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1. © 2011 Pearson Education, Inc
Time Series
Time Based observations/values.
OR
Data generated by processes over
time.

2. © 2011 Pearson Education, Inc
Descriptive v. Inferential
Analysis
• Time Series Analysis
– Picture of the behavior of the time series
– By Exponential Smoothing & Holt’s method
• Inferential Analysis (Prediction)
– Goal: Forecasting future values
By Least Square Regression Method

3. © 2011 Pearson Education, Inc
Time Series Components
Tt = secular trend (The general movements persisting over a long period
of time represented by the diagonal line which is drawn through the
irregular curve)
St = seasonal variations (the fluctuations that recur/repeat during specific
time periods usually every year)
Ct = cyclical variations (Pronounced fluctuations moving up and down
every few years throughout the length of chart. These are attributable
to business and economic conditions. These usually last longer than
a year and not regular in magnitude and length )
Rt = residual/error (what remains after other components have been
removed. Because of irregularities)

4. © 2011 Pearson Education, Inc
Time Series Components

5. © 2011 Pearson Education, Inc
Time Series Models
Additive
Yt = Tt + Ct + St + Rt
Multiplicative
Yt = Tt + Ct + St + Rt

6. © 2011 Pearson Education, Inc
Prediction: Fitting Trend Line
• Free hand method/Graphic method
• Method of Semi average
• Moving Average (3 yrs or 5 yrs)
• Least square Regression Method

7. © 2011 Pearson Education, Inc
Prediction: Simple Linear
Regression
• Model: E(Yt) = β0 + β1t
• Relates time series, Yt, to time, t
• Cautions
– Risky to extrapolate (forecast beyond observed
data)
– Does not account for cyclical effects

8. © 2011 Pearson Education, Inc
Simple Linear Regression
Example
The data shows the average
undergraduate tuition at all 4–
year institutions for the years
1996–2004 (Source: U.S.
Dept. of Education). Use least–
squares regression to fit a
linear model. Forecast the
tuition for 2005 (t = 11) and
compute a 95% prediction
interval for the forecast.

9. © 2011 Pearson Education, Inc
Simple Linear Regression
Solution
From Excel
ˆ 7997.533 528.158
t
Y t
 

10. © 2011 Pearson Education, Inc
Simple Linear Regression
Solution
$8,000
$9,000
$10,000
$11,000
$12,000
$13,000
$14,000
$15,000
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005
Year
Tuition
ˆ 7997.533 528.158
t
Y t
 