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This reference provides a synopsis of each function provided with the STSA toolbox. See STSA, The Statistical Time Series Analysis Toolbox for a description of

The following functions are located in the

`\ARMA`

directory
of the STSA distribution.
acfplot.oms | - Plot and return the autocorrelation and partial autocorrelation functions in a captioned window |

acvf.oms | - Estimate the autocovariance and autocorrelation functions |

ar_acov.oms | - Compute the theoretical autocovariances of an AR model |

ar_lad.oms | - Autoregressive estimation using Least Absolute Deviations (LAD) |

ar_noise.oms | - Autoregressive filter |

ar_order.oms | - Autoregressive order selection using AICc (corrected Akaike) and BIC (Schwarz) criteria |

ar_to_ma.oms | - AR to MA polynomial inversion |

ar_yw.oms | - Autoregressive model estimation using Levinson's algorithm (Yule-Walker) |

arma_acov.oms | - Compute the theoretical autocovariances of an ARMA model |

arma_details.oms | - Compute and optionally print estimation results and statistics from an ARMA model |

arma_estimate.oms | - Non-linear least squares (LS) estimation of an ARMA model with no backcasting |

arma_forecast.oms | - ARMA forecasting. The infinite MA representation is used for the msef |

arma_noise.oms | - ARMA filter |

arma_residual_diagnostics.oms | - Formatted screen output and residual graphs |

arma_restricted_estimate.oms | - Non-linear least squares (LS) estimation of an ARMA model with no backcasting and parameter restrictions (bounds) |

arma_roots.oms | - Get the roots of the AR and MA characteristic polynomials (bounds) |

arma_simulate.oms | - Simulate a Gaussian ARMA(p,q) model |

arma_to_ar.oms | - ARMA to AR polynomial division |

arma_to_ma.oms | - ARMA to MA polynomial division |

ccf.oms | - Compute the cross-correlation function of two time series |

dlw.oms | - The Durbin-Levinson-Whittle algorithm for best linear predictors |

dmtest.oms | - Perform the Diebold-Mariano test for evaluating the forecasts between two competing models |

granger_causality.oms | - Test for Granger-type causality between two time series |

lag.oms | - Lagging all columns of a matrix |

ma_acov.oms | - Compute the theoretical autocovariances of an MA model |

ma_noise.oms | - Moving average filter |

ma_to_ar.oms | - MA to AR polynomial inversion |

pacf.oms | - Compute the partial autocorrelation function |

packr.oms | - Eliminate row-wise all missing values from a matrix |

plot_ccf.oms | - Plot the cross-correlation function |

print_acf_summary.oms | - formatted screen output for ACF, PACF and Q-statistics |

qstat.oms | - Compute the Ljung-Box test for autocorrelation |

seqlags.oms | - Sequential lags of all columns of a matrix |

spec_acvf.oms | - Compute the ACVF and ACF using the fourier transform |

transfer_details.oms | - Transfer function details. Similar output to the arma_details function |

transfer_estimate.oms | - Estimate transfer function by non-linear least squares |

transfer_filter.oms | - Transfer function filter |

transfer_forecast.oms | - Transfer function forecasting |

transfer_noise.oms | - Transfer function noise |

var_estimate.oms | - Vector AR estimation by least squares |

var_forecast.oms | - Vector AR forecasting |

var_order.oms | - VAR order selection using AICc and BIC |

var_to_ma.oms | - VAR to MA representation through VAR(1) and the companion matrix and MSE matrix |

The following functions are located in the

`\BAYES`

directory.
FG_fseas.oms | - Get the frequencies and the observation and system matrices for the Fourier form seasonal model |

fit_fop_averageDLM.oms | - Mixture first order polynomial DLM |

fit_fop_DLM.oms | - In-sample, one-step-ahead forecasting using a first order polynomial DLM |

fit_rtoDLM.oms | - In-sample, one-step-ahead forecasting using a regression through the origin (rto) DLM with constant, unknown observational variance |

fit_tsDLM.oms | - In-sample, one-step-ahead forecasting of a time series DLM with constant system matrix and constant or time-varying observation matrix (regressors), unknown observational variance, component discounting and diffuse or reference priors |

forecast_tsDLM.oms | - Out-of-sample, h-steps-ahead forecasting of a time series DLM with constant system matrix and constant or time-varying observation matrix (regressor unknown observational variance, component discounting and diffuse or reference priors |

interval_forecast.oms | - Compute a confidence interval using the DLM forecasts |

is_observable.oms | - Test for observability in a univariate DLM |

P_seas.oms | - Get the cyclic matrix P for free form seasonal model |

reference_tsDLM.oms | - Compute reference prior for univariate, time series DLM with constant unknown observational variance |

sfe_tsDLM.oms | - Get standardized residuals |

simulate_fopDLM.oms | - Simulate a first order polynomial normal DLM with constant parameters but with constant or time-varying variances |

trend_seas.oms | - Get the observation and system matrices for trend model with or without free form seasonal |

