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Chpt 12 - 20 > chpt 17 > Flashcards

chpt 17 Flashcards

1
Q

What is time series

A

a sequence of observations on a variable measured at successive points in time or over successive periods of time

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2
Q

Define the types of measurements in time series

A 
hourly 
daily 
weekly 
monthly 
yearly 
or at any other regular interval
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3
Q

What is the pattern of data in time series

A

important factor in understanding how the time series has behaved in the past
- if such behaviour can be expected in the future, we can use the past pattern to guide us in selecting an appropriate forecasting model

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4
Q

What are the steps in time series

A
  1. construct a time series plot ////
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5
Q

What does a time series plot show us

A

graphical presentation of the relationship b/w time and the time series variable
- time or horizontal axis and time series on vertical axis

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6
Q

What are the common type of data patterns in time series

A
  1. horizontal pattern
  2. trend pattern
  3. seasonal pattern
  4. trend and seasonal pattern
  5. cyclical pattern
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7
Q

Describe the horizontal pattern

A

data fluctuates around a constant mean

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8
Q

describe statistical series

A

used to denote a time series who statistical properties are independent of time it means that

  1. the process generating the data has a constant mean
  2. the variabiity of the time series is constant over time
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9
Q

Is simply observing a horizontal patter enough evidence to conclude that the time series is stationary

A

no

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10
Q

What makes it difficult to choose an appropriate forecasting model

A

changes in business conditions
- in many situations it is important to select a forecasting method that adapts well to changes in the level of a time series

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11
Q

Describe Trend pattern

A

a time series pattern may also show gradual sifts of movement to relatively higher or low values over a longer period of time, this type of behavour, we say a trend pattern exists

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12
Q

What usually causes trend patterns

A

population increases or decreases

  • changes in demographic characteristics of teh pop
  • technology, and / or consumer preferences
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13
Q

Describe exponential relationships

A

appropriate when the % change from one period to the next is relatively constant

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14
Q

Describe seasonal patterns

A

seeing the same repeating patterns over successive periods of time

  • ex poo co expects lower sales in fall and winter months and peak sales in spring and summer
  • you might conclude that the data follows a horizontal pattern but a closer look you can see a regular pattern
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15
Q

Describe trend and seasonal pattern

A

combination of trend and seasonal pattern

- we need a forecasting method that can deal with both rend and seasonality

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16
Q

Describe cyclical pattern

A
  • an alternating sequence of points below and above the trend line lasting more than one year
  • many economic?
  • often the cyclical component is due to multi-year business cycles
  • ex. periods of moderate inflation followed by periods of rapid inflation can lead to time series that alternate below and above a generally increasing trend line (ie time series for housing costs)
  • extremely difficult if not impossible to forecast
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17
Q

how difficult is Naive forecasting

A

it’s simple

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18
Q

Describe Naive forecasting

A
  • several measures used to determine how well a particular forecast method is able to reproduce the time series data that are already available
  • select the method that has the best accuracy for the data already known, we hope to increase the likelihood that we can obtain better forecast for future periods
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19
Q

What is the formula for forecast error

A

Forecast Error = Actual value - Forecast

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20
Q

What are the measures of forecast accuracy

A
  1. mean or avg of forecast errors
  2. Absolute mean error
  3. Computing the avg of squared forecast errors (mean squared error)
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21
Q

What is the formula for Mean or Avg of Forecast Errors

A

sum (forecast error) / n-1

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22
Q

WHat can be said if the mean or avg forecast is positive

A
  • the ovserved values tend to be greater than forecasted

-

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23
Q

What is the issue with the Mean or avg forecast method

A

b/c positive and negative forecast errors tend to offset one another, the mean error is likely to be small adn tehrefore not very useful

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24
Q

What is the formula for the absolute mean error

A

MAE = avg of absolute value of forecast errors

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25
Q

Why is the MAE method of forecasting useful

A

this measure avoids teh problems of postive and negative forecast errors offseting one another

