750000 30.166667 31.583333 31.666667
## 2012 33.916667 34.416667 35.416667 34.833333 35.250000
## 2013 38.250000 38.250000 38.500000 39.416667 39.833333
## 2014 39.250000 39.250000 39.250000 39.250000 39.583333
## 2015 43.083333 43.500000 44.333333 44.500000 44.416667
## 2016 25.000000 22.166667 18.833333 15.666667 14.250000
## 2017 37.166667 40.083333 43.166667 46.666667 49.583333
## 2018
plot(M, col='blue')
lines(M.SMA12, col = 'red')
mean(M[1:12])
## [1] 8.666667
M.SMA12[12]
## [1] 8.666667
library(forecast)
## Warning: package 'forecast' was built under R version 4.0.2
## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoo
cold.pred <- HoltWinters(M, beta = FALSE, gamma = FALSE)
cold.pred
## Holt-Winters exponential smoothing without trend and without seasonal component.
##
## Call:
## HoltWinters(x = M, beta = FALSE, gamma = FALSE)
##
## Smoothing parameters:
## alpha: 0.9999339
## beta : FALSE
## gamma: FALSE
##
## Coefficients:
## [,1]
## a 24.00046
plot(cold.pred)
?HoltWinters
cold.pred2 <- predict(cold.pred, n.ahead = 10)
plot(cold.pred2)
library(forecast)
cold.pred<- HoltWinters(M,gamma = FALSE)
cold.pred2 <- predict(cold.pred, n.ahead = 10)
cold.pred2
## Jan Feb Mar Apr May Jun Jul Aug
## 2018 22.396699
## 2019 14.380197 12.776896 11.173596 9.570295 7.966995
## Sep Oct Nov Dec
## 2018 20.793399 19.190098 17.586798 15.983497
## 2019
plot(cold.pred2)
components <- decompose(M)
plot(components)
library(forecast)
cold.pred2<- HoltWinters(M)
cold.pred2 <- predict(cold.pred, n.ahead = 10)
cold.pred2
## Jan Feb Mar Apr May Jun Jul Aug
## 2018 22.396699
## 2019 14.380197 12.776896 11.173596 9.570295 7.966995
## Sep Oct Nov Dec
## 2018 20.793399 19.190098 17.586798 15.983497
## 2019
plot(cold.pred2)
library(tidyverse)
cold <- read_csv('https://raw.githubusercontent.com/ywchiu/cdc_course/master/data/cold.csv')
## Parsed with column specification:
## cols(
## month = col_character(),
## cold = col_double()
## )
head(cold)
## # A tibble: 6 x 2
## month cold
## <chr> <dbl>
## 1 2004-01 0
## 2 2004-02 13
## 3 2004-03 8
## 4 2004-04 6
## 5 2004-05 6
## 6 2004-06 0
#install.packages('quantmod')
library(quantmod)
