Note: Locators followed by “f ” and “t” refer to figures and tables respectively.

• acf(),
  • autocovariance estimation coding
  • background
  • and spectrum
  • for white noise errors
• acos()
• AIC. See Akaike's information criteria
• Akaike's information criteria (AIC)
  • as cross-validation, NYC temperatures
  • model selection with
• anova()
• arima.sim()
• ARMA(2,2) model
• AR(m) filtering matrix
  • filtering information
  • linear algebra
  • and lm()
  • to model MA(3)
  • standard computations
• AR(1) model for irregular spacing
  • final analysis
  • method
  • motivation
  • results
  • sensitivity analysis
• AR(m) structure, residuals for
  • data display
  • filtering twice
• ar.yw()
• asin()
• Assumptions
  • equal variance
    • regression
    • two- sample t-test
  • independence
  • introduction
  • logarithmic transformations, illustration of
  • normality
    • heavy tails
    • left skew
    • right skewed
• atan()
• Autocorrelation
  • AR(1)
  • AR(2)
  • estimation
  • for MA(1) models
  • for MA(2) models
  • stationarity
• Autocovariance
  • AR(1)
  • AR(2)
  • ARMA(m,l) model
  • estimation, 37
  • properties
  • stationarity
  • white noise
• Autoregressive model of order 1, AR(1)
  • adjustments
    • implications
    • skip method
  • autocorrelation
  • autocovariance
  • definition
  • examples (stable and unstable models)
  • illustration
• Autoregressive model of order 2, AR(2)
  • autocorrelation
  • autocovariance
  • examples 46t
  • and power spectrum
  • preliminary facts
  • R code
  • simulating data

• Backshift operator
  • and ARMA(m,l) models
  • definition
  • examples
  • stationary condition for AR(1) model
• Bayesian information criteria (BIC)
• Best linear unbiased estimators (BLUES)
• BIC. See Schwarz information criteria
• BLUES. See Best linear unbiased estimators
• Boise river flow data
  • data splitting
  • model selection with AIC
  • model selection with filtering
  • residuals
• Breast cancer, data analysis
  • background
  • estrogen response negative
  • estrogen response positive
  • and female colon cancer
  • first data set (1992–2001)
  • second data set (1975–2005)
    • background
    • data structure
    • data trend
    • regression analysis with filtered data
    • residuals for AR(m) structure
    • statistical analysis

• Carrington, Richard
• Complex conjugates
• Complex numbers
  • magnitude of
• Complex periodic model
  • accidental deaths
    • data splitting
    • Fourier series structure
    • model selection with AIC
    • model selection with likelihood ratio tests
    • periodic data, comments on
    • R Code, fitting large Fourier series
    • residual
    • training set model
    • validation set model
  • monthly river flows, furnas 1931–1978
    • AR(m) filtering matrix
    • data
    • data splitting
    • model selection
    • periodic model
    • predictions for AR(m)
    • saturated model
• Comprehensive R Archive Network (CRAN)
• Coronal mass ejections
• cos()
• CRAN. See Comprehensive R Archive Network
• Creek, Gregory
• Crosby, Ben
• Cross-validation, NYC temperatures
  • AIC for
  • data splitting
  • explained variation, R₂
  • leave-one-out cross-validation

• Data import
• DataMarket
  • export options
  • homepage
  • licensing agreements
  • login page
  • overview
  • time series loading
• Data simulations
• Data splitting
• d^c
• 45-Degree line model
• dmlist()
  • New York temperature data plot
• dmseries()
  • New York temperature data

• Endocrine disruptors
• Equal variance assumption
  • regression
  • two- sample t-test
• ER+. See Estrogen response positive
• ER-. See Estrogen response negative
• Estrogen response negative (ER-)
  • breast cancer
  • first data set (1992–2001)
  • rates
  • second data set (1975–2005)
• Estrogen response positive (ER+)
  • breast cancer
  • first data set (1992–2001)
  • rates
  • second data set (1975–2005)
• Euler's formula
• exp()
• Explained variation, R₂
• Export options

