introduction to r: part viib2slab.upc.edu/wp-content/uploads/2014/02/cursr_vii.pdf · introduction...

Introduction to R: Part VIIA Time Series Data Session

Alexandre Perera i Lluna 1,2

1Centre de Recerca en Enginyeria Biomèdica (CREB)Departament d’Enginyeria de Sistemes, Automàtica i Informàtica Industrial (ESAII)

Universitat Politècnica de Catalunyamailto:Alexandre.Perera@upc.edu

2Centro de Investigación Biomédica en Red en Bioingeniería, Biomateriales y Nanomedicina(CIBER-BBN)

Jan 2011 / Introduction to RUniversitat Rovira i Virgili

IntroductionMain Signal Processing Functions

Autoregresive ModelsFiltering

Contents I1 Introduction

Example DataPlotting time series objectsMissing Values and (i)regular Sampling Times

2 Main Signal Processing FunctionsSliding WindowsAutocorrelationSpectral Analysis

3 Autoregresive ModelsARMA simulationFitting ARMA(p,q) models

4 FilteringFiltersFilters Characterization

Alexandre Perera i Lluna , Introduction to R: Part VII

Contents IIO

Obtaining some time Series Data

Yahoo! Finance provides with a historic finance dataAllows free access (not real-time, 15 minutes delay)

Yahoo! Finance download> library(tseries)> telefonica <- get.hist.quote("TEF.MC", start = "2006-01-01",+ end = "2008-05-07", quote = c("Open"))

time series starts 2006-01-02

> class(telefonica)

[1] "zoo"

Index visualization

code> plot(telefonica)

2006 2007 2008

Getting raw data from time series (zoo)

code> teldata <- coredata(telefonica)> hist(teldata, 200)

Histogram of teldata

teldata

12 14 16 18 20 22

Time Series

The zoo package allows iregular sampling times and missing data> telefonica[1:10]

2006-01-02 2006-01-03 2006-01-04 2006-01-05 2006-01-0612.75 12.76 12.90 12.99 13.09

2006-01-09 2006-01-10 2006-01-11 2006-01-12 2006-01-1313.17 13.19 13.14 13.10 13.01

The ts class from stats does not:> telts <- as.ts(telefonica)> telts[1:10]

[1] 12.75 12.76 12.90 12.99 13.09 NA NA 13.17 13.19[10] 13.14

however we can deal with NA data in several ways.

Missing Values in Time Series

> plot(telts[1:25], type = "b")

● ●

●●

5 10 15 20 25

> plot(telts[1:25], type = "b")> lines(na.locf(telts[1:25]), type = "b", col = "red")

● ●

●●

5 10 15 20 25

● ●

● ● ●

●●

● ● ●

> plot(telts[1:25], type = "b")> lines(na.locf(telts[1:25]), type = "b", col = "red")> lines(na.approx(telts[1:25]), type = "b", col = "blue")

● ●

●●

5 10 15 20 25

● ●

● ● ●

●●

● ● ●

● ●

●●

> plot(telts[1:25], type = "b")> lines(na.locf(telts[1:25]), type = "b", col = "red")> lines(na.approx(telts[1:25]), type = "b", col = "blue")> lines(na.spline(telts[1:25]), type = "b", col = "green")

● ●

●●

5 10 15 20 25

● ●

● ● ●

●●

● ● ●

● ●

●●

● ●

●●

● ●

Sliding WindowsAutocorrelationSpectral Analysis

Sliding Windows (rollers)

rolling functions (applies to both ts and zoo obects)rollapply(data, width, FUN)

Sliding Windows

> mtelefonica <- rollapply(telefonica, 30, mean)> plot(mtelefonica, type = "l")

2006 2007 2008

Also available as rollmean()

Computing Autocorrelations

> coredata(telts) <- na.approx(telts)> acf(telts)

0 5 10 15 20 25 30

Computing Autocorrelations

Let’s try the differenciated signal, just for fun:> coredata(telts) <- na.approx(telts)> dtel <- diff(telts)> acf(dtel)

