Time Series Analysis and Examples

ISM TIMSAC Packages

A description of each TIMSAC package follows. Each description includes a list of the programs provided in the TIMSAC version.

TIMSAC-72

The TIMSAC-72 package analyzes and controls feedback systems (for example, a cement kiln process). Univariate- and multivariate-AR models are employed in this original TIMSAC package. The final prediction error (FPE) criterion is used for model selection.

• AUSPEC estimates the power spectrum by the Blackman-Tukey procedure.
• AUTCOR computes autocovariance and autocorrelation.
• DECONV computes the impulse response function.
• FFTCOR computes autocorrelation and crosscorrelation via the fast Fourier transform.
• FPEAUT computes AR coefficients and FPE for the univariate AR model.
• FPEC computes AR coefficients and FPE for the control system or multivariate AR model.
• MULCOR computes multiple covariance and correlation.
• MULNOS computes relative power contribution.
• MULRSP estimates the rational spectrum for multivariate data.
• MULSPE estimates the cross spectrum by Blackman-Tukey procedure.
• OPTDES performs optimal controller design.
• OPTSIM performs optimal controller simulation.
• RASPEC estimates the rational spectrum for univariate data.
• SGLFRE computes the frequency response function.
• WNOISE performs white noise simulation.

TIMSAC-74

The TIMSAC-74 package estimates and forecasts univariate and multivariate ARMA models by fitting the canonical Markovian model. A locally stationary autoregressive model is also analyzed. Akaike's information criterion (AIC) is used for model selection.

• AUTARM performs automatic univariate ARMA model fitting.
• BISPEC computes bispectrum.
• CANARM performs univariate canonical correlation analysis.
• CANOCA performs multivariate canonical correlation analysis.
• COVGEN computes the covariance from gain function.
• FRDPLY plots the frequency response function.
• MARKOV performs automatic multivariate ARMA model fitting.
• NONST estimates the locally stationary AR model.
• PRDCTR performs ARMA model prediction.
• PWDPLY plots the power spectrum.
• SIMCON performs optimal controller design and simulation.
• THIRMO computes the third-order moment.

TIMSAC-78

The TIMSAC-78 package uses the Householder transformation to estimate time series models. This package also contains Bayesian modeling and the exact maximum likelihood estimation of the ARMA model. Minimum AIC or Akaike Bayesian information criterion (ABIC) modeling is extensively used.

• BLOCAR estimates the locally stationary univariate AR model by using the Bayesian method.
• BLOMAR estimates the locally stationary multivariate AR model by using the Bayesian method.
• BSUBST estimates the univariate subset regression model by using the Bayesian method.
• EXSAR estimates the univariate AR model by using the exact maximum likelihood method.
• MLOCAR estimates the locally stationary univariate AR model by using the minimum AIC method.
• MLOMAR estimates the locally stationary multivariate AR model by using the minimum AIC method.
• MULBAR estimates the multivariate AR model by using the Bayesian method.
• MULMAR estimates the multivariate AR model by using the minimum AIC method.
• NADCON performs noise adaptive control.
• PERARS estimates the periodic AR model by using the minimum AIC method.
• UNIBAR estimates the univariate AR model by using the Bayesian method.
• UNIMAR estimates the univariate AR model by using the minimum AIC method.
• XSARMA estimates the univariate ARMA model by using the exact maximum likelihood method.

In addition, the following test subroutines are available: TSSBST, TSWIND, TSROOT, TSTIMS, and TSCANC.

TIMSAC-84

The TIMSAC-84 package contains the Bayesian time series modeling procedure, the point process data analysis, and the seasonal adjustment procedure.

• ADAR estimates the amplitude dependent AR model.
• BAYSEA performs Bayesian seasonal adjustments.
• BAYTAP performs Bayesian tidal analysis.
• DECOMP performs time series decomposition analysis by using state space modeling.
• EPTREN estimates intensity rates of either the exponential polynomial or exponential Fourier series of the nonstationary Poisson process model.
• LINLIN estimates linear intensity models of the self-exciting point process with another process input and with cyclic and trend components.
• LINSIM performs simulation of the point process estimated by the subroutine LINLIN.
• LOCCAR estimates the locally constant AR model.
• MULCON performs simulation, control, and prediction of the multivariate AR model.
• NONSPA performs nonstationary spectrum analysis by using the minimum Bayesian AIC procedure.
• PGRAPH performs graphical analysis for point process data.
• PTSPEC computes periodograms of point process data with significant bands.
• SIMBVH performs simulation of bivariate Hawkes' mutually exciting point process.
• SNDE estimates the stochastic nonlinear differential equation model.
• TVCAR estimates the time-varying AR coefficient model by using state space modeling.

Refer to Kitagawa and Akaike (1981) and Ishiguro (1987) for more information about TIMSAC programs.