• Fast Fourier transform (FFT)
• Female colon cancer
• FFT. See Fast Fourier transform
• Filtering
  • and Boise river flow data
  • comments on
  • and global warming model
• floor()
• “For” statement
• Fourier series
• Fourier series structure
• Functions (R)
  • acos()
  • asin()
  • atan()
  • cos()
  • d^c
  • exp()
  • log()
  • pi
  • sin()
  • sqrt()
  • tan()
  • see also Time series, functions

• General ARMA models
  • arima.sim()
  • and backshift operator
  • examples
  • mathematical formulation
  • representative collection
  • spectrum for
• Geometric series

• Hat matrix
• Heavy tails
• help()
• help(numericDeriv)
• High elevation (snow)
• Homepage
• Hyndman, Rob

• “If” statement
• Impulse response operator
  • computation
    • coefficients computation
    • definition
    • plotting
  • interpretation
  • intuition
  • utility
• Influential points
• Information criteria
  • Akaike's information criteria
  • and model selection
  • Schwarz information criteria
• Inquiry functions
  • anova()
  • help()
  • names()
  • summary()
• International sunspot number
• Intervention model
  • directory assistance
    • concern
    • data
    • filtering information
    • model selection
    • saturated model
  • ozone levels in Los Angeles
  • structure

• kappa()

• Leave-one-out cross-validation
• Left skew
• Leverage points
• Licensing agreements
• Likelihood ratio tests
  • model selection with
• Linear model
• lm()
  • vs. nls()
• log()
• Login page
• lowess() function
• Low (rain) elevation watersheds
  • initial fits for

• Matrix manipulation, in R
  • commands
  • OLS
• mean(x)
• Mid (mixed) elevation watersheds
  • initial fits
• Modeling
  • algorithm
  • assumption
  • example
    • AR(m) filter to model MA(3)
    • CO₂ levels at Mauna Lau
    • monthly river flow
  • skip method
• Model selection
  • with AIC
  • with likelihood ratio tests
• Monthly river flow, complex periodic model
  • AR(m) filtering matrix
    • filtering information
    • fitting a model with lm()
    • linear algebra
    • standard computations
  • data
  • data splitting
    • computations
    • linear algebra
    • overview
  • model selection
  • predictions for AR(m) model
  • saturated model
• Moving average model, MA(1)
  • acf() plots
  • and AR(m) models
  • autocorrelation for
  • simulated examples
• Moving average model, MA(2)
  • acf() plots
  • autocorrelation for
  • simulated examples

• Naïve analysis
  • CO₂ and temperature change association
  • model selection
  • saturated model
• Naïve code
• names()
• Naming conventions
• Nested models
• Newton's method (for nonlinear optimization)
• nls()
  • vs. lm()
• Noise
• Nonlinear optimization, tutorial on
  • general problem
  • introduction
  • Newton's method for
  • revisit
• Normality assumption
  • heavy tails
  • left skew
  • right skew
• numericDeriv()
• NYC temperatures
  • application
  • AR(1) prediction model
  • cross-validation
    • Akaike's information criterion
    • data splitting
    • explained variation
    • leave-one-out cross-validation
  • data
  • outlier
  • periodic function fitting
  • prediction intervals
  • simulation

• Observatory factor
• OLS. See Ordinary least squares
• Ordinary least squares (OLS)

• pacf()
• Partial autocorrelation plot
  • hypothesis tests sequence
  • pacf() function
• Periodic function fitting
• Periodic models
  • complications
    • accidental deaths
    • CO₂ data
    • sunspot data
  • daily average
  • example (NYC temperature data)
    • outlier
    • periodic function fitting
    • refitting
  • monthly average
  • weekly average
• Periodic transcendental functions
• Periodogram
  • and acf() plot
  • example
  • Naïve code for
  • periodic analysis
  • periodic behavior
  • for power spectrum
  • and smoother
  • and white noise
• Personal reduction coefficient (K)
• Phase
• Pi
• Power spectrum
  • and acf() plot
  • for ARMA processes
  • for AR(1) models
  • for AR(2) models
  • and autocorrelation function
  • definition
  • and periodogram plot
  • for white noise
• Predictions for AR(m)
• PRESS
• Prostate cancer, data analysis
  • background
  • estrogen response negative
  • estrogen response positive
  • first data set (1992–2001)
  • second data set (1975–2005)
    • background
    • data structure
    • data trend
    • regression analysis with filtered data
    • residuals for AR(m) structure
    • statistical analysis
• Prostate-specific antigen (PSA)
• PSA. See Prostate-specific antigen
• Pseudo-periodic model
• p-values