0 5 10 15 20 25 30

Periodogram

> require(signals)> plot(sunspots)

1750 1800 1850 1900 1950

Periodogram

> spectrum(sunspots)

0 1 2 3 4 5 6

frequency

Series: xRaw Periodogram

bandwidth = 0.00120

Periodogram

> spectrum(sunspots, spans = 10, xlim = c(0, 1))> abline(v = 1:3/12, lty = 3)

0.0 0.2 0.4 0.6 0.8 1.0

frequency

Series: xSmoothed Periodogram

bandwidth = 0.0122 Extracted from

http://zoonek2.free.fr/

Let’s define a two component signal:> x <- 1:256/256> x <- sin(16 * pi * x) + 0.3 * cos(56 * pi * x)

> plot(x, type='l', lwd=3,> main="Signal", xlab="", ylab="")> plot(Mod(fft(x)[1: ceiling((length(x)+1)/2) ]),> type='l', col="blue", lwd=3,> ylab="Mof(fft(x))", xlab="",> main="DTF (Discrete Fourrier Transform)")> par(op)

Extracted from http://zoonek2.free.fr/

0 50 100 150 200 250

Signal

0 20 40 60 80 100 120

DTF (Discrete Fourrier Transform)

Extracted from

http://zoonek2.free.fr/

spectrogram

Through the seewave package, we can plot spectrograms in dynamic 3Dplots:

ARMA simulationFitting ARMA(p,q) models

In AR1, we can estimate thecoefficients by performing aregression of the signal againstlag(x,1)

> y <- telts[-1]> x <- telts[-length(telts)]> r <- lm(y ~ x - 1)> coefficients(r)

x1.000345

> plot(y ~ x)> abline(r, col = "red")

●●●●●

●●●●●●●●●●●●●●●●●●●●●●●●●●

●●●●●●●

● ●●●●●●●●●●●●●●●●●●●●

●●●●●●●●●●●●●●●●●●●●

●●●●●●●●●●●●●●●●●●●●●

●●●●●●●●●●●●●●●●●●●●●●●

●●●●●●●●●●●●

●●●●●●●●●●●●●

●●●●●●

● ●●●●●●●●●●●●●

●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

● ●●●●●●●●●●

●●●●●●●●●●●●●●●●●●●●●●●●●

●●●●●●●●●●●●●●●●●●

●●●●●●●●●

● ●●●●●●●●●●●●●

●●●●●●●●●●●●●●●

●●●●●●●

●●●●●●●●

●●●●●●

●●●●

● ●●●●●●●●●●●●●

●●●●●●●

●●●

● ●●●●●● ●●●●

●●●●●●●●●●●●●●●● ●

●●●●●

●●●●●●●●●●●●●●●●●●●●

●●● ●●●●●●●

●●●●●●●●●●●●●●●●●●●

●●

● ●●● ●●●●

●●●●●

●●●

● ●●●●●●●●●●●● ●●●●●●●●●●●●

●●●●

●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

●●●●●

●●

●●●●●●●●●●●●●

● ●●●●●●●●●●

●●

● ●●●●●

●●●●●●

●●

●●●●●●

●●

●●●●●●●

●●●●●●●●●●●

●● ●●●

●●●●●●●●

●●

● ●●●●

●●●●●●●●

●●●●●●

●●●●

●●

●● ●

● ●●

●●

●●●●●●●●● ●

●●

●●●●

●●●●●

●●●●●●

● ●●●●●

● ●

●●●●

●●●

●●●●●

●● ●●●●●

●●●●●●●

●●●●

● ●

● ●●

●●●

●●●●

●●

● ●●

● ●●●●

● ●●●●●● ●

●●●●●●●●

●●●●

● ●

●●●●●●●

●●●●●

●●●●●●●

●●●●●●●●● ●●●

● ●●●●●

●●●●

●●●

● ●●●●●

●●●●●●●●●●

●●●●●●

12 14 16 18 20 22

AR(2) process

arima.sim() from stats package

Simulates an Autoregressive integrated moving average general model. AnARMA(q,p) is given by:(