The following functions are located in the

`\FILTER`

directory.
ewma.oms | - Exponentially weighted moving average smoothing |

ewma_estimate.oms | - Estimate the smoothing factor of the EWMA model |

fir_filter.oms | - Finite impulse response filtering via convolution |

global_ts_estimate.oms | - Estimate the parameters of a global trend plus seasonal components model using least squares |

global_ts_filter.oms | - Compute residuals (filtered values) based on a global trend and seasonal components |

global_ts_forecast.oms | - Compute forecasts based on a global trend and seasonal components |

holt_winters_filter.oms | - Filtering and forecasting using the additive Holt-Winters exponential smoothing model |

holt_winters_optimize.oms | - Estimate the optimal smoothing parameters for use in Holt-Winters forecasting |

holt_winters_residuals.oms | - Auxiliary function used for the optimization of the smoothing parameters in the Holt-Winters forecasting model |

ltikf.oms | - Linear, time-invariant Kalman filtering and forecasting |

ma_smooth.oms | - Smoothing using arithmetic averages |

savitzky_golay.oms | - Savitzky-Golay filtering |

ts_estimate.oms | - Estimate the parameters of the Trend + Seasonal structural model using maximum likelihood |

ts_filter.oms | - Trend + Seasonal structural model filtering and forecasting based on Kalman filtering |

ts_loglf.oms | - Negative log-likelihood function for Trend + Seasonal structural model |

The following functions are located in the

`\NONLIN`

directory.
arsign.oms | - Estimate a sign-autoregression |

derivatives_arma_garch.oms | - Compute analytical Jacobian or gradient for ARMA-GARCH model |

estimate_arma_garch.oms | - Estimate the GARCH parameters of an ARMA-GARCH model |

estimate_garch.oms | - Estimate the GARCH parameters of an ARMA-GARCH model |

filter_arma_garch.oms | - Get the innovations and the conditional variance of a time series based on an ARMA-GARCH model. |

foreval.oms | - MAE and MSE of forecast errors |

grid_search_garch11.oms | - Two-dimensional grid search on the unit square for estimating the parameters of a GARCH(1,1) model. |

KSEDtest.oms | - Compute the Kolmogorov-Smirnov test for equality of distributions |

KSEDtest_edf.oms | - Compute the empirical distribution of the Kolmogorov-Smirnov test for the equality of the distribution of two time series using the maximum entropy bootstrap |

linearityF.oms | - Perform an F-type test for non-linearity. |

loglf_arma_garch.oms | - Compute the negative of the Gaussian log-likelihood for an ARMA-GARCH model. |

log_arma_garch_t.oms | - Compute the negative of the t(df) log-likelihood for an ARMA-GARCH model. |

make_ygrid.oms | - Support function for creating a grid of values with specific number of steps. |

me_bootstrap.oms | - Bootstrap a time series using the maximum entropy bootstrap. |

start_arma_garch.oms | - Compute appropriate starting values for estimating a GARCH model. |

tar_select.oms | - TAR model selection using the BIC criterion |

tarlsq.oms | - Estimate a one-regime threshold AR (TAR) model using LS |

The following functions are located in the

`\NONPAR`

directory.
This directory contains functions for
nonparametric, nonlinear time series analysis.
arf_cubic_spline.oms | - Nonparametric autoregression and forecasting using cubic splines. |

density.oms | - Compute kernel density estimator. |

density_bandwidth.oms | - Compute reference bandwidth for density estimation. |

distribution.oms | - Compute empirical distribution. |

estimate_cubic_spline.oms | - Regression smoothing by cubic splines. |

extract_quantile.oms | - Extract a vector of conditional quantiles after conditional empirical cdf estimation. |

form_cubic_spline.oms | - Auxialiary function for forming the columns of a cubic spline. |

gaussian_kernel.oms | - Multivariate Gaussian kernel. |

isvector.oms | - Support function: check whether the input is a vector. |

lparf.oms | - Nonparametric autoregression and forecasting using local polynomial least squares. |