• qqnorm()
• Quadratic model
• Quasi-independent observations

• R (programming language)
  • code
  • common functions
  • console code
  • conventions
  • data sources
  • inquiry functions
  • matrix manipulation
  • model parameters estimation
  • smoothers in
    • lowess()
    • smooth.spline()
  • structures
• R Code, fitting large Fourier series
• rdatamarket package
• read.csv()
• read.delim()
• read.table()
• Real data
• Refitting
• Regression
• Regression model
  • matrix representation
  • OLS estimates
  • ordinary least squares
  • for periodic data
• Relative sunspot number
• Residuals analysis
  • influential points
  • lack of fit
  • nonwhite noise error
  • normality
  • outliers
  • plots
  • unequal variance
• Richer models
• Right skew
  • p-values
  • and unknown period
• R²pred

• Saturated model
  • and data fit
  • and filter
  • naïve analysis
  • pruning
  • residuals
• scan()
• Semmelweis, Ignaz Philipp
• Semmelweis data
• Semmelweis intervention
  • data
  • filtered analysis
  • inferences
  • serial correlation
  • transformations
  • vs. patch/uncut case
• Serial correlation
  • and Semmelweis intervention
• Signals
• Simple mean model
• Simple regression
  • analysis of variance
  • hypothesis tests
  • ratio tests
  • Sleuth case, global warming
    • analysis
    • data
    • filtering
    • simulation
• Simulated data
• sin()
• Skip method
• Smoothers
  • lowess() function
  • for series
    • known period
    • unknown period
  • smooth.spline() function
• smooth.spline() function
• Solar flares
• solve()
• spans()
• spec.pgram()
• sqrt()
• SSE
• SST
• Standard errors
• Statistical operations
• Straight-line model
• summary()
• sum(x)

• tan()
• Tennant, Christopher
• Time series
  • assumptions
  • data
  • extrapolation
  • prediction intervals
• Time Series Data Library
• Time series function (R)
  • acf()
  • arima.sim()
  • ar.yw()
  • pacf()
  • spec.pgram()
  • ts()
• Time series loading
• Transcendental series
• ts()
• t-tests
• Two-sample t-test
  • adjustment for AR(1)
  • assumption
  • simulation example
  • Sleuth data
  • Sleuth data analysis

• Variable lag
• Vostok ice core data
  • alignment
    • issues
    • matched dates
    • need
    • patterns
    • time stamps
  • AR(1) model for irregular spacing
    • final analysis
    • method
    • motivation
    • results
    • sensitivity analysis
  • naïve analysis
    • CO₂ and temperature change association
    • model selection
    • saturated model
  • related simulation
    • code
    • model
    • sample of
  • source

• Watersheds data
  • averaging data
  • fitting Fourier series
    • data structure
    • data to physical processes, connecting patterns in
    • Fourier series fits to data
  • high elevation (snow)
  • low (rain) elevation
  • mid (mixed) elevation
  • results
• White noise
  • and autocovariance
  • and power spectrum
• Wolf, Rudolf
• Wolf number
  • amplitude, instability in
  • background
  • data splitting (for prediction)
    • approach
    • AR-adjusted predictions
    • AR correction
    • fitting one step ahead
    • model selection
    • predictions two steps ahead
  • mean, instability in
  • nls() function
  • period, instability in
  • period determination
  • sunspot data
  • for unknown period

• Yule–Walker equations
  • AR(m) and
  • errors sequence
  • model selection (using information criteria)

• Zürich number