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26
Q

what is the formula for the avf of squared forecast errors

A

MSE = AVg of the sum of squared forecast errors

sum of forecast errors / n-1

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27
Q

What does the MSE method avoid

A

also avoids the problem of negative and postive forecast errors offsetting each other

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28
Q

What is the Mean absolute % Error formula

A

MAPE = (forecast error / actual) x 100

MAPE = sum of absolute value of % forecast errors / n-1

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29
Q

if you get a MAPE = 19.05, what cna be said

A

19.05 % of teh boserved value

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30
Q

For every forecast measure, the avg of past values provides what

A

more accurate forecast than using the most recent observations as the forecast for the next period

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31
Q

If the underlying time series is stationary, the avg of all historical data will

A

always provide the best results

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32
Q

what if the underlying time series is NOT stationary?

A

could be due to changes in business conditions, can often result in a time series that has a horizontal pattern shifting to a new level
- this would take a long time for the forecasting tha uses the avg of all historical data to adjust

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33
Q

if the underlying time series is not stationary, what can happen if you use simple naive method

A

the simple naive method adjusts very rapidly b/c it uses the most recent data
- when forecasting you must use good judgement and business knowledge and not rely to heavily on forecast measures

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34
Q

What is a weight moving avg

A

each observation in the moving avg calculation receives the same weight

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35
Q

describe the variation to the moving avg

A

select a different weight for each data value adn then compute a weighted avg. of the most recent k values as the forecast
- most cases most recent observations receive the most weight, then the weight decreases for remaining older data values

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36
Q

in a weight avg what is the sum of all weights

A

1

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37
Q

If we know that the recent past is a better predictor of the future than the distant past,

A

larger weights s/b given to the more recent observations

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38
Q

What if the time series is highly variable (for weight avg)

A

select approx equal weights is best,

- only requirement, all weights must =1

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39
Q

How do you determine whether one particular combination of data values and weights provides a more accurate forecast from another

A

use the combination of # of data values and weights that minimizes MSE

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40
Q

What is exponential smoothing

A

also uses weight avg

  • se select only one weight (the weight for the most recent observation), weights for the others are computed automatically
  • becomes smaller weights the further away
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41
Q

What is the formula for exponential smoothing

A

Ft+1 = a Yt + (1 -a)Ft

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42
Q

What does Ft +1 mean in exonential smoothing

A

forecast of the time series for period t +1

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43
Q

What does Yt mean in exponential smoothing

A

actual value of the time series in period t

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44
Q

what does Ft represent in exponential smoothing

A

forecast of teh time sereis for period t

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45
Q

what does a represent in exponential smoothing

A

smoothing constant (0<a></a>

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46
Q

What is important to remember with exonential smoothing

A

all past data do not need to be saved to compute the forecast for the next period
- once the value for the smoothing constant a is selected, only 2 pieces of info are needed

  1. Yt - the actual value of the time series in period t
  2. Ft = the forecast for period t
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47
Q

Forecast accuracy for exponential smoothing

- if we use a = .20

A

any value b/w o and 1 is acceptable

- some will yield better forecasts than others

48
Q

In trend projection, what is the linear trend equation

A

Tt - bo+b2t

49
Q

What does Tt represent in the linear trend equation

A

linear trend forecast in period t

50
Q

What does b0 represent in the linear trend equation

A

intercept of the linear trend line

51
Q

what does b1 represent in the linear trend equation

A

slope of the linear trend line

52
Q

what does b1 represent in the linear trend equation

A

slope of the linear trend line

53
Q

what does t represent in the linear trend equation

A

time period

54
Q

Computing slope and intercept for linear trend

A

t hat = avg value of t

Y hat = avg value of time series

55
Q

what is the formula for T hat in linear trend

A

total of years added / # of years

56
Q

what is the formula for Y hat

A

total sales / # of sales

57
Q

what is the formula for Y hat

A

total sales / # of sales

58
Q

how do you calculate MSE for linear trend

A

MSE = SSE / DF (n-2)

