In article <[EMAIL PROTECTED]>,
[EMAIL PROTECTED] (Brian E. Smith) wrote:
> I will be teaching Time Series and Forecasting (an MBA course) in the
Fall.
> I am looking for an inexpensive software package that is good for
> forecasting. Last year I used Minitab 12 and found it easy-to-use and
> accessible to students. It is available on our network with a site
license
> so we will use it again this year. In addition I would like to find a
> package that is available to students at a reasonable price that
includes
> some more advanced features, particularly the AIC (Akaike's
Information
> Criterion). Any ideas?
>
> Brian
>
Brian,
AFS offers easy-to-use and very comprehensive software for your
purposes. The program is called AUTOBOX and offers a number of advanced
features. We offer attractive student prices ...starting at $50 for
non-automatic version. The software offers ;
.
AUTOBOX handles a single endogenous equation incorporating either
pre-identified causal series or empirically
identified dummy series which are found to be statistically significant.
The set of pre-identified series can be
either stochastic or deterministic (dummy) in form. In its search for
the most appropriate model form and the optimal set of parameters the
final model can either be:
1. Purely empirical or
2. A starting model could be used.
A final model may require one or more of the following structures:
1. Power transforms like Log, Square Root, Reciprocal etc.
2. Variance stabilization due to deterministic changes in the background
error variance.
3. Data segmentation or splitting as evidenced by a statistically
significant change in either model form or parameters.
Enroute to its tour de force AUTOBOX will evaluate numerous possible
models/parameters that have been suggested by the data itself. In
practice,
a realistic limit is set on the maximum number of model form iterations.
The exact specifics of each tentative model is not pre-set thus the
power of
AUTOBOX emerges. The kind and form of the tentative models may never
before
been tried. Each dataset speaks for itself and suggests the iterative
process.
The Final Model could be as simple as:
1. A simple trend model or a simple ordinary least squares model.
2. An exponential smoothing model.
3. A simple weighted average where the weights are either equal or
unequal.
4. A Cochrane-Orcutt or ordinary least squares with a first order fixup.
5. A simple ordinary least squares model in differences containing some
needed lags.
5. A spline-like set of local trends superimposed with an arbitrary
ARIMA
model and perhaps a pulse or two.
The number of possible final models that AUTOBOX could find is infinite
andonly discoverable via a true expert
system like AUTOBOX. A final model may require one or more of the
following
seasonal structures:
1. Seasonal ARIMA structure where the prediction depends on some
previous
reading S periods ago.
2. Seasonal structure via a complete set of seasonal dummies reflecting
a
fixed response based upon the particular period.
3. Seasonal structure via a partial set of seasonal dummies reflecting a
fixed response based upon the particular period.
The Final Model will satisfy both:
1. Necessity tests that guarantee the estimated coefficient is
statistically significant.
2. Sufficiency tests that guarantee that the error process is:
-unpredictable on itself.
-not predictable from the set of causals.
-has a constant mean of zero.
The Final model will contain one or more of the following structures:
1. CAUSAL with correct lead/lag specification.
2. MEMORY with correct "autoregressive memory".
3. DUMMY with correct pulses, level shifts or spline time trends
AUTOBOX provides both automated, semi-automated and manual capabilities.
AUTOBOX has a complete set of forecasting features that will appeal to
both
novice and expert forecasters. Autobox's automatic features are
unparalleled in breadth and depth of implementation. Autobox is truly
the
power forecasters dream tool with a pallette of tools that allows the
forecaster to build models that work.
AFS was the first company to automate the BJ model building process. Our
approach is to program the model identification, estimation and
diagnostic
feedback loop as originally described by Box and Jenkins. This is
implemented for both ARIMA (univariate) modeling and Transfer Function
(multivariate or regression) modeling. What this means is that the user,
from novice to expert, can feed Autobox any number of series and the
programs powerful modeling heuristic can do the work for you. This
option
is implemented in a such that it can be turned on at any stage of the
modeling process. There is complete control over the statistical
sensitivities for the inclusion/exclusion of model parameters and
structures. These features allow the user complete control over the
modeling process. The user can let Autobox do as much or as little of
the
model building process as you or the complexity of the problem dictates.
Autobox comes with a complete set of indentification and modeling tools
for
use in the BJ framework. This means that you have the ability to
transform
or prewhiten the chosen series for identification purposes. Autobox
handles
both ARIMA (univariate) modeling and Transfer Function (multivariate)
modeling allowing for the inclusion of interventions (see below for more
information). Tests for interventions, need for transformations, need to
add or delete model parameters are all available. Autocorrelation (both
traditional and robust), partial autocorrelation and cross-correlation
functions and their respectives tests of significance are calculated as
needed. Model fit statistics, including R�, SSE, variance of errors,
adjusted variance of errors all reported. Information criteria
statistics
for alternate model identification approaches are provided.
One of the most powerful features of Autobox is the inclusion of
Automatic
Intervention detection capabilities in both ARIMA and Transfer Function
models. Almost all forecasting packages allow for interventions to be
included in a regression model. What these packages don't tell you is
how
sensitive all forecasting methodologies are to the impact of
interventions
or missing variables. These packages don't tell you if your series may
be
influenced by missing variables or changes that are outside the current
model. If a data series is impacted by changes in the underlying process
at
discrete points in time, both ARIMA models and Transfer Function models
will produce poor results. For example, a competitors price change
changes
the level of demand for your product. Without a variable to account for
this change you forecast model will perform poorly. Autobox implements
ground breaking techniques which quickly and accurately identify
potential
interventions (level shifts, season pulses, single point outliers and
changes in the variance of the series). These variables can then be
included in your model at your discretion. The result is more robust
models
and greater forecast accuracy.
