NAG Library Chapter Contents

G13 – Time Series Analysis

Routine
Name Mark of
Introduction
Purpose

G13AAF
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Example Data 9 nagf_tsa_uni_diff
Univariate time series, seasonal and non-seasonal differencing

G13ABF
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Example Data 9 nagf_tsa_uni_autocorr
Univariate time series, sample autocorrelation function

G13ACF
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Example Data 9 nagf_tsa_uni_autocorr_part
Univariate time series, partial autocorrelations from autocorrelations

G13ADF
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Example Data 9 nagf_tsa_uni_arima_prelim
Univariate time series, preliminary estimation, seasonal ARIMA model

G13AEF
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Example Data 9 nagf_tsa_uni_arima_estim
Univariate time series, estimation, seasonal ARIMA model (comprehensive)

G13AFF
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Example Data 9 nagf_tsa_uni_arima_estim_easy
Univariate time series, estimation, seasonal ARIMA model (easy-to-use)

G13AGF
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Example Data 9 nagf_tsa_uni_arima_update
Univariate time series, update state set for forecasting

G13AHF
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Example Data 9 nagf_tsa_uni_arima_forecast_state
Univariate time series, forecasting from state set

G13AJF
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Example Data 10 nagf_tsa_uni_arima_forcecast
Univariate time series, state set and forecasts, from fully specified seasonal ARIMA model

G13AMF
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Example Data 22 nagf_tsa_uni_smooth_exp
Univariate time series, exponential smoothing

G13ASF
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Example Data 13 nagf_tsa_uni_arima_resid
Univariate time series, diagnostic checking of residuals, following G13AEF or G13AFF

G13AUF
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Example Data 14 nagf_tsa_uni_means
Computes quantities needed for range-mean or standard deviation-mean plot

G13BAF
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Example Data 10 nagf_tsa_multi_filter_arima
Multivariate time series, filtering (pre-whitening) by an ARIMA model

G13BBF
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Example Data 11 nagf_tsa_multi_filter_transf
Multivariate time series, filtering by a transfer function model

G13BCF
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Example Data 10 nagf_tsa_multi_xcorr
Multivariate time series, cross-correlations

G13BDF
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Example Data 11 nagf_tsa_multi_transf_prelim
Multivariate time series, preliminary estimation of transfer function model

G13BEF
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Example Data 11 nagf_tsa_multi_inputmod_estim
Multivariate time series, estimation of multi-input model

G13BGF
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Example Data 11 nagf_tsa_multi_inputmod_update
Multivariate time series, update state set for forecasting from multi-input model

G13BHF
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Example Data 11 nagf_tsa_multi_inputmod_forecast_state
Multivariate time series, forecasting from state set of multi-input model

G13BJF
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Example Data 11 nagf_tsa_multi_inputmod_forecast
Multivariate time series, state set and forecasts from fully specified multi-input model

G13CAF
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Example Data 10 nagf_tsa_uni_spectrum_lag
Univariate time series, smoothed sample spectrum using rectangular, Bartlett, Tukey or Parzen lag window

G13CBF
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Example Data 10 nagf_tsa_uni_spectrum_daniell
Univariate time series, smoothed sample spectrum using spectral smoothing by the trapezium frequency (Daniell) window

G13CCF
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Example Data 10 nagf_tsa_multi_spectrum_lag
Multivariate time series, smoothed sample cross spectrum using rectangular, Bartlett, Tukey or Parzen lag window

G13CDF
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Example Data 10 nagf_tsa_multi_spectrum_daniell
Multivariate time series, smoothed sample cross spectrum using spectral smoothing by the trapezium frequency (Daniell) window

G13CEF
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Example Data 10 nagf_tsa_multi_spectrum_bivar
Multivariate time series, cross amplitude spectrum, squared coherency, bounds, univariate and bivariate (cross) spectra

G13CFF
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Example Data 10 nagf_tsa_multi_gain_bivar
Multivariate time series, gain, phase, bounds, univariate and bivariate (cross) spectra