## Warning: package 'quantmod' was built under R version 4.0.2
## Loading required package: xts
## Warning: package 'xts' was built under R version 4.0.2
## Loading required package: zoo
## Warning: package 'zoo' was built under R version 4.0.2
##
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric
##
## Attaching package: 'xts'
## The following objects are masked from 'package:dplyr':
##
## first, last
## Version 0.4-0 included new data defaults. See ?getSymbols.
library(TTR)
M <- ts(cold$cold, frequency = 12, start = c(2004,1))
M
## Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
## 2004 0 13 8 6 6 0 6 5 10 15 16 19
## 2005 29 22 11 13 19 4 0 11 7 22 23 15
## 2006 22 6 12 11 7 16 16 7 12 15 23 20
## 2007 31 18 16 15 10 14 8 16 23 22 32 35
## 2008 33 34 23 17 16 15 18 16 20 25 33 25
## 2009 27 35 32 20 31 17 23 15 32 43 42 36
## 2010 32 32 19 25 22 14 20 19 26 24 25 41
## 2011 49 38 38 28 20 26 21 14 33 29 42 42
## 2012 39 39 48 29 32 27 20 27 39 41 35 47
## 2013 66 45 51 37 33 21 21 23 39 44 46 52
## 2014 65 52 36 40 28 23 21 25 39 44 46 56
## 2015 67 50 52 46 34 28 26 29 44 54 48 55
## 2016 13 11 21 14 13 9 9 9 10 14 10 38
## 2017 72 62 51 48 44 34 28 35 45 51 52 73
## 2018 100 79 55 38 38 31 24
ts_merge <- cbind(Lag(M,-3),Lag(M,-2),Lag(M,-1), M)
colnames(ts_merge) <- c('t-3','t-2', 't-1', 'y')
head(ts_merge)
## t-3 t-2 t-1 y
## Jan 2004 NA NA NA 0
## Feb 2004 NA NA 0 13
## Mar 2004 NA 0 13 8
## Apr 2004 0 13 8 6
## May 2004 13 8 6 6
## Jun 2004 8 6 6 0
library(tidyverse)
sample_ts <- read_csv('https://raw.githubusercontent.com/ywchiu/cathayts/master/data/samples.csv')
## Warning: Missing column names filled in: 'X1' [1]
## Parsed with column specification:
## cols(
## X1 = col_character(),
## a = col_double(),
## b = col_double(),
## c = col_double(),
## d = col_double()
## )
M <- ts(sample_ts$b, frequency = 12, start = c(1950,1))
head(M)
## Jan Feb Mar Apr May Jun
## 1950 27 22 17 15 13 16
plot(M)
library(quantmod)
plot(M - Lag(M,-1))
func <- function(x){
x * 3 + 5
}
plot(seq(1,10), func(seq(1,10)), type = 'l')
a <- func(seq(1,10))
cbind(a, Lag(a, 1))
## a Lag.1
## [1,] 8 NA
## [2,] 11 8
## [3,] 14 11
## [4,] 17 14
## [5,] 20 17
## [6,] 23 20
## [7,] 26 23
## [8,] 29 26
## [9,] 32 29
## [10,] 35 32
func2 <- function(x){
2 * x^2 + 3 * x + 5
}
plot(seq(1,10), func2(seq(1,10)), type = 'l')
a <- func2(seq(1,10))
b <- a - Lag(a, 1)
b - Lag(b,1)
## Lag.1
## [1,] NA
## [2,] NA
## [3,] 4
## [4,] 4
## [5,] 4
## [6,] 4
## [7,] 4
## [8,] 4
## [9,] 4
## [10,] 4
func <- function(x){
x * 3 + 5
}
s <- seq(1,10)
plot(s, func(s), type='l')
## Regression
# x => s
# y => func(s)
## Time Series
# x => Lag(func(s), -n)...Lag(func(s), -2),Lag(func(s), -1)
# y => func(s)
library(tidyverse)
cold <- read_csv('https://raw.githubusercontent.com/ywchiu/cdc_course/master/data/cold.csv')
## Parsed with column specification:
## cols(
## month = col_character(),
## cold = col_double()
## )
head(cold)
## # A tibble: 6 x 2
## month cold
## <chr> <dbl>
## 1 2004-01 0
## 2 2004-02 13
## 3 2004-03 8
## 4 2004-04 6
## 5 2004-05 6
## 6 2004-06 0
M <- ts(cold$cold, frequency = 12, start = c(2004,1))
plot(M)
M.diff <- diff(M, lag = 1, differences = 1)
plot(M.diff)
acf(M.diff)
acf(M)
pacf(M.diff[-1])
plot(M.diff)
a <- data.frame(col = c('001', '002','003'))
paste(a$col, collapse = "','")
## [1] "001','002','003"
library(tseries)
## Warning: package 'tseries' was built under R version 4.0.2
adf.test(M)
## Warning in adf.test(M): p-value smaller than printed p-value
##
## Augmented Dickey-Fuller Test
##
## data: M
## Dickey-Fuller = -5.9284, Lag order = 5, p-value = 0.01
## alternative hypothesis: stationary
adf.test(M.diff)
## Warning in adf.test(M.diff): p-value smaller than printed p-value
##
## Augmented Dickey-Fuller Test
##
## data: M.diff
## Dickey-Fuller = -8.6215, Lag order = 5, p-value = 0.01
## alternative hypothesis: stationary
?arima
library(forecast)
plot(M)
ar_ts <- arima(M, order = c(0,1,0))
ar_forecast <- forecast(ar_ts, 12)
plot(ar_forecast)
M.arima <- auto.arima(M, ic= 'aic')
M.forecast <- forecast(M.arima, h = 12)
plot(M.forecast)
ts_merge <- cbind(Lag(M,-3),Lag(M,-2),Lag(M,-1), M)
dataset <- na.remove(ts_merge)
colnames(dataset) <- c('t_3', 't_2', 't_1', 'y')
fit <- lm(y ~ t_3+ t_2 + t_1, data = dataset)
fit
##
## Call:
## lm(formula = y ~ t_3 + t_2 + t_1, data = dataset)
##
## Coefficients:
## (Intercept) t_3 t_2 t_1
## 6.10644 -0.03917 -0.07634 0.90781