# Time Series Analysis and Forecasting

## GENERAL METHODLOGY

### TIME SERIES TRANSFORMATION

ROUTINE DESCRIPTION
BCTR Performs a forward or an inverse Box-Cox (power) transformation.
DIFF Differences a time series.
ESTIMATE_MISSING Estimates missing values in a time series.
SEASONAL_FIT Determines an optimal differencing for seasonal adjustments of a time series.

### TIME SERIES TRANSFORMATION

ROUTINE DESCRIPTION
ACF Computes the sample autocorrelation function of a stationary time series.
PACF Computes the sample partial autocorrelation function of a stationary time series.
CCF Computes the sample cross-correlation function of two stationary time series
MCCF Computes the multichannel cross-correlation function of two mutually stationary multichannel time series.

## TIME DOMAIN METHODOLOGY

### NONSEASONAL TIME SERIES MODEL ESTIMATION

ROUTINE DESCRIPTION
ARMME Computes method of moments estimates of the autoregressive parameters of an ARMA model.
MAMME Computes method of moments estimates of the moving average parameters of an ARMA model.
NSPE Computes preliminary estimates of the autoregressive and moving average parameters of an ARMA model.
NSLSE Computes least-squares estimates of parameters for a nonseasonal ARMA model.
MAX_ARMA Exact maximum likelihood estimation of the parameters in a univariate ARMA (autoregressive, moving average) time series model.
REG_ARIMA Fits a univariate, non-seasonal ARIMA time series model with the inclusion of one or more regression variables.
GARCH Computes estimates of the parameters of a GARCH(p,q) model.
GARCH Computes the Wiener forecast operator for a stationary stochastic process.
NSBJF Computes Box-Jenkins forecasts and their associated probability limits for a nonseasonal ARMA model.

### TRANSFER FUNCTION MODEL

ROUTINE DESCRIPTION
IRNSE Computes estimates of the impulse response weights and noise series of a univariate transfer function model.
TFPE Computes preliminary estimates of parameters for a univariate transfer function model.

### MULTICHANNEL TIME SERIES

ROUTINE DESCRIPTION
MLSE Computes least-squares estimates of a linear regression model for a multichannel time series with a specified base channel.
MWFE Computes least-squares estimates of the multichannel Wiener filter coefficients for two mutually stationary multichannel time series.
KALMN Performs Kalman filtering and evaluates the likelihood function for the stat-espace model.

### AUTOMATIC MODEL SELECTION FITTING

ROUTINE DESCRIPTION
AUTO_UNI_AR Automatic selection and fitting of a univariate autoregressive time series model.
TS_OUTLIER_IDENTIFICATION Detects and determines outliers and simultaneously estimates the model parameters in a time series whose underlying outlier free series follows a general seasonal or nonseasonal ARMA model.
TS_OUTLIER_FORECAST Computes forecasts, associated probability limits and Ψ weights for an outlier contaminated time series.
AUTO_ARIMA Automatically identifies time series outliers, determines parameters of a multiplicative seasonal ARIMA (p,0, q) x (0, d,0)s model and produces forecasts that incorporate the effects of outliers whose effects persist beyond the end of the series.
AUTO_FPE_UNI_AR Automatic selection and fitting of a univariate autoregressive time series model using Akaike's Final Prediction Error (FPE) criteria.
AUTO_PARM Estimates structural breaks in non-stationary univariate time series.
AUTO_MUL_AR Automatic selection and fitting of a multivariate autoregressive time series model.
AUTO_FPE_MUL_AR Automatic selection and fitting of a multivariate autoregressive time series model using Akaike's Multivariate Final Prediction Error (MFPE) criteria.

### BAYESIAN TIME SERIES ESTIMATION

ROUTINE DESCRIPTION
BAY_SEA Bayesian seasonal adjustment modeling. The model allows for a decomposition of a time series into trend, seasonal, and an error component.

### CONTROLLER DESIGN

ROUTINE DESCRIPTION
OPT_DES Optimal controller design which allows for multiple channels for both the controlled and manipulated variables.

### DIAGNOSTICS

ROUTINE DESCRIPTION
LOFCF Performs lack-of-fit test for a univariate time series or transfer function given the appropriate correlation function.

### CONTROLLER DESIGN

ROUTINE DESCRIPTION
OPT_DES Optimal controller design which allows for multiple channels for both the controlled and manipulated variables.

## FREQUENCY DOMAIN METHODOLOGY

### SMOOTHING FUNCTIONS

ROUTINE DESCRIPTION
DIRIC Computes the Dirichlet kernel.
FEJER Computes the Fejér kernel.

### SPECTRAL DENSITY ESTIMATION

ROUTINE DESCRIPTION
ARMA_SPEC Calculates the rational power spectrum for an ARMA model.
PFFT Calculates the rational power spectrum for an ARMA model.
SSWD Estimates the nonnormalized spectral density of a stationary time series using a spectral window given the time series data.
SSWP Estimates the nonnormalized spectral density of a stationary time series using a spectral window given the periodogram.
SWED Estimates the nonnormalized spectral density of a stationary time series based on specified periodogram weights given the time series data.
SWEP Estimates the nonnormalized spectral density of a stationary time series based on specified periodogram weights given the periodogram.

### CROSS-SPECTRAL DENSITY ESTIMATION

ROUTINE DESCRIPTION
CPFFT Computes the cross periodogram of two stationary time series using a fast Fourier transform.
CSSWD Estimates the nonnormalized cross-spectral density of two stationary time series using a spectral window given the time series data.
CSSWP Estimates the nonnormalized cross-spectral density of two stationary time series using a spectral window given the spectral densities and cross periodogram
CSWED Estimates the nonnormalized cross-spectral density of two stationary time series using a weighted cross periodogram given the time series data.
CSWEP Estimates the nonnormalized cross-spectral density of two stationary time series using a weighted cross periodogram given the spectral densities and cross periodogram.