Time Series
Minitab抯 time series procedures can be used to
analyze data collected over time,commonly called a
time series.These procedures include simple
forecasting and smoothing methods,correlation
analysis methods,and ARIMA modeling.Although
correlation analysis may be performed separately from
ARIMA modeling,we present the correlation methods as
part of ARIMA modeling.
Simple forecasting and smoothing methods are based on
the idea that reliable forecasts can be achieved by
modeling patterns in the data that are usually visible
in a time series plot,and then extrapolating those
patterns to the future.Your choice of method should
be based upon whether the patterns are static
(constant in time) or dynamic (changes in time),the
nature of the trend and seasonal components,and how
far ahead that you wish to forecast.These methods are
generally easy and quick to apply.
ARIMA modeling also makes use of patterns in the data,
but these patterns may not be easily visible in a plot
of the data.Instead,ARIMA modeling uses differencing
and the autocorrelation and partial autocorrelation
functions to help identify an acceptable model.ARIMA
stands for Autoregressive Integrated Moving Average,
which represent the filtering steps taken in
constructing the ARIMA model until only random noise
remains.While ARIMA models are valuable for modeling
temporal processes and are also used for forecasting,
fitting a model is an iterative approach that may not
lend itself to application speed and volume.
Simple forecasting and smoothing methods
The simple forecasting and smoothing methods model
components in a series that are usually easy to see in
a time series plot of the data.This approach
decomposes the data into its component parts,and then
extends the estimates of the components into the
future to provide forecasts.You can choose from the
static methods of trend analysis and decomposition,or
the dynamic methods of moving average,single and
double exponential smoothing,and Winters?method.
Static methods have components that do not change over
time; dynamic methods have components that do change
over time and estimates are updated using neighboring
values.
You may use two methods in combination.That is,you
may choose a static method to model one component and
a dynamic method to model another component.For
example,you may fit a static trend using trend
analysis and dynamically model the seasonal component
in the residuals using Winters?method.Or,you may fit
a static seasonal model using decomposition and
dynamically model the trend component in the residuals
using double exponential smoothing.You might also
apply a trend analysis and decomposition together so
that you can use the wider selection of trend models
offered by trend analysis (see Example of trend
analysis and Example of decomposition).A disadvantage
of combining methods is that the confidence intervals
for forecasts are not valid.
For each of the methods,the following table provides
a summary and a graph of fits and forecasts of typical
data.
Command Forecast Example
Trend AnalysisFits a general trend model to time
series data.Choose among the linear,quadratic,
exponential growth or decay,and S-curve models.Use
this procedure to fit trend when there is no seasonal
component to your series.Length:longProfile:
extension of trend line