Forecasting and Time Series Modeling Using Personal Computers

Power at Your Fingertips
The PC SCA System gives you the power to analyze time series data using comprehensive modeling capabilities and delivers accurate forecasts that you can depend on. Available as individual products or as a combined set of modules, the PC 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.

Basic System Features of the PC SCA System
System Requirements
Extending Core System Capabilities through SCA Applet Technology

The information on this page is specific to the 32-bit version of the PC SCA System. Please call SCA for more information if you are interested in purchasing a 16-bit version of the software.

You may choose among the modules listed below to address your individual forecasting and modeling needs:

Power at Your Fingertips
The PC SCA System gives you the power to analyze time series data using comprehensive modeling capabilities and delivers accurate forecasts that you can depend on. Available as individual products or as a combined set of modules, the PC 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.

The information on this page is specific to the 32-bit version of the PC SCA System. Please call Unlimted Learning Resources for more information if you are interested in purchasing a 16-bit version of the software.

You may choose among the modules listed below to address your individual forecasting and modeling needs:

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PC-UTS

The PC-UTS is not licensed as a stand alone module. It has been merged into the PC-EXPERT module.

Univariate time series modeling and analysis

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

• Box-Jenkins ARIMA modeling
  
• 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

• 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.

• 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

• 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.

• 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.

• The SCA System provides both a conditional and an exact maximum likelihood 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 PC-EXPERT module below for more details.

Automatic time series modeling using an expert system approach

The PC-EXPERT module 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 on large amounts of data. The PC-EXPERT product features,

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

The PC-EXPERT module also 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. These capabilities address,

• Automatic outlier detection and adjustment capabilities that allow for the joint estimation and of outlier effects and model parameters based on the published works of C. Chen and L.-M. Liu Automatically handles level shifts, temporary changes, additive outliers, 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 PC-UTS

Multivariate Time Series Modeling and Analysis

The PC-MTS module contains state-of-the-art capabilities for modeling and forecasting multivariate time series data using vector ARMA models and simultaneous transfer function (STF) models. These modeling approaches are well-suited to business, econometric, industrial and social science time series data.

• Vector ARMA Modeling
  
• Simultaneous Transfer Function Modeling

The Vector ARMA approach to model multiple time series data was developed by G.C. Tiao and G.E.P. Box. It is an extremely valuable modeling method to analyze and forecast dynamic variable systems in terms of leading, lagging, and feedback relationships. The PC-MTS module features,

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

• 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.

STF models allow for a system of transfer function models to be estimated and forecasted jointly. STF models may be specified in reduced form, similar to vector ARMA models, or in structural form allowing for contemporaneous relationships to exist between variables. Furthermore, STF models may also include model components to handle interventions as well as trading day and moving holiday effects that often occur in business and economic applications.

Econometric Modeling Using STF Models

• Traditional econometric modeling and time series analysis are blended using simultaneous transfer function methodologies. 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. Within the STF modeling framework, such erroneous results may be avoided by adding an ARIMA component to each individual equation that violates the assumption of serially independent error.
• 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.

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.

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

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PC-GSA The PC-GSA product provides capabilities for general statistical analysis. This module is available as a stand-alone product or as an add-on capability to other SCA products for forecasting and time series analysis.

The PC-GSA product features,

• 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

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SCAGRAF

The SCAGRAF module is a convenient and easy to use capability providing high resolution color graphics for applications in time series analysis, quality control, and general data analysis. SCAGRAF is an integrated component of the PC SCA System for Windows. SCAGRAF features,

• Single and multiple time series plots
  
• Single and multiple scatter plots
  
• Autocorrelation and partial autocorrelation plots
  
• Forecast plots with confidence bands
  
• Outlier plots with AO, IO, LS and TC designation
  
• Temporal aggregation plots
  
• Scatter plots with regression line
  
• Box-Cox transformation plots
  
• Contour plots
  
• S, x, p, np, c and u quality control charts
  
• Provides a file interface with SCA WorkBench and SCA Applets

Basic System Features under MS Windows (All products)

• Compatible with MS Windows 95/98/NT
  
• High resolution color graphics
  
• Convenient and powerful command interface
  
• Extensive analytic functions and matrix operations
  
• Programmable command language
  
• Task automation through macro procedures
  
• Launch from spreadsheet/database applications as a statistical forecasting engine
  
• Execute external programs through SCA Applet technology
  
• Data generation, editing, sorting, and ranking
  
• Example-driven and easy to use documentation
  
• Expert statistical and user support services
  
• Integrates with SCA WorkBench to manage analyses of large number of series or datasets

System Requirements

• IBM PC or compatible (Pentium or above)
  
• MS Windows 95/98, or Windows NT
  
• Please call for MS Windows 3.x products
  
• Minimum RAM is 32MB