1 −p∑

q∑i−1

)εt (1)

To simulate an AR(2) process:> n <- 300> r <- arima.sim(list(ar = c(0.9, -0.2)), n)> plot(r)

AR(2) process

0 50 100 150 200 250 300

MA(2) process

1 −p∑

q∑i−1

)εt (2)

To simulate an MA(2) process:> n <- 300> r <- arima.sim(list(ma = c(-0.7, -0.1)), n)> plot(r)

MA(2) process

0 50 100 150 200 250 300

ARMA(p,q) process

1 −p∑

q∑i−1

)εt (3)

To simulate an ARMA(2,2) process:> n <- 300> r <- arima.sim(list(ma = c(-0.7, 1), ar = c(0.9,+ -0.2)), n)> plot(r)

ARMA(q,p) process

0 50 100 150 200 250 300

Using arima() to fit ARMA models

> mod <- arima(r, order = c(2, 0, 2))> coef(mod)

ar1 ar2 ma1 ma2 intercept0.9274427 -0.2271395 -0.6929875 0.9999988 0.4574083

FiltersFilters Characterization

Defining filters

Filter objects (signal package)

Filters are created and stored as objects. The filter function applies anydefined filter to any signal.

Example (3 order, 10Hz low-pass Butterworth filter> library(signal)> bf = butter(3, 0.1)> t = seq(0, 1, len = 100)> x = sin(2 * pi * t * 2.3) + 0.25 * rnorm(length(t))> z = filter(bf, x)> class(z)

[1] "ts"

Filters

0.0 0.2 0.4 0.6 0.8 1.0

Filter Functions in signal package

fltfilt()

fir1(),fir2()

butter()

hamming(),hanning(),flattopwin(),gausswin(),kaiser(),blackman(),boxcar()

Savitzsky Golay filtersParks McClellan optimal FIR filter design (remez)... and more

Frequency response

freqz(fir1(40,0.3))

Filter characterization

b = c(1, 2)a = c(1, 1)w = linspace(0, 4, 128)freqs(b, a, w)

The tuneR package

> library(tuneR)> s7 <- readWave("mysong.wav", from = 1, to = 5, units = "seconds")> s7

Wave ObjectNumber of Samples: 32000Duration (seconds): 4Samplingrate (Hertz): 8000Channels (Mono/Stereo): MonoBit (8/16/24/32): 16

The sound package

> library(sound)> s <- loadSample("mysong.wav", from = 1, to = 5, units = "seconds")> s

type : monorate : 8000 samples / secondquality : 16 bits / samplelength : 480000 samplesR memory : 1920000 bytesHD memory : 960044 bytesduration : 60 seconds

The audio package

> library(audio)> s <- load.wave("mysong.wav")> head(s)

sample rate: 8000Hz, mono, 16-bits[1] 0.0000000 0.7070923 0.9999695 0.7070923 0.0000000 -0.7071139

To a file

To a .txt file:> data(tico)> export(tico, f = 22050, header = FALSE, filename = "tico_Gold.txt"))

To a .wav file (e.g.through seewave):> savewav(ticofirst, filename = "tico_firstnote.wav")

To an audio device:

Using play from the tuneR package:> play(s)

Using listen from the seewave package:> listen(s1, f=8000, from=0.3, to=5)

End Part VII

introduction to r: part viib2slab.upc.edu/wp-content/uploads/2014/02/cursr_vii.pdf · introduction...

Documents

cobit5 introduction spanish

rational numbers introduction

alternative fuels introduction

introduction to linked data

ea introduction spanish

teacher's book. introduction

introduction to catalan culture

excel 2010-introduction-part-i-150528044201-lva1-app6891

pintu metales introduction

mongo db course introduction

cmc introduction

introduction to candlesticks

introduction - telecom falcon

introduction - sld.cu

introduction keystone español 1

balambe introduction

universidad nacional autónoma de nicaragua facultad de...

introduction to spanish language

1 introduction class

01 introduction