Chapter 8: Time Series Analysis and Forecasting

Routines

General Methodology

Time Series Transformation

Box-Cox transformation........................................................................................... BCTR

Nonseasonal and seasonal difference........................................................................ DIFF

Estimates missing values in a time series.......................................... ESTIMATE_MISSING

Determines an optimal differencing for seasonal
adjustment of a time series...................................................................... SEASONAL_FIT

Sample Correlation Function

Autocorrelation function............................................................................................. ACF

Partial autocorrelation function................................................................................. PACF

Cross-correlation function.......................................................................................... CCF

Multichannel cross-correlation function.................................................................... MCCF

Time Domain Methodology

Nonseasonal Time Series Model Estimation

Method of moments estimation of AR parameters.................................................. ARMME

Method of moments estimation of MA parameters................................................. MAMME

Preliminary estimation of ARMA parameters............................................................. NSPE

Least-squares estimation of ARMA models............................................................ NSLSE

Maximum likelihood estimation of ARMA models............................................. MAX_ARMA

Fit a univariate, non-seasonal ARIMA time
series model................................................................................................ REG_ARIMA

Estimation of GARCH (p,q) models....................................................................... GARCH

Wiener forecast operator estimates......................................................................... SPWF

Box-Jenkins forecast............................................................................................. NSBJF

Transfer Function Model

Estimation of impulse response and noise series..................................................... IRNSE

Preliminary estimation of parameters........................................................................ TFPE

Multichannel Time Series

Least-squares estimation of parameters................................................................... MLSE

Estimation of multichannel Wiener filter.................................................................. MWFE

Kalman filter........................................................................................................ KALMN

Automatic Model Selection Fitting

AIC selection for univariate AR models........................................................ AUTO_UNI_AR

Detects and determines outliers and simultaneously estimates the
model parameters in a time series...................................... TS_OUTLIER_IDENTIFICATION

Computes forecasts for an outlier contaminated
time series............................................................................... TS_OUTLIER_FORECAST

Automatic ARIMA modeling and forecasting in the
presence of possible outliers....................................................................... AUTO_ARIMA

FPE selection for univariate AR models.............................................. AUTO_FPE_UNI_AR

Estimates structural breaks in non-stationary
univariate time series models....................................................................... AUTO_PARM

AIC selection for multivariate AR models.................................................... AUTO_MUL_AR

MFPE selection for multivariate
AR models..................................................................................... AUTO_FPE_MUL_AR

Bayesian Time Series Estimation

Bayesian seasonal adjustment modeling........................................................... BAY_SEA

Controller Design

Optimum controller design................................................................................ OPT_DES

Diagnostics

Lack of fit test based on the correlation function...................................................... LOFCF

Frequency Domain Methodology

Smoothing Functions

Dirichlet kernel function........................................................................................... DIRIC

Fejér kernel function.............................................................................................. FEJER

Spectral Density Estimation

ARMA rational spectrum estimation............................................................. ARMA_SPEC
Periodogram using fast Fourier transform.................................................................. PFFT

Using spectral window given data........................................................................... SSWD

Using spectral window given periodogram................................................................ SSWP

Using weight sequence given data.......................................................................... SWED

Using weight sequence given periodogram............................................................... SWEP

Cross-Spectral Density Estimation

Cross periodogram using fast Fourier transform....................................................... CPFFT

Using spectral window given data......................................................................... CSSWD

Using spectral window given cross periodogram..................................................... CSSWP

Using weight sequence given data........................................................................ CSWED

Using weight sequence given cross periodogram................................................... CSWEP



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