lparf_mcv.oms | - Multifold cross-validation for nonparametric autoregression. |

lpfarf.oms | - Nonparametric functional coefficient (stochastic) autoregression using local linear least squares |

lpfarf_mcv.oms | - Multifold cross-validation for nonparametric functional autoregression. |

lpflsq.oms | - Nonparametric functional coefficient (stochastic) regression using local linear least squares. |

lpgcv.oms | - Bandwidth selection using the nonparametric version of bias-corrected AIC and GCV. |

lplsq.oms | - Nonparametric regression using local polynomial least squares. |

moments.oms | - Compute sample moments. |

npdf.oms | - The standard normal pdf. |

npsmooth.oms | - Nonparametric smoothing and forecasting (trend extrapolation) of a time series. |

optimal_kernel.oms | - The "optimal" (Epanechnikov) kernel. |

plm.oms | - Nonparametric estimation of a partially linear model. |

wcecdf.oms | - Conditional empirical cdf estimation for vectors of evaluation points yt and xt using the weighted NW estimator. |

wcecdf_yx.oms | - Support functions for conditional empirical cdf estimation at single evaluation points yt and xt using a weighted NW estimator. See the function wcecdf.oms for the main function that is called in applications with user's data. |

The following functions are located in the

`\POD`

directory.
This directory contains functions for performing Singular Spectrum
Analysis (SSA) on univariate time series. SSA is part of the more
general class of procedures grouped under the name
Proper Orthogonal Decomposition (POD).
colquartiles.oms | - Compute the quartiles (25%,50% and 75% quantiles) of the columns of a matrix. |

decompose_trajectory.oms | - Perform SVD decomposition of the trajectory matrix. |

diagonal_averaging.oms | - Perform diagonal averaging on a matrix. |

eigenvalue_plot.oms | - Plot the eigenvalues of the decomposed trajectory matrix. |

forecast_trajectory.oms | - Forecast components of decomposed time series. |

make_trajectory.oms | - Construct trajectory matrix of original time series. |

reconstruct_trajectory.oms | - Reconstruct a component of the decomposition of the original time series. |

weighted_correlation2.oms | - Compute the weighted correlation coefficient between two reconstructed components; accurate separation of components is indicated by low values of the weighted correlation. |

The following functions are located in the

`\SPECTRAL`

directory.
acov_FD.oms | - Compute the autocovariances of a fractionally integrated series |

acov_FGN.oms | - Compute the autocovariances of fractional Gaussian noise |

acvf_cspectrum.oms | - Cross-spectral estimation using the DFT of the smoothed cross-covariance function |

acvf_spectrum.oms | - Spectral estimation using the DFT of the smoothed autocovariance function |

amplitude_phase.oms | - Compute the amplitude and phase of two time series |

ar_spectrum.oms | - Spectral estimation using an autoregressive approximation |

arfima_estimate.oms | - ARFIMA(p,d,q) model estimation by LS using the STSA gauss_newton function |

arfima_filter.oms | - ARFIMA filter |

arfima_forecast.oms | - ARFIMA forecasting using AR approximation |

fdiff.oms | - Fractional differencing |

fft_acov.oms | - Auxiliary function for simulation of fractionally integrated series |

fourier.oms | - Compute the fourier transform and periodogram for a time series |

fractional_GPH.oms | - Estimate the fractional order of a time series using the Geweke and Porter-Hudak regression |

fractional_Whittle.oms | - Estimate the fractional order of a time series using the Whittle likelihood approximation |

impulse_response.oms | - Compute and optionally plot the impulse response coefficients of a linear filter |

plot_fourier.oms | - Plot the time series, the fourier transform and the periodogram |

plot_spectrum.oms | - Plot the spectrum |

simulate_FD.oms | - Simulate a fractionally integrated time series |

simulate_FGN.oms | - Simulate a fractional Gaussian noise series |

sinetaper.oms | - Compute the sine taper function |

spectrum.oms | - Compute the fourier spectrum using the sine taper |

squared_coherence.oms | - Compute and optionally plot the squared coherency function between two time series |