G13CGF
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Example Data 10 nagf_tsa_multi_noise_bivar
Multivariate time series, noise spectrum, bounds, impulse response function and its standard error

G13DBF
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Example Data 11 nagf_tsa_multi_autocorr_part
Multivariate time series, multiple squared partial autocorrelations

G13DDF
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Example Data 22 nagf_tsa_multi_varma_estimate
Multivariate time series, estimation of VARMA model

G13DJF
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Example Data 15 nagf_tsa_multi_varma_forecast
Multivariate time series, forecasts and their standard errors

G13DKF
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Example Data 15 nagf_tsa_multi_varma_update
Multivariate time series, updates forecasts and their standard errors

G13DLF
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Example Data 15 nagf_tsa_multi_diff
Multivariate time series, differences and/or transforms

G13DMF
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Example Data 15 nagf_tsa_multi_corrmat_cross
Multivariate time series, sample cross-correlation or cross-covariance matrices

G13DNF
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Example Data 15 nagf_tsa_multi_corrmat_partlag
Multivariate time series, sample partial lag correlation matrices, ${\chi }^2$ statistics and significance levels

G13DPF
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Example Data 16 nagf_tsa_multi_regmat_partial
Multivariate time series, partial autoregression matrices

G13DSF
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Example Data 13 nagf_tsa_multi_varma_diag
Multivariate time series, diagnostic checking of residuals, following G13DDF

G13DXF
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Example Data 15 nagf_tsa_uni_arma_roots
Calculates the zeros of a vector autoregressive (or moving average) operator

G13EAF
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Example Data 17 nagf_tsa_multi_kalman_sqrt_var
Combined measurement and time update, one iteration of Kalman filter, time-varying, square root covariance filter

G13EBF
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Example Data 17 nagf_tsa_multi_kalman_sqrt_invar
Combined measurement and time update, one iteration of Kalman filter, time-invariant, square root covariance filter

G13FAF
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Example Data 20 nagf_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 ${\left({\epsilon }_{t-1}+\gamma \right)}^2$

G13FBF 20 nagf_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 ${\left({\epsilon }_{t-1}+\gamma \right)}^2$

G13FCF
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Example Data 20 nagf_tsa_uni_garch_asym2_estim
Univariate time series, parameter estimation for a GARCH process with asymmetry of the form ${\left(\left|{\epsilon }_{t-1}\right|+\gamma {\epsilon }_{t-1}\right)}^2$

G13FDF 20 nagf_tsa_uni_garch_asym2_forecast
Univariate time series, forecast function for a GARCH process with asymmetry of the form ${\left(\left|{\epsilon }_{t-1}\right|+\gamma {\epsilon }_{t-1}\right)}^2$

G13FEF
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Example Data 20 nagf_tsa_uni_garch_GJR_estim
Univariate time series, parameter estimation for an asymmetric Glosten, Jagannathan and Runkle (GJR) GARCH process

G13FFF 20 nagf_tsa_uni_garch_GJR_forecast
Univariate time series, forecast function for an asymmetric Glosten, Jagannathan and Runkle (GJR) GARCH process

G13FGF
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Example Data 20 nagf_tsa_uni_garch_exp_estim
Univariate time series, parameter estimation for an exponential GARCH (EGARCH) process

G13FHF 20 nagf_tsa_uni_garch_exp_forecast
Univariate time series, forecast function for an exponential GARCH (EGARCH) process

G13MEF
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Example Data
Example Plot 24 nagf_tsa_inhom_iema
Computes the iterated exponential moving average for a univariate inhomogeneous time series

G13MFF
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Example Data 24 nagf_tsa_inhom_iema_all
Computes the iterated exponential moving average for a univariate inhomogeneous time series, intermediate results are also returned

G13MGF
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Example Data 24 nagf_tsa_inhom_ma
Computes the exponential moving average for a univariate inhomogeneous time series