# NAG CL InterfaceG13 (Tsa)Time Series Analysis

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G13 (Tsa) Chapter Introduction – A description of the Chapter and an overview of the algorithms available.

Function
Mark of
Introduction

Purpose
g13aac 7 nag_tsa_uni_diff
Univariate time series, seasonal and non-seasonal differencing
g13abc 2 nag_tsa_uni_autocorr
Sample autocorrelation function
g13acc 2 nag_tsa_uni_autocorr_part
Partial autocorrelation function
g13amc 9 nag_tsa_uni_smooth_exp
Univariate time series, exponential smoothing
g13asc 6 nag_tsa_uni_arima_resid
Univariate time series, diagnostic checking of residuals, following g13bec
g13auc 7 nag_tsa_uni_means
Computes quantities needed for range-mean or standard deviation-mean plot
g13awc 25 nag_tsa_uni_dickey_fuller_unit
Computes (augmented) Dickey–Fuller unit root test statistic
g13bac 7 nag_tsa_multi_filter_arima
Multivariate time series, filtering (pre-whitening) by an ARIMA model
g13bbc 7 nag_tsa_multi_filter_transf
Multivariate time series, filtering by a transfer function model
g13bcc 7 nag_tsa_multi_xcorr
Multivariate time series, cross-correlations
g13bdc 7 nag_tsa_multi_transf_prelim
Multivariate time series, preliminary estimation of transfer function model
g13bec 2 nag_tsa_multi_inputmod_estim
Estimation for time series models
g13bgc 8 nag_tsa_multi_inputmod_update
Multivariate time series, update state set for forecasting from multi-input model
g13bjc 2 nag_tsa_multi_inputmod_forecast
Forecasting function
g13bxc 2 nag_tsa_options_init
Initialization function for option setting
g13byc 2 nag_tsa_transf_orders
Allocates memory to transfer function model orders
g13bzc 2 nag_tsa_trans_free
Freeing function for the structure holding the transfer function model orders
g13cac 7 nag_tsa_uni_spectrum_lag
Univariate time series, smoothed sample spectrum using rectangular, Bartlett, Tukey or Parzen lag window
g13cbc 4 nag_tsa_uni_spectrum_daniell
Univariate time series, smoothed sample spectrum using spectral smoothing by the trapezium frequency (Daniell) window
g13ccc 7 nag_tsa_multi_spectrum_lag
Multivariate time series, smoothed sample cross spectrum using rectangular, Bartlett, Tukey or Parzen lag window
g13cdc 4 nag_tsa_multi_spectrum_daniell
Multivariate time series, smoothed sample cross spectrum using spectral smoothing by the trapezium frequency (Daniell) window
g13cec 4 nag_tsa_multi_spectrum_bivar
Multivariate time series, cross amplitude spectrum, squared coherency, bounds, univariate and bivariate (cross) spectra
g13cfc 4 nag_tsa_multi_gain_bivar
Multivariate time series, gain, phase, bounds, univariate and bivariate (cross) spectra
g13cgc 4 nag_tsa_multi_noise_bivar
Multivariate time series, noise spectrum, bounds, impulse response function and its standard error
g13dbc 7 nag_tsa_multi_autocorr_part
Multivariate time series, multiple squared partial autocorrelations
g13ddc 8 nag_tsa_multi_varma_estimate
Multivariate time series, estimation of VARMA model
g13djc 8 nag_tsa_multi_varma_forecast
Multivariate time series, forecasts and their standard errors
g13dkc 8 nag_tsa_multi_varma_update
Multivariate time series, updates forecasts and their standard errors
g13dlc 7 nag_tsa_multi_diff
Multivariate time series, differences and/or transforms
g13dmc 7 nag_tsa_multi_corrmat_cross
Multivariate time series, sample cross-correlation or cross-covariance matrices
g13dnc 7 nag_tsa_multi_corrmat_partlag
Multivariate time series, sample partial lag correlation matrices, ${\chi }^{2}$ statistics and significance levels
g13dpc 7 nag_tsa_multi_regmat_partial
Multivariate time series, partial autoregression matrices
