SCA Forecasting and Time Series Analysis

The SCA Statistical System is available for personal computers, unix workstations, and mainframe computing environments. The information provided below focuses on the unix workstation and mainframe version of SCA software. The SCA System gives you the power to analyze time series data using comprehensive modeling capabilities and delivers accurate forecasts that you can depend on. The SCA System is the solution to your modeling and forecasting needs. The System's flexibility, ease of use, and ability to grow with its user form an impressive combination. You may choose among the modules listed below to address your individual forecasting and modeling needs:

Basic System Features of the SCA System for unix workstations and mainframes System Availability

SCA Products	General Description
SCA-UTS	Univariate time series modeling and analysis including Box-Jenkins ARIMA, transfer function, and intervention models.
Extended UTS	Extended capabilities for automatic outlier detection and adjustment.
SCA-EXPERT	Automatic time series modeling using an advanced expert system approach.
SCA-ECON/M	Econometric modeling using simultaneous transfer function (STF) modeling. Also includes seasonal adjustment capabilities.
SCA-MTS	Multivariate time series modeling and analysis using vector ARMA models.
SCA-GSA	The GSA component provides commonly used general statistical analysis capabilities including descriptive statistics, multiple-linear regression, ANOVA, nonparametric statistics and more. The GSA module is an integrated component of all SCA Editions

SCA-UTS

Univariate Time Series Modeling and Analysis

The SCA-UTS product includes extensive forecasting and time series modeling capabilities. It is this fundamental module on which other SCA forecasting and time series products are built. The SCA-UTS product focuses on user directed modeling capabilities, providing all the necessary tools to identify, estimate, diagnostically check, and forecast various time series models. The SCA-UTS product features,

Box-Jenkins ARIMA models Lagged (dynamic) regression Regression with autocorrelated errors Convenient transfer function modeling Intervention (impact) analysis Spectral analysis Exponential smoothing using Simple, Double, Holt's, Winters' additive, Winters' Multiplicative, Seasonal indicator, and Harmonic smoothing methods Trading day adjustment Time series simulation Constrained parameter estimation Exact estimation algorithm

Adjustment for trading days and holiday effects

Data that are compiled and reported on a monthly basis are often subjected to variation due to the composition of the calendar. In addition, the occurrence of traditional festivals or holidays, such as Easter, can be important. Variation arising because a series varies with the days of the week is known as trading day variation. The SCA System provides some simple, but effective, schemes to account for both trading day variation and the variation due to the Easter holiday. The methods are based on the research and contributions of S.C. Hillmer, W.R. Bell, G.C. Tiao, L.-M. Liu, and others.

Spectral analysis

Estimation of spectra or cross-spectra based on periodograms Estimation of spectra or cross-spectra based on covariances and autocovariances Estimation of spectra based on an ARIMA model Filtering using band-pass of band-reject filters

Tools for tentative model identification

The SCA System provides a wide array of statistical techniques useful in the tentative identification of an ARIMA model. These include the traditional sample autocorrelation function (ACF) and sample partial auto correlation function (PACF). In addition, two methods developed by G.C. Tiao and R.S. Tsay are included. These are the extended sample autocorrelation function (EACF) and the smallest canonical correlation (SCAN) methods. The EACF and SCAN methods have been found to be very effective in the identification of mixed ARIMA models. The SCA System provides a choice of identification techniques for transfer function modeling. One is based on the traditional Box-Jenkins cross correlation approach. The other employs a linear transfer function method by L.-M. Liu and D.M. Hanssens. This newer method has also shown itself to be very effective for the identification of ARIMA models in the presence of trading day and holiday effects.

Unlimited modeling capability

Any number of different models can be specified and retained during an SCA session. All models can reside in memory simultaneously. Additionally, the System has no special restrictions on the number of parameters, the number of variables, or the number of observations in a model. The only restriction is in the overall size of the SCA memory space allocated by the user.

Model estimation-System accuracy

The SCA System provides both a conditional and an exact maximumlikelihood algorithm for univariate ARIMA model estimation. The exact likelihood algorithm is especially important in the estimation of seasonal ARIMA models. A modified algorithm developed by L.-M. Liu is utilized in the estimation of transfer function models. This algorithm avoids a major flaw in transfer function estimation of other estimation algorithms. The SCA System has respected reputation for accuracy. It is cited frequently in statistical journals and is used for critical analyzes for time series research at corporations, governments, universities, and research organizations worldwide.

Outlier detection

A time series is often subjected to influences of external events. If these events, and their related effects, are either unknown or not accounted for, inappropriate models or biased parameter estimates can result The SCA System provides capabilities for the detection and classification of various types of outliers (spurious observations) in a time series. These methods are based on the original work of S. C. Hillmer, W.R. Bell, G.C. Tiao, I. Chang, and C. Chen. The SCA System provides extended capabilities to jointly estimate outlier effects and model parameters in an automated fashion. Please see the Extended UTS component below for more details.

