Time series

transformation

Models

White noise

Random walk

autoregression

simple moving average

R functions

Simulations

modeling

forecasting

Plot/ts.plot()

ts()

is.ts()

Predicting the future:Some time series exhibit predictability when strong periodic or seasonal patterns are present. Other time series exhibit predictability when positive autocorrelation - or correlation among neighboring observations - induces what appear as short-term trends.

not exhibit any clear trends over time

Linear

Rapid Growth

Periodic

Variance

Sample Transformations: log() :check ; can linearize a rapid growth trend

Sample transformations: diff() can remove a linear trend

Sample Transformations: diff(..,s) seasonal difference transformation, can remove periodic trends

White Noise Model:

A fixed constant mean

A fixed, constant variance

No correelation over time

ARIMA is an abbreviation for the autoregressive integrated moving average class of models

ARIMA(p, d, q) model has three parts, the autoregressive order p, the order of integration (or differencing) d, and the moving average order q

Random Walk (RW) Model

Non - stationary process

No specified mean or variance

Strong dependence over time

Its changes or increlents are WN

Random Walk with and without draft

pairs()

Correlations: Standardized version of covariance

+1: perfectyly positive linear relationship

-1: perfectly negative linear relationship

0: no linear association

Autocorrelation:(lagged correlation) are used to assess whether a time series is dependent on its past

(x[t], x[t-1])

acf(..., lag.max = 1, plot = FALSE)

xts: A matrix indexed on a time-based object

periodicity

nmonths

ndays

nyears

Forecast

ts(mydata[,2:4], start = c(1981, 1), frequency = 4): Creating time series objects

Time series plots: autoplot(), gglagplot(), ggAcf()

forecast and ggplot2, fpp2

Seasonal plots: ggseasonplot(polar = T), ggsubseriesplot()

Trends, seasonality and cyclicity

White noise: ljung-Box test: small p-value indicates the data are probably not white noise

Forecast

naive forecast: use the most recent observation

naive

snaive

checkresiduals

Well done! A good model forecasts well (so has low RMSE on the test set) and uses all available information in the training data (so has white noise residuals).

tsCV()

mean

Exponentially weighted forecasts

ses: no trend or seasonality

holt

ETS models