59
Q

how do you calculate MSE for linear trend

A

MSE = SSE / DF (n-2)

60
Q

What is Holt’s linear exponential smoothing

A

forecast a time series with a linear trend

  • uses two smoothing constants
  • a & B
61
Q

What are the 3 equations for Holt’s Linear exponential smoothing

A
  1. LT = estimate of the level of the time series in period t
  2. bt = estimate of the slope of the time series in period t
  3. Ft+k = forecast for k periods ahead
62
Q

What is the formula for the estimate of the level of the time series in period t

A

Lt = aYt+(1-a)(Lt-1 + bt-1)

63
Q

What is the formula for the estimate of the slope of the time series in period t

A

bt = B (Lt - Lt-1)+ (1-B) bt-1

64
Q

What is the formula for the forecast of k periods ahead

A

Ft+k = Lt + btk

65
Q

what does a represent in HOlt’s linear exponential smoothing

A

a = smoothing constant for the level of the time series

66
Q

What does B represent in Holt’s linear exponential smoothing

A

B = smoothing constant for the slope of the time series

67
Q

What does k represent in Holt’s linear exonential smoothing

A

of periods to be forecasted

68
Q

What is the nonlinear trend regression used for

A

for series that have a curvilinear or nonlinear trend

69
Q

How does the plot look when it is a nonlinear trend

A

the time series plot indicates an overall increasing upward trend

70
Q

What is the quadratic equation for the nonlinear trend regression

A

Tt = b0 + b1t + b2t sqaured

71
Q

What is the quadratic equation for the nonlinear trend regression

A

Tt = b0 + b1t + b2t squared

72
Q

what does t = 2 correspond to in nonlinear trend

A

year 2

73
Q

What is the exponential trend equation

A

another alternative that can be sued to model the nonlinear pattern

74
Q

what is the exponential trend equation

A

Tt = b0(b1) to the exponent t

75
Q

what is important to note about Tt in expoenential trend equation

A

Tt is not increasing by a constant amount as in the case of the linear trend mode but by a constant %

76
Q

what is important to note about Tt in exponential trend equation

A

Tt is not increasing by a constant amount as in the case of the linear trend mode but by a constant %

77
Q

what is important to note about Tt in exponential trend equation

A

Tt is not increasing by a constant amount as in the case of the linear trend mode but by a constant %

78
Q

what is seasonlity without trend

A
  • the time series plot does not indicate any long term trend in sales
  • unless you look carefully, you might think it follows a horizontal pattern and that single exponential smoothing could be used to forecast sales
  • closer look you can see a pattern
79
Q

with seaonality trend do you use dummy variables

A

yes

80
Q

what is the # of dummy variables for seasonality without trend

A

k-1 dummy variables required

81
Q

how many dummy variables for a monthly data

A

k - 1 so 12 - 1 = 11

82
Q

What is time series decomposition used for

A

used to separate or decompose a time series into seasonal trend and irregular components
- can be used for forecasting

83
Q

what is the primary applicability for time series decomposition

A

to get better understanding of the time series

84
Q

what types of businesses use time series decomposition

A

many businesses in econmic time series are maintained and published by gov. agencies such as census bureau and bureau of labour statistics use time series decomp to create deseasonalized time series

85
Q

what does timeereis create

A

deseasonalized time series

86
Q

what does deseasonalized data help us to understand

A

what is really going on with time series

87
Q

what is an example of using dessaonalized data

A

we might want to know if electrical consumption is increasing our area
- suppose we learn its down 3% in sept form Aug, we could make a decision that is wrong b/c seasonality is effecting it, if we do not deseasonalize it

88
Q

what does time sereis create

A

deseasonalized time series

89
Q

what is an example of using dessaonalized data

A

we might want to know if electrical consumption is increasing our area
- suppose we learn its down 3% in sept form Aug, we could make a decision that is wrong b/c seasonality is effecting it, if we do not deseasonalize it