The following RNG functions are located in the

`\RNG`

directory.
The STSA RNG functions supplement, and work with the
Statistics Functions
provided in the base O-Matrix package.
ccauchy.oms | - Returns the cumulative density function (cdf) of the Cauchy distribution |

cexpo.oms | - Returns the cumulative density function (cdf) of the exponential distribution |

cgaussian.oms | - Returns the cumulative density function (cdf) of the Gaussian (normal) distribution |

cgumbel.oms | - Returns the cumulative density function (cdf) of the Gumbel (extreme value) distribution |

clogistic.oms | - Returns the cumulative density function (cdf) of the Gumbel (extreme value) distribution |

cstudent.oms | - Returns the cumulative density function (cdf) of the t distribution, (Student) distribution |

cuniform.oms | - Returns the cumulative density function (cdf) of the uniform distribution in the interval [a,b] |

icauchy.oms | - Returns the inverse cdf of the Cauchy distribution |

iexpo.oms | - Returns the inverse cdf of the exponential distribution |

igaussian.oms | - Returns the inverse cdf of the Gaussian distribution |

igumbel.oms | - Returns the inverse cdf of the Gumbel (extreme value) distribution |

ilogistic.oms | - Returns the inverse cdf of the logistic distribution |

istudent.oms | - Returns the inverse cdf of the t (Student) distribution |

iuniform.oms | - Returns the inverse cdf of the uniform distribution in the interval [a,b] |

The following functions are located in the

`\OPTIMIZE`

directory.
bhhh_ml.oms | - Nonlinear Maximum Likelihood (ML) estimation using the Berndt, Hall, Hall and Hausman (BHHH) algorithm |

gauss_newton.oms | - Nonlinear least squares optimization using Gauss-Newton |

newton_raphson.oms | - Nonlinear optimization using Newton-Raphson with optional BFGS rank 2 symmetric update |

The STSA toolbox provides numerous general and time-series specific statistics functions which are available in the

`\STATS`

directory.
The STSA statistical analysis and visualization functions
supplement, and work with the
Statistics Functions
provided in the base O-Matrix package.
boxcox_estimate.oms | - Estimate the optimal Box-Cox transformation exponent using maximum likelihood |

boxcox_invert.oms | - Invert the Box-Cox transformation |

boxcox_loglf.oms | - The Box-Cox transformation negative log-likelihood function |

boxcox_transform.oms | - The Box-Cox transformation to near Gaussianity |

boxplot.oms | - Box and whiskers plot |

cdfchi.oms | - The chi-squared cdf complement |

cmoments.oms | - Compute sample central moments |

complement.oms | - Given a set of indexes s1 from the set of the first K integers, compute the complement set |

descriptives.oms | - Compute, and optionally print, descriptive statistics |

dlog.oms | - Compute the growth rate (log-differences) of a time series |

expand.oms | - Expand a vector into a symmetric matrix |

expfit.oms | - Non-linear least squares (LS) estimation of an exponential decay/growth model, with unknown y-offset, of the form y = A*exp(B*x) + C + error |

factor_analysis_pca.oms | - Factor Analysis using Principal Components |

fast_plot.oms | - Fast plotting of a time series with title, color, style, grid and axis title controls with the remaining plotting parameters set to defaults. The plot is made in a new graphics window |

Gaussianity_ADtest.oms | - Compute the Anderson-Darling test for Gaussianity |

Gaussianity_CVMtest.oms | - Compute the Cramer-Von Misses test for Gaussianity |

Gaussianity_Ftest.oms | - Tests for Gaussianity based on sample moments |

Gaussianity_KStest.oms | - Empirical cdf and the Kolmogorov-Smirnov test for Gaussianity |

lad.oms | - Estimation of a linear regression model using Least Absolute Deviations (LAD) |

load_binary.oms | - Load a previously saved binary data file into an O-Matrix data matrix |

lsq.oms | - Linear Least Squares |

make_dates.oms | - Making a string with monthly or quarterly dates |

pca.oms | - Principal Components Analysis |

pdfchi.oms | - The chi-squared pdf |

print_estimation_results.oms | - Auxiliary function for formatted screen output |

qqplot.oms | - Quantile-Quantile (QQ) plot and QQ correlation coefficient |

quantiles.oms | - Compute the sample quantiles of a time series |

regress.oms | - Linear Least Squares with screen output |

returns.oms | - Compute the pth order return of a time series (log-differences at lag p) |

rolling_lsq.oms | - Rolling Linear Least Squares |

save_binary.oms | - Save an O-Matrix data matrix into binary format |

scatterplot.oms | - Produces a scatterplot with non-parametric regression fit |

screeplot.oms | - Plot the eigenvalues or the cumulative proportion of explained variance after PCA |

seqret.oms | - Compute a matrix of sequential returns |

standardize.oms | - Standardize a matrix of observations |

trend.oms | - Estimate a polynomial time trend |

vcov.oms | - Estimate the sample mean, contemporaneous covariance and correlation as well as the lagged covariances and correlations and the long-run covariance and correlation (zero frequency spectral matrix) |