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