All forecast packages allow for you to produce forecasts using the
models
you have constructed. Autobox presents the critical information you need
to
determine if those forecasts are acceptable. Autobox has options that
allow
you to analyze the stability and forecasting ability of your forecast
model. This is achieved through a series of ex-poste forecast analyses.
You
can automatically withhold any number of observations, re-estimate the
model
form and forecast. Observations are then added back one at a time and
the
model is re-estimated and reforecast. Forecast accuracy statistics,
including Mean Absolute Percent Error (MAPE) and Bias, are calculated at
each forecast end point. Thus the stability of the model and its ability
to
forecast from various end points can be analyzed. Finally, you can
optionally allow Autobox to actually re-identify the model form at each
level of withheld data to see if the model form is unduly influenced by
recent observations.
AUTOBOX provides a very comprehensive range of causal models , including
but not limited to incorporating lead effects as well as contemporaneous
and lag effects. It can detect and compensate for changes in variance ,
changes in model form and changes in parameters Multiple Regression was
originally developed for cross-sectional data but
Statisticians/Economists
have been applying it ( mostly incorrectly ) to chronological or
longitudinal data with little regard for the Gaussian assumptions of
constant mean of the errors, constant variance, identical distribution
of
the errors and independence of the errors. AUTOBOX tests for and
remedies
any proven violations.
Following is a brief introduction to time series analysis
Time series = a sequence of observations taken on a variable or multiple
variables at successive points in time.
Objectives of time series analysis:
1. To understand the structure of the time series (how
it depends on time, itself, and other time series variables)
2. To forecast/predict future values of the time series
What is wrong with using regression for modeling time series?
* Perhaps nothing. The test is whether the residuals satisfy the
regression
assumptions: linearity, homoscedasticity, independence, and (if
necessary)
normality.
It is important to test for Pulses or one-time unusual values and to
either
adjust the data or to incorporate a Pulse Intervention variable to
account
for the identified anomaly. Unusual values can often arise Seasonally ,
thus one has to identify and incorporate Seasonal Intervention
variables.
Unusual values can often arise at successive points in time earmarking
the
need for either a Level Shift Intervention to deal with the proven mean
shift in the residuals.
* Often, time series analyzed by regression suffer from autocorrelated
residuals. In practice, positive autocorrelation seems to occur much
more
frequently than negative.
* Positively autocorrelated residuals make regression tests more
significant than they should be and confidence intervals too narrow;
negatively autocorrelated residuals do the reverse.
* In some time series regression models, autocorrelation makes biased
estimates, where the bias cannot be fixed no matter how many data points
or
observations that you have. To use regression methods on time series
data,
first plot the data over time. Study the plot for evidence of trend and
seasonality. Use numerical tests for autocorrelation, if not apparent
from
the plot.
* Trend can be dealt with by using functions of time as predictors.
Sometimes we have multiple trends and the trick is to identify the
beginning and end periods for each of the trends.
* Seasonality can be dealt with by using seasonal indicators (Seasonal
Pulses) as predictors or by allowing specic auto-dependence or
auto-projection such that the historical values ( Y(t-s) ) are used to
predict Y(t)
* Autocorrelation can be dealt with by using lags of the response
variable
Y as predictors.
* Run the regression and diagnose how well the regression assumptions
are
met.
* the residuals should have approximately the same variance
(homoscedasticity) otherwise some form of "weighted" analysis might be
needed.
* the model form/parameters should be invariant i.e. unchanging over
time.
If not then we perhaps have too much data and need to determine at what
points in time the model form or parameters changed.
Time series data presents a number of problems/opportunities that
standard
statistical packages either avoid or ignore.
1. How to determine the temporal relationship for each input series
,i.e.
is the relationship contemporaneous, lead or lag or some combination ? (
How to identify the form of a multi-input transfer function without
assuming independence of the inputs .)
2. How to determine the arima model for the noise structure reflecting
omitted variables.
3. How to do this in a ROBUST MANNER where pulses, seasonal pulses ,
level shifts and local time trends are identified and incorporated.
4. How to test for and include specific structure to deal with
non-constant variance of the error process.
5 How to test for and treat non-constancy of parameters or model form.
6. Do we model the original series or the differenced series ? AUTOBOX
deals with these issues and more .
A very natural question arises in the selection and utilization of
models.
One asks,"Why not use simple models that provide uncomplicated
solutions?"
The answer is very straightforward, "Use enough complexity to deal with
the
problem and not an ounce more". Restated, let the data speak and
validate
all assumptions underlying the model. Don't assume a simple model will
adequately describe the data. Use identification/validation schemes to
identify the model.
A transfer function can be expressed as a lagged autoregression in all
variables in the model. AUTOBOX reports this form so users can go
directly
to spreadsheets for the purposes that you require. Care should be taken
to
deal with Gaussian violations such as Outliers (pulses) , Level Shifts ,
Seasonal Pulses , Local time trends , changes in variance , changes in
parameters , changes in models ...... just to name a few ..
________________________________________________________________________
___
>
> Brian E. Smith TEL: 514-398-4038 (Work)
> McGill University FAX: 514-398-3876 (Work)
> 1001 Sherbrooke St. West FAX: 514-482-1639 (Home)
> Montreal, QC, Canada H3A 1G5 EMAIL:
[EMAIL PROTECTED]
>
> Url: http://www.management.mcgill.ca/homepage/profs/smithb
>
________________________________________________________________________
___
>
> No human investigation can be called real science if it cannot be
> demonstrated mathematically. Leonardo da Vinci
>
________________________________________________________________________
___
>
>
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