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Extended UTS

Extended capabilities for automatic outlier detection and adjustment

The SCA Extended UTS product provides cutting edge capabilities to conveniently handle contaminated or interrupted time series that may otherwise distort the underlying model structure, cause bias in parameter estimates, and lead to a deterioration in forecast performance. The Extended UTS product provides,

Automatic outlier detection and adjustment capabilities that allow for the joint estimation of outlier effects and model parameters using an algorithm published by C. Chen and L.-M. Liu Automatically handles level shifts, temporary changes, additive, and innovational outliers Model identification and estimation with missing data Weighted model estimation effective in handling clustered outliers, and desensitizing parameter estimates from temporary structural changes in a time series Better forecasting results by special handling of outliers occurring at the end of a time series Improved estimation of intervention and transfer function models (removes bias in parameter estimates and avoids inflated variance) Includes the complete capabilities of SCA-UTS

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SCA-EXPERT

Automatic time series modeling using an expert system algorithm

The SCA-EXPERT product employs an intelligent algorithm for automatic time series modeling. It is very easy to use, and is an asset to novices and experts alike, offering a quick and effective solution to handle repetitive modeling tasks. The SCA-EXPERT product features,

Automatic identification of seasonal and non-seasonal ARIMA models Automatic transfer function modeling and intervention (impact) analysis Automatic vector ARMA modeling Reliable and accurate results relieving mundane modeling chores Manual override of models allowing complete flexibility Includes the complete capabilities of SCA-UTS

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SCA-ECON/M

Econometric Modeling and Seasonal Adjustment

Traditional econometric modeling and time series analysis are blended in the capabilities present the SCA-ECON/M Module. Using this approach, many potential problems found in classical econometric analysis are avoided. One major problem of traditional econometric models is the assumption that disturbance (error) components are serially independent. Such an assumption can cause erroneous results when econometric models are applied to time series data. Now ARIMA models can be employed in the disturbance term of each equation in the system of equations. An added feature is that the coefficient of each input variable of an equation can be represented in either a linear or a rational form. This class of econometric models is also referred to a simultaneous transfer function(STF) models, or as rational distributed lag structured form (RSF) models.

Encompassing conventional modeling approaches:

Expressing models in a STF forms results in encompassing the following conventional econometric modeling features:

Regression with first of second order serial correlation (Cochrane-Orcutt and Hildreth-Lu methods) Generalized Least Squares (GLS) with first or second order serial correlation Lagged regression models with AR, MA, or ARMA noise Geometric lag models with ARMA noise Rational distributed lag models with ARMA noise Ridge regression Seemingly unrelated regression Linear Structural form and reduced form models Rational structural form and reduced form models

Model specification and estimation

Simultaneous equation systems are easily specified. Each individual equation is specified as if a univariate time series model. Bringing together individual equations, and any identity equation, is then directly done. Initial parameter values can be created by the System, be the results of previous univariate modeling or be specified directly by the user. Parameters of a simultaneous system are estimated using the full information maximum likelihood (FIML) method. Estimated values can be retained for future use.

Seasonal adjustment procedures

X-11 X-11-ARIMA An ARIMA model-based procedure developed by S.C. Hillmer and G.C. Tiao

The program for the X-11 and X-11-ARIMA procedures has been developed and is provided by Statistics Canada.

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SCA-MTS

Multivariate vector ARMA time series modeling and analysis

The SCA System contains state-of-the-art software for modeling and forecasting vector time series models. Developed by G.C. Tiao and G.E.P. Box, vector ARIMA models are extremely valuable in the analysis and forecasting of dynamic system in terms of leading, lagging and feedback relationships.

Comprehsensive model identification techniques Conditional and exact maximum likelihood estimation Principal component analyses Canonical analysis

Tentative model identification

The multivariate extensions to the univariate sample autocorrelation function (PACF) are provided. They are sample cross-correlation matrices (CCM) and stepwise autoregressive fits(STEPAR). Additionally, the multivariate extensions of the univariate extended sample autocorrelation function (EACF) and the smallest canonical correlation (SCAN) are also provided. These extensions, developed by G.C. Tiao and R.S. Tsay, are very effective in the identification of mixed ARMA models and in discovering underlying relationships between series.

Model estimation

Parameters of a vector model can be estimated using either a conditional or exact maximum likelihood algorithm. In addition, ARMA parameters may be held to fixed values during the estimation process (such as zero), or can be constrained to be equal to other parameters.

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SCA-GSA

The GSA component provides capabilities for general statistical analysis. This module is an integrated component of all SCA Editions. The GSA component provides,

Descriptive statistics and correlation Plots, histograms, and two-way tables Multiple regression analysis One-way to n-way ANOVA Analysis of covariance Two-sample tests of significance Cross tabulation Nonparametric statistics Distribution and model simulation

More Details of GSA module

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Basic system features are:

Same command language at all computing levels On-line HELP and prompting Extendability to handle user prepared procedures or programs Access to the computer's operating system while in an SCA session Dynamic storage allocation Commands to save and retrieve the System's memory between user sessions Data generation and editing, sorting and ranking Interface with other software

Mainframe/workstation availability:

VAX, AlphaVax, AlphaDec, VaxStation and DECstation (VMS, OpenVMS, OSF1, ULTRIX) SUN, HP, RS/6000, Silicon Graphics, and other UNIX workstations

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