Chapter 20 Time Series Analysis And Forecasting

Question 1

Time series

Answer 1

A variable that is measured over time in sequential order

Question 2

Time series components

Answer 2

1. Long term trend
2. Cyclical variation
3. Seasonal variation
4. Random variation

Question 3

Trend

Answer 3

Aka secular trend

A long-term, relatively smooth pattern or direction exhibited by a series (with a duration of more than one year)

Not necessarily linear

Question 4

Cyclical variation

Answer 4

A wavelike pattern describing a long-term trend that is generally apparent over a number of years (resulting in a cyclical effect)

Over more than one year

Rarely consistent and predictable

Question 5

Seasonal variation

Answer 5

Cycles that occur over short, repetitive calendar periods and, by definition, have a duration of less than one year.

May refer to traditional four seasons or to any systemic pattern that occurs during a set period of time

Question 6

Random variation

Answer 6

Caused by irregular and unpredictable changes in a time series that are not caused by any other components

Tends to mask existence of more predictable components

Exists in all time series so must try to reduce random variation in order to measure other components

Question 7

Smoothing techniques

Answer 7

Ways to reduce random variation to smooth a time series

• moving averages
• exponential smoothing

Question 8

Moving averages

Answer 8

The arithmetic mean of the values in a given time period and those periods close to it

Average shown for the value in the middle of the values average (1st moving average for a three period moving average is in period 2, calculated with periods 1,2, and 3)

Generally use an odd number of periods

Longer time period = more smoothing. May show only long term trends or may smooth too much and eliminate too many elements

Question 9

Moving average in excel

Answer 9

Place data in a single column
Data
Data analysis
Specify input range, periods for moving average, output range

Delete any n/a cells

Question 10

Centered moving averages

Answer 10

When using an even number of periods for a moving average the average is placed in the middle of the middle two periods

Essentially compute the two period moving average from the two multiperiod calculations on either side of period and divide by 2

Question 11

Drawbacks to moving average method for smoothing time series data

Answer 11

• do not have data points for first and last sets of time periods (major problem of there are a small number of observations
• moving average “forgets” most of the previous time-series values

Question 12

Exponentially smoothed time series

Answer 12

St= wyt+(1-w)S(t-1) for t>=2

St= exponentially smoothed time series at time period t

yt= time series at time period t

S(t-1)= exponentially smoothed time series at time period t-1

w= smoothing constant where 0<=w<=1

S1=y1 and then build from there

Smoothed time series in period t depends on all the previous observations in the time series

Question 13

Smoothing constant

Answer 13

Between 0 and 1

Chosen on the basis of how much smoothing is required

Small constant (w) = a lot of smoothing

Large w = minimal smoothing

Question 14

Exponential smoothing in excel

Answer 14

Put data into one column

• data
• data analysis
• exponential smoothing
• specify input range, damping factor (1- smoothing factor) and output range

May have to drag down the final cell

Question 15

Linear long term trend analysis

Answer 15

If believe a long term trend is approximately linear use regression analysis and model

y= B0 + B1t + e

Question 16

Nonlinear long-term trend analysis

Answer 16

If believe long term trend is non - linear use regression analysis and polynomial model

y= B0 + B1t + B2t^2 +e

Used less often than linear

Question 17

Analyzing seasonal variation

Answer 17

Use seasonal indexes

Question 18

Seasonal indexes

Answer 18

Guage the degree to which the seasons differ from one another

To calculate must have sufficient time period of observations to cover variable over several seasons

Question 19

Computing seasonal indexes

Answer 19

1) compute sample regression line (to remove effect of seasonal and random variation)
yhat(t) = b0 + b1t

2) for each time period compute the ratio (y(t)/yhat(t)) (this removes most of the trend variation
3) for each type of season compute the averages of the ratios in step 2 (removes most random variation)
4) adjust average so that average of all seasons is 1

Question 20

Yhat

Answer 20

The value of the independent variable calculated from the regression equation

Question 21

Deseasonalizing a time series

Answer 21

Removing the seasonal variation in a time series to produce a “seasonally adjusted time series”

Allows for comparison of times across seasons (shows “real” increases or decreases)

Time series divided by seasonal index