g13dsc 8 nag_tsa_multi_varma_diag
Multivariate time series, diagnostic checking of residuals, following g13ddc
g13dxc 7 nag_tsa_uni_arma_roots
Calculates the zeros of a vector autoregressive (or moving average) operator
g13eac 3 nag_tsa_multi_kalman_sqrt_var
One iteration step of the time-varying Kalman filter recursion using the square root covariance implementation
g13ebc 3 nag_tsa_multi_kalman_sqrt_invar
One iteration step of the time-invariant Kalman filter recursion using the square root covariance implementation with $\left(A,C\right)$ in lower observer Hessenberg form
g13ecc 3 nag_tsa_kalman_sqrt_filt_info_var
One iteration step of the time-varying Kalman filter recursion using the square root information implementation
g13edc 3 nag_tsa_kalman_sqrt_filt_info_invar
One iteration step of the time-invariant Kalman filter recursion using the square root information implementation with $\left({A}^{-1},{A}^{-1}B\right)$ in upper controller Hessenberg form
g13ejc 25 nag_tsa_kalman_unscented_state_revcom
Combined time and measurement update, one iteration of the Unscented Kalman Filter for a nonlinear state space model, with additive noise (reverse communication)
g13ekc 25 nag_tsa_kalman_unscented_state
Combined time and measurement update, one iteration of the Unscented Kalman Filter for a nonlinear state space model, with additive noise
g13ewc 3 nag_tsa_trans_hessenberg_observer
Unitary state-space transformation to reduce $\left(A,C\right)$ to lower or upper observer Hessenberg form
g13exc 3 nag_tsa_trans_hessenberg_controller
Unitary state-space transformation to reduce $\left(B,A\right)$ to lower or upper controller Hessenberg form
g13fac 6 nag_tsa_uni_garch_asym1_estim
Univariate time series, parameter estimation for either a symmetric GARCH process or a GARCH process with asymmetry of the form ${\left({\epsilon }_{t-1}+\gamma \right)}^{2}$
g13fbc 6 nag_tsa_uni_garch_asym1_forecast
Univariate time series, forecast function for either a symmetric GARCH process or a GARCH process with asymmetry of the form ${\left({\epsilon }_{t-1}+\gamma \right)}^{2}$
g13fcc 6 nag_tsa_uni_garch_asym2_estim
Univariate time series, parameter estimation for a GARCH process with asymmetry of the form ${\left(|{\epsilon }_{t-1}|+\gamma {\epsilon }_{t-1}\right)}^{2}$
g13fdc 6 nag_tsa_uni_garch_asym2_forecast
Univariate time series, forecast function for a GARCH process with asymmetry of the form ${\left(|{\epsilon }_{t-1}|+\gamma {\epsilon }_{t-1}\right)}^{2}$
g13fec 6 nag_tsa_uni_garch_gjr_estim
Univariate time series, parameter estimation for an asymmetric Glosten, Jagannathan and Runkle (GJR) GARCH process
g13ffc 6 nag_tsa_uni_garch_gjr_forecast
Univariate time series, forecast function for an asymmetric Glosten, Jagannathan and Runkle (GJR) GARCH process
g13mec 24 nag_tsa_inhom_iema
Computes the iterated exponential moving average for a univariate inhomogeneous time series
g13mfc 24 nag_tsa_inhom_iema_all
Computes the iterated exponential moving average for a univariate inhomogeneous time series, intermediate results are also returned
g13mgc 24 nag_tsa_inhom_ma
Computes the exponential moving average for a univariate inhomogeneous time series
g13nac 25 nag_tsa_cp_pelt
Change point detection, using the PELT algorithm
g13nbc 25 nag_tsa_cp_pelt_user
Change points detection using the PELT algorithm, user supplied cost function
g13ndc 25 nag_tsa_cp_binary
Change point detection, using binary segmentation
g13nec 25 nag_tsa_cp_binary_user
Change point detection, using binary segmentation, user supplied cost function
g13xzc 2 nag_tsa_free
Freeing function for use with g13 option setting