Lecture 5
Forecasting
Source:
/1
/
D.R.Anderson, D.J.Sweeney, T.A.Williams. Quantitative Methods for Business, South
Western College Publishing, 11th edition.
Chapter 6.
Contents:
5.1
Components of a time series
5.2
Smoothing methods
5.3
Trend projection
Planning for the future
is an essential aspect of managing.
But for good planning we should make
good forecasts
.
How should we go about providing forecasts?
In this Lecture we discuss
two
Time Series Methods
:
1.
Smoothing
(moving averages, weighted moving averages, and exponential smoothing),
2.
Trend projection
,
________________________
Time series methods
discover a pattern in the historical data (time series) and then
extrapolate
this pattern into the future.
_________________________
5.1 Components of a time series
A
time series
is a set of observations of a variable measured at successive points in time or
over successive periods of time.
The pattern or behavior of the data in a time series has several components. The usual
assumption is that four separate components—
trend, cyclical, seasonal,
and
irregular
—combine to
provide specific values for the time series.
Trend Component
In time series analysis, the measurements may be taken every hour, day, week, month, or year, or at
any other regular interval. Although time series data generally exhibit random fluctuations, the time
series may still show
gradual shifts or movements to relatively higher or lower values over a
longer period of time.
The gradual shifting of the time series over long period of time is referred to as the
trend
in the time series.
This shifting or trend is usually the result of long term factors such as changes in the population,
demographic characteristics of the population, technology, and consumer preferences.
For example
, a manufacturer of photographic equipment may observe substantial monthtomonth
variability in the number of cameras sold. However, in reviewing sales over the past 10 to 15 years,
this manufacturer may note a gradual increase in the annual sales volume. Suppose that the sales
volume was approximately 1700 cameras per month in 1996, 2300 cameras per month in 2001, and
2500 cameras per month in 2006. Although actual monthtomonth sales volumes may vary
substantially, this gradual growth in sales shows an upward trend for the time series.
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View Full DocumentFigure 5.1
shows a straight line that may be a good approximation of the trend in camera
sales. Although the trend for camera sales appears to be linear and increasing over time, sometimes
the trend in a time series can be described better by some other pattern.
Linear trend of camera sales
Figure 5.1.
Figure 5.2
shows some other possible time series trend patterns. Part (a) shows a nonlinear
trend; in this case, the time series shows little growth initially, then a period of rapid growth, and
finally a leveling off. This trend pattern might be a good approximation of sales for a product from
introduction through a growth period and into a period of market saturation. The linear decreasing
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 Spring '11
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 Forecasting, Time series analysis, series A

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