90
Q

what two models do we have for deseasonalizing data

A
  1. Additive

2. Multiplicative

91
Q

what is Trend t represent in additive or multiplicative models

A

trend value at time period t

92
Q

What is Seasonal t represent in additive or multiplicative models

A

seasonal value a time period t

93
Q

what is irregular t represent in additive or multiplicative modesl

A

irregular value at time period t corresponds to error term in simple linear regression

94
Q

what is irregular t represent in additive or multiplicative models

A

irregular value at time period t corresponds to error term in simple linear regression

95
Q

describe the additive model of deseasonalizing

A
  • values for the 3 components are called together to get the actual time series value for Yt
96
Q

what is the formula for the additive model of deseaonalizing

A

Yt = Trendt + Seasonal t + Irregular t

97
Q

When do you use the additive model

A

use when seasonal fluctuations do not depend upon the level of the time series
- if the sizes of seasonal influctuations are in earlier time periods are about the same as in later time periods, use this model

98
Q

What is the formula for the Multiplicative Decomposition Model

A

Yt = Trend t x Seasonal t x Irregular t

99
Q

How is the trend measured in multiplicative decomposition model

A

trend is measured in units of the item being forecast

- seasonal and irregular components are measured in relative terms

100
Q

IN the multiplicative decomposition model, what do values above 1 indicate

A

effects below the trend

101
Q

when is the multiplicative decomposition model most used

A

most of the time we use this method - this is the one we will study in the text

102
Q

What is seasonal indexes

A

removes the combined seasonal and irregular effects

- leaving data with only trend and any remaining random variation not removed

103
Q

HOw do you compute the seasonal indexes

A
  1. compute a moving avg

2. Centred moving Avg

104
Q

How do you compute a moving avg

A

1st moving avg: 4.8 +4.1 + 6.0 + 6.5 / 4 = 5.35

2nd moving avg: 4.4 + 6.0 + 6.5 + 5.8 /4 = 5.60

105
Q

How do you calculate centred moving avg

A

(moving avg 1 + moving avg 2) / 2 = 5.475

106
Q

What is really going on with a moving avg and why do we need the centred moving avg

A
  1. 35 from the moving avg really corresonds to period 2.5 and the last 1/2 of Qrt 2 and 1st 1/2 of Qrt 3
    - we can resolve this by calculating the avg of 2 moving avgs
107
Q

What does centred moving avg do

A

this tends to smooth out both seasonal and irregular fluctuations

108
Q

How do you find seasonal irregular values

A

divided each side of the equation by trend compoent Tt,

109
Q

What can dividing each side of the equation by trend compoent help us do

A

we can identify the combined seasonal-irregular effect

110
Q

What is the formula for seasonal irregular values

A

Yt / Trend t =( Trend t x seasonal t x iregg t ) / Trend t

= seasonal t x irreg t

111
Q

what would a seasonal irregular value of 1.096 indicate

A

indicates effects above trend estimate b/c great than 1.00

- do for each qrt

112
Q

What is deseasonalizing the time series

A

the process of using the seasonal indexes to remove the seasonal effects form a time series

113
Q

What is the formula for deseasonlized sales

A

Series observed (sales) / Seasonal index

  • this shows only trend and random variability (irregular component)
  • now we use the deseasonalized time series values instead of observed values Yt in computing b0 and B1
114
Q

Deseasonalized qaurterly forecast x seasona index is what

A

seasonal adjustment

115
Q

If the business is using monthly data what changes are needed

A
  1. use 12 month moving avg (instead of 4)

2. use 12 month seasonal indexes

116
Q

Cyclical component - what can be said

A

expressed as a %

  • due to the length of time involved, getting enough relevant data to estimate the cyclical component is often difficult
  • cycles also usually vary in length (another difficulty)
117
Q

What is the formula for cyclical component

A

Yt = Trendt x cyclical t x seasonal t x irregular t

Chpt 12 - 20 (10 decks)

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