Statistical techniques in business ecohomics chap019

Time Series and ForecastingGOALS When you have completed this chapter, you will be able to: FIVE Use trend equations to forecast future time periods and to develop seasonally adjusted fo

Time Series and Forecasting

Time Series and Forecasting

GOALS

When you have completed this chapter, you

will be able to:

FIVE

Use trend equations to forecast future time periods and

to develop seasonally adjusted forecasts

Components of a Time Series

A Time Series is a collection of data recorded over a Time Series period of time The data may be recorded weekly,

Cyclical Variation

25-Year Sales of Real Estate

0 20 40 60 80 100 120 140

The Secular Trend

Six-year sales by Season

0 2 4 6 8 10 12 14 16

The Secular Trend is the smooth long run direction of

the time series.

Seasonal Variation

The Seasonal Variation is the pattern of change in a time series within a year These patterns tend to repeat

themselves from year to year.

Six-year sales by Season

0 2 4 6 8 10 12 14 16

Components of a Time

Series

Residual variationsare random in nature and

cannot be identified

The Irregular Variation is divided into two

components:

Episodic

Variations

are unpredictable,

but can usually

be identified,

such as a flood or

hurricane

o b is the slope of the line

o t is an value of time that is selected

Example 1

for the next couple of years of new homes that

will be constructed in the Pittsburgh area Listed below are the sales of new homes constructed in

the area for the last 5 years.

y = 1.44x + 3

0 2 4 6 8 10 12

The same results

Nonlinear Trends

If the trend is not linear but rather the increases tend to be a constant percent, the Y values are converted to logarithms, and a least squares

equation is determined using the logs

Technological advances are so rapid that often

initial prices decrease at an exponential rate from

month to month Hi-Tech Company provides the

following information for the 12-month period

after releasing its latest product

Example 2

Price of new product: First 24 months

Month Unit Price Log Price Month Unit Price Log Price

Using logs of price values

Take antilog to find

estimate Thus, the

estimated sales price

for the 25th period

would be:

Price25 = antilog(-.0476*25+2.9596)

= 58.830

Example 2 continued

The Moving-Average method is used to smooth out a

time series This is accomplished by “moving” the

arithmetic mean through the time series.

The moving-average is the basic method used in measuring the seasonal fluctuation

Seasonal Variation

The numbers that result are called the

Typical Seasonal Indexes

The method most commonly used to compute the typical seasonal pattern is called the Ratio-to-Moving-

Average method.

It eliminates the trend, cyclical, and irregular components from the original data

(Y).

Determining a Seasonal Index

Using an example of sales in a large toy company, let us look

at the steps in using the moving average method

Step 1: Determine the moving total for the time series.

Step 2: Determine the moving average for the time

series.

Step 3: The moving averages are then centered.

Step 4: The specific seasonal for each period is then computed by dividing the Y values with the centered moving averages.

Step 5: Organize the specific seasonals in a table.

Step 6: Apply the correction factor.

Deseasonalizing Data

A set of typical indexes is very useful in adjusting a series

(sales, for example)

The reason for deseasonalizing

a series (sales) is to remove the

seasonal fluctuations so that

the trend and cycle can be

studied.